Gravitation-Based Edge Detection in Hyperspectral Images - MDPI

remote sensing Article

Gravitation-Based Edge Detection in Hyperspectral Images Genyun Sun 1,2 , Aizhu Zhang 1,2, *, Jinchang Ren 3 , Jingsheng Ma 4 , Peng Wang 1,2 , Yuanzhi Zhang 5 and Xiuping Jia 6 1 2 3 4 5 6

*

School of Geosciences, China University of Petroleum (East China), Qingdao 266580, China; [email protected] (G.S.); [email protected] (P.W.) Laboratory for Marine Mineral Resources Qingdao National Laboratory for Marine Science and Technology, Qingdao 266071, China Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1XQ, UK; [email protected] Institute of Petroleum, Heriot-Watt University, Edinburgh EH14 4AS, UK; [email protected] Key Lab of Lunar Science and Deep-Exploration, Chinese Academy of Sciences, Beijing 100012, China; [email protected] School of Engineering and Information Technology, The University of New South Wales at Canberra, Canberra ACT 2600, Australia; [email protected] Correspondence: [email protected]; Tel./Fax: +86-532-8698-1952

Academic Editors: Eyal Ben-Dor and Prasad S. Thenkabail Received: 28 March 2017; Accepted: 8 June 2017; Published: 11 June 2017

Abstract: Edge detection is one of the key issues in the field of computer vision and remote sensing image analysis. Although many different edge-detection methods have been proposed for gray-scale, color, and multispectral images, they still face difficulties when extracting edge features from hyperspectral images (HSIs) that contain a large number of bands with very narrow gap in the spectral domain. Inspired by the clustering characteristic of the gravitational theory, a novel edge-detection algorithm for HSIs is presented in this paper. In the proposed method, we first construct a joint feature space by combining the spatial and spectral features. Each pixel of HSI is assumed to be a celestial object in the joint feature space, which exerts gravitational force to each of its neighboring pixel. Accordingly, each object travels in the joint feature space until it reaches a stable equilibrium. At the equilibrium, the image is smoothed and the edges are enhanced, where the edge pixels can be easily distinguished by calculating the gravitational potential energy. The proposed edge-detection method is tested on several benchmark HSIs and the obtained results were compared with those of four state-of-the-art approaches. The experimental results confirm the efficacy of the proposed method. Keywords: edge detection; hyperspectral image; gravitation; remote sensing; feature space

1. Introduction With the development of optic-electronics and data transmission technologies, hyperspectral sensors are able to capture hundreds of spectral bands simultaneously with good spatial resolution. A few well-known hyperspectral imaging systems, such as AVIRIS (the Airborne Visible Infrared Imaging Spectrometer), HYDICE (the Hyperspectral Digital Imagery Collection Experiment), and EnMap (the Environmental Mapping and Analysis Program), can provide 126–512 spectral bands with a spatial resolution from 3 m to 30 m. The growing availability of hyperspectral images (HSIs) with both fine spectral and spatial resolution has opened the door to numerous new applications in remote sensing [1]. In many application areas for HSIs, segmentation is required as an important image processing step because it divides an image into meaningful homogeneous regions [2]. However, because Remote Sens. 2017, 9, 592; doi:10.3390/rs9060592

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Remote Sens. 2017, 9, 592

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the imaged scenes are complex scenes and may not have clear boundaries, image segmentation is always a big challenging task. Effective edge detection algorithms have been found useful for image segmentation since they delineate boundaries of regions and determine segmentation results [2,3]. Especially for the advanced HSIs with high spatial resolution, the clearly depicted edges could be of great benefit in characterizing the spatial structures of landscapes [4]. Over the past few decades, a large number of edge-detection techniques have been proposed, such as Canny [5], Marr [6], SUSAN (Univalue Segment Assimilating Nucleus) [7] and active contour based methods [8]. However, these approaches are designed primarily for gray, color or multispectral images and few studies have paid attention to edge detection on HSIs [9,10]. In previous studies [10,11], edge-detection tasks are completed by adapting color or multispectral approaches to hyperspectral images (HSIs). Accordingly, existing approaches for color or multispectral based edge detection are discussed as follows. In general, most approaches for color or multispectral based edge detection can be grouped into three categories: (1) monochromatic approaches; (2) vector based approaches; and (3) feature-space based approaches. Monochromatic approaches combine all edge maps after applying well-established gray-scale edge detectors on each band, and typical rules for combining edges include the maximum rule [12], the summation rule [13] and the logic OR operation [14]. Although the fine spectral resolution of HSI provides invaluable and abundant information regarding the physical nature of different materials [10], edge features may be only observable over a small subset of bands in the HSI [15]. That is to say, different spectral bands may even contain inconsistent edges, which can easily leads to false edges by simple combination. To overcome this drawback caused by the combination rules, Lei and Fan combined the first principal component and hue component of color images to obtain complete object edges [16]. Different from monochromatic approaches, vector-based approaches consider each pixel as a spectral vector and then use vector operations to detect edges [17–24]. In these approaches, the gradient magnitude and direction are defined in a vector field by extending the gray-scale edge definition [11]. Di Zenzo’s gradient operator [17], which uses the tensor gradient to define the edge magnitude and direction, is a widely used vector-based method. However, Di Zeno’s method is sensitive to small changes in intensity because it is based on the measure of the squared local contrast variation of multispectral images. To overcome this problem, in Drewniok [19], Di Zeno’s method is combined with the Canny edge detector with a Gaussian pre-filter model applied to each band for smoothing the image. Drewniok’s method has better effectiveness, but it results in a localization error when the Gaussian scale parameter is large [25]. To remove both the effect of noise and the localization error caused by pre-filtering, a novel method based on robust color morphological gradient (RCMG) is proposed, where the edge strength of a pixel is defined as the maximum distance between any two pixels in its surrounding window [24]. The RCMG is robust to noise and helps top reserve accurate spatial structures due to a non-linear scheme is implied in the process [10]. Generally speaking, vector based approaches are superior to monochromatic approaches in multispectral edge detection since they take the spectral correlation of the bands into consideration. Different from color images or multispectral images, however, HSIs usually consist of hundreds of contiguous spectral bands. Although the high spectral resolution of HSIs provides potential for more accurate identification of targets, it still suffers from three problems in edge detection, various interferences that lead to low homogeneity inside regions [26], spectral mixtures or edges that appear in a small subset of bands often cause weak edges [26] and inconsistent edges from narrow and abundant channels [27], which have made edge detection more challenging in HSIs. Dimension reduction has been investigated using signal subspace approach and proposed the local rank based edge detection method [28], however the performance is limited. It is necessary to consider the spatial relationships between spectral vectors [29]. In Reference [30], a modified Simultaneous Spectral/Spatial Detection of Edges (SSSDE) [31] for HSIs was proposed to exploit spectral information and identify boundaries (edges) between different materials. This is a kind of constructive attempt to joint utilization of


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spatial and spectral information. Recently, many researchers have tried to develop feature-based new edge-detection methods because edge pixels have saliency in the feature space [32]. In Lin [32], color image edge detection is proposed based on a subspace classification in which multivariate features are utilized to determine edge pixels. In Dinh [27], MSI edge detection is achieved via clustering the gradient feature. The feature space is suitable to analyze HSIs because it is capable of showing data from various land cover types in groups [33]. In particular, a spatial-spectral joined feature space, which takes into consideration both the spatial and spectral correlation between pixels, has attracted increasing attention [1,29]. In addition to edge detection, feature space has also been widely used in other fields of image processing, such as hyperspectral feature selection [34,35], target detection [36], and image segmentation [37,38]. However, few studies focus on edge detection for HSIs using feature space. Physical models that mimic real-world systems can be used to analyze complex scientific and engineering problems [37,39,40]. The ongoing research of physical models has motivated the exploration of new ways to handle image-processing tasks. As a typical physical model, Newton’s law of universal gravitation [41] has received considerable attention, based on which, a series of image-processing algorithms has been proposed, such as the stochastic gravitational approach to feature-based color image segmentation (SGISA) [37], the improved gravitational search algorithm for image multi-level image thresholding [42] and the gravitational collapse (CTCGC) approach for color texture classification [43]. Other gravitation model based approaches for classification include data gravitation classification (DGC) [44–46] and gravitational self-organizing maps (GSOM) [47]. The advantages of the gravity field model have inspired the development of new edge-detection method for gray-scale images [48,49]. Although the image-processing procedure using gravitational theory is relatively easy for understanding, this theory is rarely used in edge detection for HSIs. As the gravitational theory describes the movements of objects in the three-dimensional feature space of the real world, we can easily extend it to n-dimensional feature space and apply it for edge detection in HSIs. In this paper, a novel edge-detection method for HSIs based on gravitation (GEDHSI) is proposed. The main ideas of the proposed GEDHSI are as follows: (1) there exists a type of “force”, called gravitation, between any two pixels in the feature space; (2) computational gravitation obeys the law of gravitation in the physical world; (3) all pixels move in the feature space according to the law of motion until the stopping criteria are satisfied, and then the image system reaches a stable equilibrium; and (4) the edge pixels and non-edge pixels are classified into two different clusters. Therefore, in the equilibrium system, edge responses can be obtained by computing the gravitational potential energy due to the relative positions. Different from our previous approach for gravitation based edge detection in gray-scale images [49], the proposed method features a dynamic scheme. By imitating the gravitational theory, all pixels move in the joint spatial-spectral feature space, which makes the GEDHSI more attractive and effective for HSIs. The experiment results illustrate both the efficiency and efficacy of the proposed method for HSI edge-detection problems. The rest of the paper is organized as follows: The law of universal gravity is briefly reviewed in Section 2. The proposed gravitation-based edge detection method is presented in Section 3. The experimental validations of the proposed algorithm using both artificial and real HSIs are given in Section 4. Finally, the paper is concluded in Section 5. 2. Background of the Universal Law of Gravitation According to gravitational theory [35], any two objects exert gravitational force onto each other. The forces between them are equal to each other but reverse in direction. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them, as shown in Equation (1):


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→ → Mi M j F i,j = G 3 ( Zi − Zj ), → → Zi − Zj

→

(1)

→

where F i,j is the vector-form magnitude of the gravitational force between objects i and j, and their →

masses are denoted as Mi and M j (Mi < M j ), respectively. G is the universal gravitational constant, Zi →

and Zj represent the position vector of objects i and j. Newton’s second law says that when a force, →

→

F i,j , is applied to object i, its acceleration, ai , depends only on the force and its mass, Mi [50]: → → ai

Fi,j = . Mi

(2)

For Mi , two types of mass are defined in theoretical physics: Gravitational mass, MiG , is a measure of the strength of the gravitational field due to a particular object. The gravitational field of an object with small gravitational mass is weaker than an object with larger gravitational mass. Inertial mass, MiI , is a measure of an object’s resistance to changing its state of motion when a force is applied. An object with large inertial mass changes its motion more slowly, and an object with small inertial mass changes it rapidly. In physics, gravitational mass and inertial mass are usually treated as the same. In this paper, they are treated separately to enhance the adaptability of gravitational theory for HSI edge detection. →

That is to say, the gravitational force, F i,j , that acts on object i by object j is proportional to the product of the gravitational mass of objects j and i and inversely proportional to the square distance between →

→

them. ai is proportional to F i,j and inversely proportional to inertia mass of object i. More precisely, we rewrite Equations (1) and (2) as follows: →

F i,j

MiG M jG → → = G ( Zi − Zj ), → → 3 Zi − Zj

(3)

→ → ai

=

F i,j MiI

,

(4)

where MiG and M jG represent the gravitational mass of objects i and j, respectively. MiI represents the inertial mass of object i. The gravitational force obeys the superposition principle. Thus, for any object k in the space, the gravitational force exerted by objects i and j is calculated by Equation (5). → → → → → MG MG → MG MG → Fk = F i,k + F j,k = G i k 3 ( Zi − Zk ) + G i k 3 ( Zj − Zk ), → → → → Zi − Zk Zj − Zk →

(5)

where Zk is the position of object k in space Ω, and MkG is the gravitational mass of object k. The resultant force forms the gravitational field. Because the gravitational field is conservative, there is a scalar potential energy (SPE) per unit mass at each point in the space associated within the gravitational fields. The SPE of object i exerted by object j is determined by Equation (6) [51] as follows:


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φi , j = − G

G i

M M →

→

G j

.

−M Z i iG Z jG M j φi,j = − G → → . i − Zj the SPE also Z obeys the

(6) (6)

Similar to the gravitational force, superposition principle. The SPE is closely linked with forces. It can be concluded that the force is the negative Similarof tothe theSPE gravitational force, the SPE also obeys the superposition principle. differential [52], which is expressed as follows: The SPE is closely linked with forces. It can be concluded that the force is the negative differential → of the SPE [52], which is expressed as follows: (7) F i , j = −∇ φi , j , →

F i,j = −∇φi,j , (7) where ∇ is the delta operator. The SPE function is extendable to high dimensional feature space and capable of reflecting the inhomogeneity of data, which is a key point for edge detection. where ∇ is the delta operator. The SPE function is extendable to high dimensional feature space and In gravitational systems, all objects move under the gravitational force until an equilibrium capable of reflecting the inhomogeneity of data, which is a key point for edge detection. phase is reached. In the equilibrium phase, all similar objects aggregate to form a cluster. Different In gravitational systems, all objects move under the gravitational force until an equilibrium clusters have different properties, such as SPE. Some gravitation-based algorithms are inspired from phase is reached. In the equilibrium phase, all similar objects aggregate to form a cluster. Different the characteristics of gravitational theory [37,50]. In this paper, we assume that edge and non-edge clusters have different properties, such as SPE. Some gravitation-based algorithms are inspired from pixels are by nature two different clusters. Therefore, they will have different SPEs. These properties the characteristics of gravitational theory [37,50]. In this paper, we assume that edge and non-edge constitute the background of the proposed method. pixels are by nature two different clusters. Therefore, they will have different SPEs. These properties constitute the background of the proposed method. 3. Gravitation-Based Edge Detection in Hyperspectral Image (GEDHSI) 3. Gravitation-Based Edge Detection in Hyperspectral Image (GEDHSI) 3.1. Overview 3.1. Overview GEDHSI is proposed in this study based on the Newton’s law of universal gravitation. It contains threeismain phases illustrated in Figure The firstlaw phase is image gravitation. mapping which maps GEDHSI proposed in as this study based on the 1. Newton’s of universal It contains a HSImain into aphases joint spatial-spectral detailed 3.2. In thewhich joint space, three as illustrated infeature Figurespace, 1. Theasfirst phaseinisSection image mapping maps aevery HSI pixela is considered as an object which each in other via 3.2. the In gravitational force.every The pixel second into joint spatial-spectral feature space,attracts as detailed Section the joint space, is phase is theaspixel traveling phase as detailed in Section 3.3 where an force. iterative is used to considered an object which attracts each other via the gravitational Theprocedure second phase is the allowtraveling all pixels move within the joint spatial-spectral featureprocedure space under the toinfluence the pixel phase as detailed in Section 3.3 where an iterative is used allow all of pixels gravitational force until the image system reaches a stable equilibrium. this state, the edge move within the joint spatial-spectral feature space under the influence ofIn the gravitational forcepixels until andimage non-edge pixels willa stable have different scalar potential energy based on their relative the system reaches equilibrium. In this state, the edge (SPEs) pixels and non-edge pixels will positions. Consequently, in theenergy third phase, edge is obtained based on the determined have different scalar potential (SPEs)the based onresponse their relative positions. Consequently, in the SPE ofphase, each pixel. third the edge response is obtained based on the determined SPE of each pixel.

Figure 1. Overview of of the proposed EdgeDetection DetectionininHyperspectral Hyperspectral Image). Figure 1. Overview the proposedGEDHSI GEDHSI(Gravitation-Based (Gravitation-Based Edge Image).

3.2. Image Mapping 3.2. Image Mapping The gravitational theory is derived from three-dimensional real-world space. To simulate the The gravitational theory is derived from three-dimensional real-world space. To simulate the H ×W ×B theory,we wefirst first need to map the into HSIa into a feature space. a HSIbydenoted , the theory, need to map the HSI feature space. For a HSIFor denoted I H ×W × B by , theIparameters parameters H, W and B represent height, the width of number the image and the number of bands, H, W and B represent height, the width of the image and the of bands, respectively. A simple respectively. A simple feature space is composed only of its bands. This type of feature space feature space is composed only of its bands. This type of feature space primarily uses spectral


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information. To make full use of spatial and spectral information, inspired by Reference [37], we define a spatial-spectral jointed feature space containing (B + 2) features (dimensions). In the feature space, each pixel addresses a location in the space: →

→ →

Zi = (Vi , Si ) = (v1i , v2i ..., vib , · · · , viB , xi , yi ), for i = 1, 2, . . . , N,

(8)

→

where N = H × W is the total number of pixels in the image, Vi = (v1i , v2i , ..., viB ) is the spectral →

components of the pixel i, and Si = ( xi , yi ) is its spatial position. 3.3. Pixel Traveling Once the joint spatial-spectral feature space is constructed, we consider each pixel as a mass object in the space. Thereby, as introduced in Section 2, each pixel can attract others through the gravitational force and then moves in the joint feature space according to the gravitational theory. In other words, in the traveling stage, all objects move step by step within the joint feature space under the gravitational force until the stopping criteria are met. Specifically, the pixel traveling phase contains the following three steps in an iterative way until the whole image based system becomes stable:

• • •

Calculation of the acceleration; Calculation of the traveling step size; Location updating.

(1)

Calculation of the Acceleration →

In GEDHSI, for a pixel i at time t, its acceleration ai (t) is computed according to Equation (9) as follow: → → F (t) ai ( t ) = i I , (9) Mi ( t ) →

where Fi (t) is the gravitational force of the pixel i exerted by the other pixels at time t, and MiI (t) is the inertial mass of the pixel i at time t. According to Equation (7), the gravitational force is proportional to the delta of SPE and along the decreased direction of SPE. Therefore, we first calculate the SPE of the pixels i produced by a pixel j as follows: M jG (t) · MiG (t) φi,j (t) = − G , (10) (dij (t)) where dij (t) is the distance between the pixels i and j, and MiG (t) and M jG (t) are the gravitational mass of the pixels i and j. In this paper, to simplify the calculation, gravitational mass of each object is set as a unit value. → → Obviously, the distance dij is a dominant factor in Equation (10). The distance measure 1/ Zi − Zj used in Equation (1) will result in singularity. To avoid this problem and make

1 di,j

smooth and finite,

the distance in GEDHSI is redefined by Equation (11), as follows: →

→

k Zi (t) − Zj (t)k 2 ) , di,j (t) = 1 + ( σ →

→

(11)

where k Zi (t) − Zj (t)k is the Euclidean distance between pixels i and j, and σ is an influence factor.


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Then, by substituting Equations (10) and (11) into Equation (7), we can obtain the gravitational force of pixel i exerted by the pixel j as follows: → Fi,j (t)

= −∇φi,j = 2G

MiG (t) · MG j (t)

·

σ

→

→

→

→

( Zj (t) − Zi (t))

.

(12)

(1 + (k Zi (t) − Zj (t)k/σ)2 )2

Because the gravitational force obeys the superposition principle, for a dataset D that consists of m pixels, the gravitational force of pixel i exerted by the dataset D is determined as the accumulated force for each pixel within D as follows: → Fi

=

∑ 2G

j∈ D

MiG · MG j σ

→

→

→

→

( Zj − Zi )

·

.

(13)

(1 + (k Zi − Zj k/σ)2 )2

According to Equation (13), the dataset D is a key factor for computing gravitational force. In general cases, all pixels are involved to compute the gravitational force. However, this will lead to high computational time. According to Equation (13), the gravitational force attenuates toward zero when the distance increases. Thus, for those pixels that exceed a pre-specified range, we can safely assume that their gravitational forces are zero to simplify the computation. To this end, the dataset D can be constructed by → → → → D = j kSi − S j k < r and kVi − Vj k < δ ,

(14)

where r is the radius of a local circular window in the spatial domain, δ is the radius in the spectral domain, and j is the neighbor pixel around the pixel i. r and δ construct a local suprasphere in the feature space. Here, to balance the effect of the spatial and spectral distance, the position of each pixel →

→

→

is stretched in spectral domain by Vi0 = Vi · δr . Thus, the influence factor σ is equal to r, and Zi is →

→ →

replaced by Zi = (Vi0 , Si ). All pixels inside the suprasphere compose the dataset D. According to Equation (9), in addition to resultant force, inertial mass is critical in the traveling procedure. In the proposed method, the inertial mass MiI (t) of pixel i, is defined as follows: →

→

k Zj (t) − Zi (t)k 2 MiI (t) = ∑ exp(−( ) ). σ j∈ D

(15)

Obviously, the inertial mass is capable of capturing the local information with self-adaptation when traveling. (2)

Calculation of the Traveling Step

After obtaining the acceleration, we can calculate the traveling step size using the law of motion (Equation (16)). → → 1→ ∆ Zi (t) = ai (t)∆t2 + vi (t)∆t, (16) 2 →

where v i (t) is the velocity of pixel i at time t. To make the pixel move directly toward the potential → center, v i (t) is considered zero in ∆t time. ∆t is the time interval in two adjacent iterations and is set to 1. Thus, Equation (16) is replaced by Equation (17): →

∆ Zi (t) = (3)

Location Updating

1→ a ( t ). 2 i

(17)


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Based on the traveling step size, the location of the pixel i can be updated as follows: → Zi (t + 1)

=

→ → Zi (t) + ∆ Zi (t)

=

→ Zi (t) +

→

F (t) . 2MiI (t)

(18)

The traveling procedure is an iterative procedure and will be repeated until the following stopping →

criteria are met: (1) the maximum step size Smax (t) < ε where Smax (t) =

max

i ∈[1,2,..,H ×W ]

( abs( Zi (t)));

or (2) the iterations reach a maximum T. In this stage, each pixel moves along the direction of the associated gravitational force. By traveling, they can find other, similar pixels, which remove the influence of noise and preserves the structural detail. 3.4. Edge Detection When the traveling stops, the image system reaches a stable equilibrium where similar pixels will cluster together. Thereby, due to the relative positions, different pixels have various SPEs. The SPE of each pixel can be calculated. For edge pixels, the SPE is relatively high, whereas for non-edge pixels, the SPE is relatively low. Thus, we take the SPE of each pixel as the edge response. The calculation of the SPE of each object is also restricted to the dataset D and using Equation (19). Φi =

∑

ϕi,j =

j∈ D

∑

−G

j∈ D

M jG MiG →

→

.

(19)

(1 + (k Zi − Zj k/σ)2 )

Apparently, finding an appropriate threshold will classify the edge and non-edge pixels into two categories and the edge will be finally detected. According to Reference [35], a good edge detection method should keep a thin and accurate localization of edges. To satisfy such requirements, information about edges’ directions is necessary for non-maximum suppression. In accordance with Reference [49], we first project the SPE to the horizontal and vertical directions in the spatial domain, as shown in Equation (20). ΦiX =

∑ ϕi,j · q

j∈ D

xj

( x j + y j )2

and ΦYi =

∑ φi,j · q

j∈ D

yj

( x j + y j )2

,

(20)

where ΦiX and ΦYi are the SPE of pixel i projected onto the horizontal and vertical directions, respectively. Then, the edge direction is estimated by Equation (21) as follows: θi = arctan(ΦiX /ΦYi ).

(21)

With Φ and θ, non-maximum suppression and automatic hysteresis thresholding [53] can be applied to obtain the exact edge. Figure 2 depicts the flowchart of the proposed GEDHSI.


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Figure 2. Flowchart of the proposed GEDHSI. Figure 2. Flowchart of the proposed GEDHSI.

4. Experimental Results and Discussion 4. Experimental Results and Discussion To demonstrate the efficacy and efficiency of the proposed method, we carried out three groups To demonstrate the efficacy and efficiency of the proposed method, we carried outCPU threeruntime. groups of of experimental validation, including quantitative and qualitative evaluation and experimental validation, including quantitative and qualitative evaluation and CPU runtime. Group Group 1, was designed to quantitatively compare the performances of different edge detectors by 1, was designed to quantitatively compare the performances of different edge detectors by using two using two artificial images, AI 1 and AI 2 (Section 4.3). Group 2 was designed to validate the artificial images, and AI 2approach (Section on 4.3). 2 wassensing designed to and validate the performance performance of AI the 1proposed twoGroup real remote HSIs two ground scene HSIs of the(Section proposed on two real remote sensing HSIs and efficiency two ground scene HSIs 4.4). 4.4).approach Group 3 was designed to test the computational of different edge(Section detectors Group wastwo designed test the computational of different edge using two using3 the remote to sensing HSIs (Section 4.5).efficiency Detailed introduction of thedetectors tested data sets the used in experiments and (Section evaluation methods are introduction given in Sections 4.1tested and 4.2, respectively. remote sensing HSIs 4.5). Detailed of the data sets used in experiments In all experiments, allgiven edge in results were between the proposed method and four and evaluation methods are Sections 4.1compared and 4.2, respectively. other state-of-the-art multispectral edge detection methods, which include those from Di Zenzo [17], In all experiments, all edge results were compared between the proposed method and four Drewniok [19], RCMG [24] and SSSDE [30]. Di Zenzo initially used the Sobel operator other state-of-the-art multispectral edge detection methods, which include those from Di Zenzo as [17], channel-wise gradient technique [17],[30]. which sensitive to noise. the anti-noise anility, Drewniok [19], RCMG [24] and SSSDE DiisZenzo initially usedTo theimprove Sobel operator as channel-wise we prefer to use the ANDD-based gradient considering noisewe robustness. gradient technique [17], which is sensitive to [46,54] noise. To improve its thesuperiority anti-noise in anility, prefer toItuse is worth noting that the implementation codes of the comparative methods are directly taken from the ANDD-based gradient [46,54] considering its superiority in noise robustness. It is worth noting that the authors for fair and consistent comparison. We selected their optimized parameters by trial-error the implementation codes of the comparative methods are directly taken from the authors for fair and methods. The parameters of GEDHSI were set as ε = 0.0001 , T = 20 , r = 4 and δ = 50 in this consistent comparison. We selected their optimized parameters by trial-error methods. The parameters paper. The parameter σ was set to the same value as r as discussed in Section 3.3. All the of GEDHSI were set as ε = 0.0001, T = 20, r = 4 and δ = 50 in this paper. The parameter σ was experiments were conducted under the following settings: Matlab2013a, 64 bit Windows 7 system, set to the same value as r as discussed in Section 3.3. All the experiments were conducted under 2.9 GHz Intel Pentium CPU with 6 GB RAM. the following settings: Matlab2013a, 64 bit Windows 7 system, 2.9 GHz Intel Pentium CPU with 6 GB 4.1.RAM. Test Datasets hyperspectral data sets in three groups that include two artificial ones and four real natural 4.1. TestSix Datasets scenes are used in our experiments for performance assessment as listed in Table 1. The first two Six hyperspectral sets in three groups that include artificial and real natural artificial images aredata synthesized using the HYDRA [55]two which wereones used tofour evaluate the scenes are used in our experiments for performance assessment as listed in Table 1. The first two performance in dealing with background clutter and weak edges. The real HSIs include two remote artificial images are synthesized using the HYDRA [55] which were used to evaluate the performance


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in dealing with9,background clutter and weak edges. The real HSIs include two remote sensing10HSIs Remote Sens. 2017, 592 of 23 and two ground scene HSIs. The first remote sensing HSI is Farmland image is an AVIRIS flight line sensing HSIs and two groundIndiana scene HSIs. The firstremote remotesensing sensing HSI Farmland image an over a farmland of east-central [56]. Another HSI is aisHYDICE flight line is over AVIRIS flight line over [57]. a farmland east-central Indiana [56]. Another HSI [58] is a the Washington DC Mall The twoof ground scene HSIs are chosen from theremote Foster’ssensing HSI dataset HYDICE line over the Washington DC Mall [57]. The two ground scene HSIs All are these chosen from to further flight investigate the performance of the proposed method on real ground scenes. images the suitable Foster’s to HSI datasetthe [58]performance to further investigate the performance of theand proposed method on real are evaluate of connectivity, edge resolution the ability to suppress ground scenes. All these images are suitable to evaluate the performance of connectivity, edge false edges. resolution and the ability to suppress false edges. Table 1. Properties of the data sets used in experiments. Table 1. Properties of the data sets used in experiments.

1 1 22 3 44

Datasets Datasets AI 1 AI 1 AI AI 22 Farmland Farmland Washington DCMall Mall Washington DC

5 5

Foster’s Scene 5 Foster’s Scene 5

6 6

Foster’s Scene 7 Foster’s Scene 7

Data Data Source Source Artificial Artificial

Remote sensing sensing Ground Ground scene scene

Characteristic Characteristic background clutter background clutter weakedge, edge,spectral spectralmixture mixture weak straightlined linedboundary, boundary, textured textured straight many tiny objects, cluttered many tiny objects, cluttered man-made objects, textured wall, man-made objects, textured wall, desk, desk,ball, ball,blocks, blocks,etc. etc. textured wall, grass, shadow, etc. textured wall, grass, shadow, etc.

Spatial Spatial Resolution Resolution N/A N/A High High Very Very high high

No. of No. of Bands Bands 224 224 224 224 224 224 191 191

Size Size (Pixels)

(Pixels) 180 × 180 180 × 180 180 180×× 180 180 400 400×× 200 200 466×× 307 307 466

31 31

820 × 820 820 × 820

31 31

690 × 425 690 × 425

4.2. Evaluation Methods 4.2. Evaluation Methods Most edge detection techniques utilize thinning and binarization to obtain the final edge results edge detection utilize thinning andinto binarization to obtainprocess. the finalInedge [59]. Most In this study, we puttechniques all these edge strength maps the same thinning this results [59]. In this study, we put all these edge strength maps into the same thinning process. process, a pixel is only considered as an edge if it is a local maximum in the horizontal or vertical In this process, pixel is only as an edge if it is aand local maximum in the horizontal or direction. Then, awe applied theconsidered automatic threshold selection hysteresis thresholding technique vertical direction. Then, we applied the automatic threshold selection and hysteresis thresholding [53] on the edge strength maps to generate the binary edges. technique [53] on the edge maps to generate thesubjective binary edges. We investigated edgestrength detection results with both and quantitative evaluations. For We investigated edge detection results3, with quantitative evaluation, as shown in Figure pixelsboth in thesubjective candidateand edgequantitative image were evaluations. classified as For quantitative evaluation, as shown in Figure 3, pixels in the candidate edge image were classified as TP (True Positive), TN (True Negative), FP (False Positive) and FN (False Negative), from which the TP (True and Positive), (True Negative), (False as Positive) and FNThe (False which precision recall TN evolutions could be FP obtained Prec and Rec. PrecNegative), shows thefrom correct ratethe of precision and recall evolutions could be obtained as Prec and Rec. The Prec shows the correct rate of the detected edges while the Rec implies the sensitivity of an edge detector to true edges. Because the edges while the Rec the sensitivity of an edge detector to and true backgrounds edges. Because thea the detected two evaluation methods mayimplies be unfaithful when the number of objects has two may unfaithful when number of objectsfrom and backgrounds a great greatevaluation different, methods according to be Reference [25], thethe F-measure derived Prec and Rec has is used to different, according to Reference [25], the F-measure derived from Prec and Rec is used to evaluate the evaluate the overall performance. overall performance. Prec× × Rec Prec Rec , (22) Fα =Fα = , (22) Prec (1α α ⋅ + α · Prec + (1 −)α⋅ )Rec · Rec where setset to where αα∈∈[0,1] [0,1]isisaaparameter parameterweighing weighingthe thecontributions contributionsof ofPrec Precand and Rec. Rec. In In this this paper, paper, ααwas was 0.5 to balance the Prec and Rec. As a statistical error measure, F-measure works well for FP and FN, to 0.5 to balance the Prec and Rec. As a statistical error measure, F-measure works well for FP and where a good detection has higher F-measure value. FN, where a good detection has higher F-measure value.

Figure 3. 3. Confusion Confusion matrix matrix for for the the edge edge detection detection problem. problem. Figure

4.3. Evaluation on Artificial Datasets In practice, two cases make edge detection a challenge. The first one is objects that are embedded by background clutter, and the second is weak edges caused by spectral mixture or just appearing in a small subset of bands. As a result, we constructed two artificial images, AI 1 and AI 2, to evaluate the performance of our proposed edge detection approach under these two cases.


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4.3. Evaluation on Artificial Datasets In practice, two cases make edge detection a challenge. The first one is objects that are embedded by background clutter, and the second is weak edges caused by spectral mixture or just appearing in a small of9,bands. As a result, we constructed two artificial images, AI 1 and AI 2, to evaluate the Remote subset Sens. 2017, 592 11 of 23 performance of our proposed edge detection approach under these two cases.

A. Experiment Experiment on on AI AI 11 A. In this experiment, experiment, we we investigated investigated the the behaviors behaviors of of the the five five edge-detection edge-detection methods when the objects in an image are embedded by background background clutter. clutter. The tested image AI 1 is composed of one object (in the middle) and a background, where the object is located between column 60 and column 120. Thus, edge pixels are located at columns 60 and 120. To simulate different levels of background clutter, we we added added Gaussian Gaussian noises with various Signal Noise Ratio (SNR) to AI 1. The object noise is fixed to SNR SNR == 16 16 dB, dB, whereas whereas the the background background noise noise varies varies from 0.1 to 3.0 dB. Figure Figure 4a shows the content of the synthetic image without noise. Figure Figure 4b 4b shows shows aa channel channel for the background with SNR = 0.2 dB.

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Figure 4. 4. A noise (object is Figure A channel channel in in the the AI AI11dataset: dataset:(a) (a)The Thecontent contentofofthe thesynthetic syntheticimage imagewithout without noise (object located in the middle); andand (b) a(b) corrupted image withwith SNRSNR = 16 dB (where SNR stands SignalSignal Noise is located in the middle); a corrupted image = 16 dB (where SNR stands Ratio) in the object region and SNR = 0.2 dB in the background region. The dark color indicates low Noise Ratio) in the object region and SNR = 0.2 dB in the background region. The dark color indicates intensity. low intensity.

Figure 5 shows an edge-detection example for AI 1, where the background noise is SNR = 0.2 Figure 5 shows an edge-detection example for AI 1, where the background noise is SNR = 0.2 dB. dB. The edge-strength maps and corresponding binary edge maps were shown in the first row and The edge-strength maps and corresponding binary edge maps were shown in the first row and the the second row, respectively, in Figure 5. For Di Zenzo’s method, the strength of the edge pixels is second row, respectively, in Figure 5. For Di Zenzo’s method, the strength of the edge pixels is slightly slightly larger than the background (Figure 5b). Although we can set a pair of thresholds to larger than the background (Figure 5b). Although we can set a pair of thresholds to separate edge and separate edge and non-edge pixels, severe false positive detections cannot be avoided, as shown in non-edge pixels, severe false positive detections cannot be avoided, as shown in Figure 5g. For the Figure 5g. For the RCMG, the strength of noisy pixels is larger than that of edge pixels, as shown in RCMG, the strength of noisy pixels is larger than that of edge pixels, as shown in Figure 5c; thus, Figure 5c; thus, the boundaries of the object were concealed from the noisy background (Figure 5h). the boundaries of the object were concealed from the noisy background (Figure 5h). According to According to Figure 5d,i, the results of Drewniok’s method are better than those of Di Zenzo’s and Figure 5d,i, the results of Drewniok’s method are better than those of Di Zenzo’s and the RCMG the RCMG method, but they blurred the edges to some extent (Figure 5d). Therefore, the object’s method, but they blurred the edges to some extent (Figure 5d). Therefore, the object’s edges were edges were blurred with burrs, as shown in Figure 5i. For the SSSDE, the strength of almost all the blurred with burrs, as shown in Figure 5i. For the SSSDE, the strength of almost all the edge pixels is edge pixels is larger than that of the noise pixels as depicted in Figure 5e. However, some false larger than that of the noise pixels as depicted in Figure 5e. However, some false edges are detected edges are detected in the object, as shown in Figure 5j. Compared to the other four methods, the in the object, as shown in Figure 5j. Compared to the other four methods, the better performance of better performance of the presented detector is clearly perceivable, and the strength of the edge the presented detector is clearly perceivable, and the strength of the edge pixels is larger than that of pixels is larger than that of the noise pixels (Figure 5a). It is therefore easy to set appropriate the noise pixels (Figure 5a). It is therefore easy to set appropriate thresholds to separate the edge and thresholds to separate the edge and non-edge pixels, as shown in Figure 5e. non-edge pixels, as shown in Figure 5e.

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edges were blurred with burrs, as shown in Figure 5i. For the SSSDE, the strength of almost all the edge pixels is larger than that of the noise pixels as depicted in Figure 5e. However, some false edges are detected in the object, as shown in Figure 5j. Compared to the other four methods, the better performance of the presented detector is clearly perceivable, and the strength of the edge pixels larger than that of the noise pixels (Figure 5a). It is therefore easy to set appropriate Remote Sens.is2017, 9, 592 12 of 23 thresholds to separate the edge and non-edge pixels, as shown in Figure 5e.

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(f) (g) (h) (i) (j) (f) (g) (h) (i) (j) Figure 5. Edge-strength maps and corresponding binary edges of AI 1 with SNR = 0.2 dB. Figure 5.5.Edge-strength maps andand corresponding binary edges of AI 1 withAI SNR =with 0.2 dB. Edge-strength Figure Edge-strength maps corresponding 1 Color SNR = 0.2 dB. Edge-strength maps of: (a) GEDHSI; (b) Di Zenzo’s binary method;edges (c) theofRobust Morphological maps of: (a) GEDHSI; (b) Di Zenzo’s method; (c) the Robust Color Morphological Gradient (RCMG) Edge-strength maps of: (a) GEDHSI; (b) Di Zenzo’s method; (c) the Robust Color Morphological Gradient (RCMG) method; (d) Drewniok’s method; and (e) the modified Simultaneous Spectral/Spatial method; (d) Drewniok’s method; and (e) method; the modified Simultaneous Detection of Gradient (RCMG) method; Drewniok’s and (e) thecorresponding modifiedSpectral/Spatial Simultaneous Spectral/Spatial Detection of Edges (SSSDE)(d) method. (f–j) Binary edge maps of results of (a–e). Edges (SSSDE) method. (f–j) Binary edge maps of corresponding results of (a–e). Detection of Edges (SSSDE) method. (f–j) Binary edge maps of corresponding results of (a–e).

The robustness to the background clutter of the GEDHSI was further demonstrated in Figure 6, Figure Thedifferent robustness to the background clutter was further under background-noise levels from of 0.1the dB GEDHSI to 3 dB. From Figure demonstrated 6b we can findin that the 6, under different background-noise levels from 0.1 dB to 3 dB. From Figure 6b we can find that the GEDHSI produces better Rec values in almost all the noise levels. This indicates the successful levels from 0.1 dB to 3 dB. From Figure 6b detection of almost all Rec theRec edges, which is also confirmed by Figure 5f. Although the the Precsuccessful values GEDHSI produces better values in almost allnoise the levels. noise levels. This indicates GEDHSI produces better values in almost all the This indicates the successful detection obtained theedges, GEDHSI are occasionally slightly worse than that of Di Zenzo’s method, itobtained increases detection ofbyalmost all the edges, which is also by confirmed Figure 5f.the Although the Prec values of almost all the which is also confirmed Figure 5f.by Although Prec values by quickly as SNR raised as shown in Figure 6a. For the F-measure in Figure 6c, we can see that under obtained by the GEDHSI are occasionally slightly worse than that of Di Zenzo’s method, it increases the GEDHSI are occasionally slightly worse than that of Di Zenzo’s method, it increases quickly high levels (SNR approximately dB), GEDHSI produced ansee F-measure quickly as SNRasraised as in shown in 6a. Figure the0.1 F-measure in Figure 6c, wesee can that under as SNRbackground-noise raised shown Figure For6a. theFor F-measure in the Figure 6c, we can that under high value larger than 0.9, whereas the F-measure values produced by the other four methods areF-measure all less high background-noise approximately 0.1the dB),GEDHSI the GEDHSI produced an background-noise levelslevels (SNR (SNR approximately 0.1 dB), produced an F-measure value thanlarger 0.7. When the surpasses 0.9, the F-measure value the GEDHSI reaches approximately value than 0.9,SNR whereas the F-measure values produced the other four methods allthan less larger than 0.9, whereas the F-measure values produced byfor theby other four methods are allare less 1.0, whereas for the other four methods the F-measure values increased slowly. It is obvious that the thanWhen 0.7. When the SNR surpasses 0.9,F-measure the F-measure value for GEDHSI the GEDHSI reaches approximately 0.7. the SNR surpasses 0.9, the value for the reaches approximately 1.0, other four methods are weaker than the GEDHSI in addressing such severe background clutter. 1.0, whereas for the other four methods the F-measure values increased slowly. It is obvious that the whereas for the other four methods the F-measure values increased slowly. It is obvious that the other With severe noise interference, the large difference between a noisy pixel and its neighbors usually othermethods four methods are than weaker the in GEDHSI in addressing severe background four are weaker the than GEDHSI addressing such severesuch background clutter. Withclutter. severe leads to a high gradient magnitude for that noisy pixel, a magnitude even larger than that of the With interference, severe noise the interference, the large difference between a noisy pixel andusually its neighbors noise large difference between a noisy pixel and its neighbors leads tousually a high true edge pixels. As a result, this will inevitably cause incorrect edges because of failing to make the leads to a high gradient magnitude for that noisy pixel, a magnitude even larger than that the gradient magnitude for that noisy pixel, a magnitude even larger than that of the true edge pixels.ofAs a full use of the spatial information of the image, especially inadequate consideration of the true edge pixels. As a result, thisincorrect will inevitably cause incorrect edges because of failing tothe make the result, this will inevitably cause edges because of failing to make the full use of spatial relationships among the pixels within a local window. full use of of thethespatial of the image, especially inadequate consideration the information image,information especially inadequate consideration of the relationships among theof pixels relationships the pixels within a local window. within a local among window.

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Figure 6. Performance evaluation on AI 1 under various noise levels. Performance of: (a) Precision; (b) (c) (b) Recall;(a) and (c) F-measure.

Figure 6. Performance evaluation on AI 1 under various noise levels. Performance of: (a) Precision;

Figure 6. Performance B. Experiment on(c)AIF-measure. 2 evaluation on AI 1 under various noise levels. Performance of: (a) Precision; (b) Recall; and (b) Recall; and (c) F-measure.

In this experiment, we analyze the behaviors of the five edge-detection methods in dealing with B.weak Experiment on AI 2 edges between B. Experiment on AI 2objects. For HSIs, weak edges are usually caused by spectral mixture between objects or edges appearing in only a small subset of bands [17]. To tackle this problem, we In this this experiment, experiment, we we analyze the the behaviors behaviors of of the the five methods in in dealing dealing with with In five edge-detection edge-detection generated a well-designed analyze image AI 2 with a spatial dimension of 180 × 180 inmethods nine regions. The size weak edges between objects. For HSIs, weak edges are usually caused by spectral mixture between weak edges between ForWe HSIs, edges are usually caused by spectral between of each region is 60 ×objects. 60 pixels. firstweak selected three types of endmembers from themixture USGS Spectral objects or edges appearing in only a small subset of bands [17]. To tackle this problem, we Library [60], as shown in Figure 7a. generated a well-designed image AI 2 with a spatial dimension of 180 × 180 in nine regions. The size of each region is 60 × 60 pixels. We first selected three types of endmembers from the USGS Spectral Library [60], as shown in Figure 7a.


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objects or edges appearing in only a small subset of bands [17]. To tackle this problem, we generated a well-designed image AI 2 with a spatial dimension of 180 × 180 in nine regions. The size of each region is 60 × 60 pixels. We first selected three types of endmembers from the USGS Spectral Library [60], as shown Figure Remote Sens.in 2017, 9, 5927a. 13 of 23

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Figure7.7.Materials Materialsfor forAI AI2:2:(a)(a)curve curve endmembers; diagram of 2; AIand 2; and a band AI 2 Figure of of endmembers; (b)(b) diagram of AI (c) a (c) band of AI of 2 with with SNR = 10 dB. SNR = 10 dB.

According to Figure 7a, the two endmembers A and C are found to be very similar in the range According to Figure 7a, the two endmembers A and C are found to be very similar in the range of 0.6 µm to 1.4 µm, whereas the two endmembers B and C are very similar in the range of 1.5 µm of 0.6 µm to 1.4 µm, whereas the two endmembers B and C are very similar in the range of 1.5 µm to 2.1 µm. A diagram of AI 2 is shown in Figure 7b, where the symbol of each region denotes which to 2.1 µm. A diagram of AI 2 is shown in Figure 7b, where the symbol of each region denotes which endmembers the region is formed. For example, the “A” of Region A means the region was endmembers the region is formed. For example, the “A” of Region A means the region was generated generated only using endmember A, Region AB was generated by using endmembers A and B, only using endmember A, Region AB was generated by using endmembers A and B, whereas Region whereas Region BA was composed of endmembers B and A, etc. Except for the three regions BA was composed of endmembers B and A, etc. Except for the three regions located in the principal located in the principal diagonal, all regions were mixed by different endmembers. The mixed ratio diagonal, all regions were mixed by different endmembers. The mixed ratio was fixed as 0.4:0.6 for was fixed as 0.4:0.6 for these regions. We then added Gaussian noise to AI 2 and result in a varying these regions. We then added Gaussian noise to AI 2 and result in a varying SNR between 1 and SNR between 1 and 30 dB. Figure 7c shows an example band with SNR = 10 dB. Due to the spectral 30 dB. Figure 7c shows an example band with SNR = 10 dB. Due to the spectral mixture and spectral mixture and spectral similarity in many bands, there are several weak edges. Under such similarity in many bands, there are several weak edges. Under such conditions, weak edges may be conditions, weak edges may be easily vanished in noise when white Gaussian noise was added. easily vanished in noise when white Gaussian noise was added. For the noise-degraded AI 2 with a SNR of 10 dB, Figure 8 shows the edge-strength maps (the For the noise-degraded AI 2 with a SNR of 10 dB, Figure 8 shows the edge-strength maps first row) and their corresponding binary edge maps (the second row) generated by the five (the first row) and their corresponding binary edge maps (the second row) generated by the five methods. As seen from the edge-strength maps generated by Di Zenzo’s method (Figure 8b), the methods. As seen from the edge-strength maps generated by Di Zenzo’s method (Figure 8b), the RCMG (Figure 8c), Drewniok’s method (Figure 8d) and SSSDE method (Figure 8e), the strength of RCMG (Figure 8c), Drewniok’s method (Figure 8d) and SSSDE method (Figure 8e), the strength of upper horizontal and left vertical edge pixels is close to that of the noisy pixels. Therefore, it is upper horizontal and left vertical edge pixels is close to that of the noisy pixels. Therefore, it is difficult difficult to set appropriate thresholds for these edge-strength maps. According to Figure 8g, Di Zenzo’s to set appropriate thresholds for these edge-strength maps. According to Figure 8g, Di Zenzo’s method method seems to produce discontinuous edges and severe false edges. Although RCMG is slightly better seems to produce discontinuous edges and severe false edges. Although RCMG is slightly better than Di Zenzo’s as shown in Figure 8h, the results still contains some spurious edges. The similar than Di Zenzo’s as shown in Figure 8h, the results still contains some spurious edges. The similar problems exist in the results of SSSDE as illustrated in Figure 8j through the SSSDE generate much better problems exist in the results of SSSDE as illustrated in Figure 8j through the SSSDE generate much results than RCMG. Although Drewniok’s method has removed almost all noise, the edges are hackly better results than RCMG. Although Drewniok’s method has removed almost all noise, the edges are due to the displacement caused by Gaussian smoothing in each band. For comparison, the intensity of hackly due to the displacement caused by Gaussian smoothing in each band. For comparison, the the edge pixels is dramatically larger than that of the noisy pixels, as shown in Figure 8a. Thus, intensity of the edge pixels is dramatically larger than that of the noisy pixels, as shown in Figure 8a. thresholding can easily classify edge and non-edge pixels, as shown in Figure 8f. Thus, thresholding can easily classify edge and non-edge pixels, as shown in Figure 8f. Figure 9 shows the performance comparison of the five methods under noise from 1.0 dB to 30 dB. As seen in Figure 9c, due to the simplicity of the tested image, all five methods produced good results when the level of noise is low (SNR > 10 db). With the increase of noise level, especially when SNR < 7 db, the F-measure values of the four compared algorithms decreased rapidly while the proposed GEDHSI still produce much better results. Furthermore, GEDHSI obtained better results on both Prec and Rec values than Di Zenzo’s, RCMG and SSSDE methods as illustrated in Figure 9a,b. This demonstrates the GEDHSI can detect the edges in the HSIs with higher accuracy in the complicated environments. For Drewniok’s method, although its Rec values are better than that of the GEDHSI to some extent, (a)

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methods. As seen from the edge-strength maps generated by Di Zenzo’s method (Figure 8b), the RCMG (Figure 8c), Drewniok’s method (Figure 8d) and SSSDE method (Figure 8e), the strength of upper horizontal and left vertical edge pixels is close to that of the noisy pixels. Therefore, it is difficult to set appropriate thresholds for these edge-strength maps. According to Figure 8g, Di Zenzo’s method seems to produce discontinuous edges and severe false edges. Although RCMG is slightly better Remote 2017, 9, 592 14 of 23 thanSens. Di Zenzo’s as shown in Figure 8h, the results still contains some spurious edges. The similar problems exist in the results of SSSDE as illustrated in Figure 8j through the SSSDE generate much better Remote Sens. 2017, 9, 592 14 of 23 results than RCMG. Although Drewniok’s method has removed almost all noise, the edges are hackly its Prec values are remarkably worse. This implies that Drewniok’s method is easily affected by the due to the displacement caused by Gaussian smoothing in each band. For comparison, the intensity of noise, which is also by larger the F-measure Figure 9c. Moreover, jagged8a. boundaries the edge pixels is confirmed dramatically than thatshown of the in noisy pixels, as shown the in Figure Thus, between different edges in Figure 8i also confirm that Drewniok’s method produces many false edges. thresholding can easily classify edge and non-edge pixels, as shown in Figure 8f. To this end, we can reasonably conclude that GEDHSI is more robust to severe noise and weak edges than the other four methods.

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Figure 8. Edge-strength maps and corresponding binary edges of AI 2 with SNR = 10 dB. Edge-strength maps of: (a) GEDHSI; (b) Di Zenzo’s method; (c) the RCMG method; (d) Drewniok’s method; and (e) SSSDE method. (f–j) Binary edge maps of corresponding results of (a–e) by applying automatic hysteresis thresholding and thinning processes. Remote Sens. 2017, 9, 592

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Figure 9 shows the performance comparison of the five methods under noise from 1.0 dB to 30 dB. As seen in Figure 9c, due to the simplicity of the tested image, all five methods produced good results when the level of noise is low (SNR > 10 db). With the increase of noise level, especially when SNR < 7 db, the F-measure values of the four compared algorithms decreased rapidly while the proposed GEDHSI still produce much better results. Furthermore, GEDHSI obtained better results on both Prec and Rec values than Di Zenzo’s, RCMG and SSSDE methods as illustrated in Figure 9a,b. This demonstrates the GEDHSI can detect the edges in the HSIs with higher accuracy in the complicated environments. For Drewniok’s than (f) (g) (h) method, although(i)its Rec values are better (j) that of the GEDHSI to some extent, its Prec values are remarkably worse. This implies that Figure 8. Edge-strength maps and corresponding binary edges of AI 2 with SNR = 10 dB. Figure 8. Edge-strength mapsaffected and corresponding binary edges of AIconfirmed 2 with SNRby = 10 Edge-strength Drewniok’s method is easily by the noise, which is also thedB. F-measure shown Edge-strength maps of: (a) GEDHSI; (b) Di Zenzo’s method; (c) the RCMG method; (d) Drewniok’s maps of: (a) GEDHSI; (b) Di Zenzo’s method; (c) the RCMG method; (d) Drewniok’s method; and in Figure 9c. Moreover, the jagged boundaries between different edges in Figure 8i also confirm method; and (e) SSSDE method. (f–j) Binary edge maps of corresponding results of (a–e) by (e)Drewniok’s SSSDE method. (f–j) produces Binary edge maps of corresponding of (a–e) by applyingconclude automatic that method many false Toprocesses. thisresults end, we can reasonably that applying automatic hysteresis thresholding andedges. thinning hysteresis thresholding and thinning processes. GEDHSI is more robust to severe noise and weak edges than the other four methods. Figure 9 shows the performance comparison of the five methods under noise from 1.0 dB to 30 dB. As seen in Figure 9c, due to the simplicity of the tested image, all five methods produced good results when the level of noise is low (SNR > 10 db). With the increase of noise level, especially when SNR < 7 db, the F-measure values of the four compared algorithms decreased rapidly while the proposed GEDHSI still produce much better results. Furthermore, GEDHSI obtained better results on both Prec and Rec values than Di Zenzo’s, RCMG and SSSDE methods as illustrated in Figure 9a,b. This demonstrates the GEDHSI can detect the edges in the HSIs with higher accuracy in the complicated environments. For Drewniok’s method, although its Rec values are better than that of the GEDHSI to some extent, its Prec values are remarkably worse. This implies that (a) (b) (c) Drewniok’s method is easily affected by the noise, which is also confirmed by the F-measure shown in Figure 9c.9. Moreover, jagged on boundaries different in Figure 8i also Figure Performancethe evaluation AI 2 underbetween various noise levels: edges (a) precision; (b) recall; andconfirm (c) Figure 9. Performance evaluation on AI 2 under various noise levels: (a) precision; (b) recall; F-measure. method produces many false edges. To this end, we can reasonably conclude that that Drewniok’s and (c) F-measure. GEDHSI is more robust to severe noise and weak edges than the other four methods. 4.4. Evaluation on Real World Datasets 4.4. Evaluation on Real World Datasets 4.4.1. Experiments on Remote Sensing Datasets 4.4.1. Experiments on Remote Sensing Datasets For remote sensing images, due to the complexity of land cover based surface feature, For remote sensing images, due to the complexity of land cover based surface feature, illumination illumination and atmospheric effects as well as spectral mixing of pixels, edges are always and atmospheric well as spectral mixing ofthere pixels, edgesexist are always deteriorated proper deteriorated foreffects properasdetection. More seriously, usually some noisy bands infor remote detection. thereedge usually exist some bands remotethe sensing HSIs, which make sensing More HSIs, seriously, which make detection very noisy difficult. To in validate performance of edge edge detection very difficult. To validate the performance of edge detection on remote sensing HSIs, detection on remote sensing HSIs, we selected two remote sensing HSIs, the Farmland and weWashington selected two remote sensing HSIs, the Farmland and Washington DC Mall image as shown DC Mall image as shown in Figures 10 and 12, to conduct experiments in this section. in (a) to conduct experiments in this(b) (c) Figures 10 and 12, section. A. Experiment on the Farmland HSIs Figure 9. Performance evaluation on AI 2 under various noise levels: (a) precision; (b) recall; and (c) A. Experiment on the Farmland HSIs F-measure. Figure 10 is the Farmland image obtained by AVIRIS. The AVIRIS instrument contains 224 Figure 10 is the Farmland image obtained by AVIRIS. The AVIRIS instrument contains 224 different different detectors, where the spectral band width is approximately 0.01 µm, allowing it to cover 4.4. Evaluation Realspectral World Datasets detectors, whereonthe band width is approximately 0.01 µm, allowing it to cover the entire 4.4.1. Experiments on Remote Sensing Datasets For remote sensing images, due to the complexity of land cover based surface feature, illumination and atmospheric effects as well as spectral mixing of pixels, edges are always deteriorated for proper detection. More seriously, there usually exist some noisy bands in remote


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range between µm and µm. are There several low SNR low bands in bands the AVIRIS one the entire range0.4 between 0.42.5 µm andThere 2.5 µm. are several SNR in theimage, AVIRISand image, example is shown in Figure 10a where the edges are nearly invisible. Even in some noiseless bands, and one example is shown in Figure 10a where the edges are nearly invisible. Even in some as shown bands, in Figure thein edges are10b, still the veryedges vague. with three low correlation bands, noiseless as 10b, shown Figure areComposited still very vague. Composited with three low the edge structure can be much clearer as shown in Figure 10c. This is mainly due to the effective correlation bands, the edge structure can be much clearer as shown in Figure 10c. This is mainly utilization spectral information. addition,information. as shown in Figure 10c, theasboundaries regions due to theofeffective utilization ofInspectral In addition, shown in between Figure 10c, the are clearer, which make it appropriate for the evaluation of edge detection algorithms. However, in the boundaries between regions are clearer, which make it appropriate for the evaluation of edge composited image, theHowever, pixels inside thecomposited region are heavily edge detection a detection algorithms. in the image, textured, the pixelswhich insidemakes the region are heavily difficult textured,problem. which makes edge detection a difficult problem.

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Figure 10. 10. Farmland Farmland image: image: (a) (a) noisy noisy image image in in gray-scale gray-scale (band (band 1); 1); (b) (b) noiseless noiseless image image in in gray-scale gray-scale Figure (band 87); 87); and and (c) (c) three-band three-band false falsecolor colorcomposite composite(bands (bands25, 25,60, 60,128). 128). (band

Figure 11 illustrates the results of edge detection from the four methods. Overall, the better Figure 11 illustrates the results of edge detection from the four methods. Overall, the better performance of the GEDHSI on the image is clearly perceivable. The proposed GEDHSI has performance of the GEDHSI on the image is clearly perceivable. The proposed GEDHSI has produced produced continuous, compact and clear edges, where the most edge structures are well preserved continuous, compact and clear edges, where the most edge structures are well preserved as shown in as shown in Figure 11a. For Di Zenzo's method, almost all of edges produced are broken as shown Figure 11a. For Di Zenzo's method, almost all of edges produced are broken as shown in Figure 11b. in Figure 11b. Drewniok’s method generates many spurious edges within regions and some line Drewniok’s method generates many spurious edges within regions and some line edges are distorted edges are distorted at the place where it should be straight according to Figure 11d. RCMG and at the place where it should be straight according to Figure 11d. RCMG and SSSDE produce similar SSSDE produce similar results as GEDHSI. However, there are many grainy edges with some fine results as GEDHSI. However, there are many grainy edges with some fine edge structures missing edge structures missing or distorted to some degree, as shown in Figure 11c,e. Specifically, as or distorted to some degree, as shown in Figure 11c,e. Specifically, as labeled by the red rectangles, labeled by the red rectangles, Di Zenzo’s method has detected serious broken edges. Drewniok’s Di Zenzo’s methodmany has detected serious broken edges. Drewniok’s generates many small method generates small and severe spurious edges and fails method to capture the main structure. and severe spurious edges and fails to capture the main structure. Moreover, Drewniok’s method Moreover, Drewniok’s method results in distortion and flexuous edges. The RCMG produces some results distortion and flexuous edges. The RCMG produces some by grainy and slightly distorted grainy in and slightly distorted edges. In contrast, the edges produced the proposed GEDHSI are edges. In contrast, the edges produced by the proposed GEDHSI are straight and continuous. straight and continuous.


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(a)

(b)

(c)

(d)

(e)

Figure 11. The binary(b) edge maps of the Farmland image by: (a) GEDHSI; (b) Di Zenzo’s (e) method; (c) (a) (c) (d)

Figure 11. The binary edge maps of the Farmland image by: (a) GEDHSI; (b) Di Zenzo’s method; the RCMG method; (d) Drewniok’s method ( σ = 1 . 0 ); and (e) SSSDE method. Figure The binary edge of the Farmland by: (a) GEDHSI; (b) Di Zenzo’s method; (c) (c) the11. RCMG method; (d)maps Drewniok’s methodimage (σ = 1.0); and (e) SSSDE method. the RCMG method; (d) Drewniok’s method ( σ = 1 . 0 ); and (e) SSSDE method.

B. Experiment on the Washington DC Mall HSIs

B. Experiment on the Washington DC Mall HSIs

B. Experiment Washington DC Mall HSIs Figureon 12the is an image obtained by HYDICE, which has 210 bands ranging from 0.4 µm to 2.4 Figure 12 is an image obtained by HYDICE, which has 210 bands ranging from 0.4 µm to 2.4 µm µm and covers the visible and (near) infrared spectrum. Bands in the 0.9 µm and 1.4 µm regions Figure 12 an image obtained by HYDICE, which has 210in bands ranging from µm to 2.4 where andwhere coversthe theisatmosphere visible and (near) infrared Bands the µm and 1.40.4 µm is opaque have spectrum. been omitted from the 0.9 dataset, leaving 191regions bands for µm and covers the visible and (near) infrared spectrum. Bands in the 0.9 µm and 1.4 µm the experiments. atmosphere is been 12a, omitted from thecontains dataset,complex leavingand 191 cluttered bands forregions experiments. Asopaque shown have in Figure the dataset landcovers. where the atmosphere is opaque have been omitted from the dataset, leaving 191 bands for As shown in Figure 12a, theofdataset complex and cluttered landcovers. in the Especially in the middle Figure contains 12a, as highlighted within a dotted rectangle, Especially various roofs, experiments. As shown in Figure 12a, the dataset contains complex and cluttered landcovers. middle of trails, Figuregrass, 12a, as highlighted within a dotted rectangle, various roofs,the roads, trails, grass,of trees roads, trees and shadow are cluttered. For better visual effect, enlarged version Especially in the middle of Figure 12a, as highlighted within a dotted rectangle, various roofs, this part of the image is shown in Figure 12b. This is used for testing as it contains abundant tinny and shadow are cluttered. For better visual effect, the enlarged version of this part of the image is roads, trails, grass, trees and shadow are cluttered. For better visual effect, the enlarged version of edges which is12b. difficult toisbeused detected completely. Examples of these tiny structures can be found in shown for 12b. testing contains abundant tinny edges which is difficult this partin of Figure the image is This shown in Figure Thisasisitused for testing as it contains abundant tinny thedetected two ellipses in Figure 12b, where local details such as the boxes on the roof and the two footpath are in to be completely. Examples of these tiny structures can be found in the ellipses edges which is difficult to be detected completely. Examples of these tiny structures can be found in clearly visible yet harddetails for detection. Figure where local such as details the boxes footpath arefootpath clearly visible yet the two 12b, ellipses in Figure 12b, where local suchon asthe the roof boxesand on the the roof and the are hard for detection. clearly visible yet hard for detection.

(a)

(b)

Figure 12. False color data: (a) the whole (a) representation of the Washington DC Mall hyperspectral (b) data; and (b) the detail display of the doted rectangle region of (a) with two regions emphasized in Figure 12. False color representation of the Washington DC Mall hyperspectral data: (a) the whole Figure 12. False color ellipses to show localrepresentation tiny structures.of the Washington DC Mall hyperspectral data: (a) the whole data; and (b) the detail display of the doted rectangle region of (a) with two regions emphasized in data; and (b) the detail display of the doted rectangle region of (a) with two regions emphasized in ellipses to show local tiny structures.

Figure 13 illustrates edge results for Figure 13b produced by the five methods. According ellipses to show local tinythe structures. to the criteria of Reference [54], a good detection should keep good edge resolution and Figure 13 illustrates the edge results for Figure 13b produced by the five methods. According connectivity. The superiority of the proposed method on these criteria is clearly visible as shown in to theFigure criteria of Reference good for detection keep good edge 13 illustrates the[54], edgearesults Figure should 13b produced by the fiveresolution methods. and According connectivity. The of thea proposed methodshould on these criteria clearly visible as and shown in to the criteria of superiority Reference [54], good detection keep goodisedge resolution connectivity.


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Remote Sens. 2017, 9, 17 of 23 13. The superiority of592 the proposed method on these criteria is clearly visible as shown in Figure The edge image of Di Zenzo’s method is poor and contains many broken edges as shown in Figure 13b. Figure 13. The edge image of Di Zenzo’s method is poor and contains many broken edges as shown The RCMG and SSSDE are better than Di Zenzo’s method, but they still produce many grainy and in Figure 13b. The RCMG and SSSDE are better than Di Zenzo’s method, but they still produce many spurious edges (Figure 13c,e). Compared with RCMG and SSSDE, the edge map produced by the grainy and spurious edges (Figure 13c,e). Compared with RCMG and SSSDE, the edge map produced Drewniok’s method in Figure 13d contains more grainy edges within regions and more spurious edges. by the Drewniok’s method in Figure 13d contains more grainy edges within regions and more spurious In edges. contrast, edgesthe in Figure 13aFigure produced by our approach clearerare andclearer of better In the contrast, edges in 13a produced by our are approach andconnectivity, of better where most of fine edge structures from different land covers are successfully detected. connectivity, where most of fine edge structures from different land covers are successfully detected.

(a)

(b)

(c)

(d)

(e)

Figure 13. The binary edge maps of the Washington DC Mall by: (a) GEDHSI; (b) Di Zenzo’s method; Figure 13. The binary edge maps of the Washington DC Mall by: (a) GEDHSI; (b) Di Zenzo’s method; (c) the RCMG method; (d) Drewniok’s method ( σ = 1.0); and (e) SSSDE method. (c) the RCMG method; (d) Drewniok’s method (σ = 1.0); and (e) SSSDE method.

For the edge resolution criterion, the better performance of the proposed method is also For the edge resolution criterion, the ellipse better performance of the is alsomethods obviously obviously perceivable. In the upper left of Figure 13b,d, the proposed Di Zenzo’smethod and RCMG perceivable. In the upper left ellipse of Figure 13b,d, the Di Zenzo’s and RCMG methods have missed have missed the edge structures, while the proposed GEDHSI preserves such tiny structures very the lower right ellipse of Figure 13c–e, the RCMG, Drewniok’s, and SSSDE methods thewell. edgeInstructures, whilecorner the proposed GEDHSI preserves such tiny structures very well. In the lower notcorner only fail to obtain continuous edge but also miss oneand sideSSSDE of themethods edge. Onnot the contrary, the right ellipse of Figure 13c–e, the RCMG, Drewniok’s, only fail to obtain proposed GEDHSI can detect complete edges at both side of the path. Overall, the proposed continuous edge but also miss one side of the edge. On the contrary, the proposed GEDHSI can detect approach is more effective thepath. other Overall, four methods for detecting edges from these HSIs. than the complete edges at both sidethan of the the proposed approach is more effective other four methods for detecting edges from these HSIs. 4.4.2. Experiments on Ground Scene Datasets

4.4.2. Experiments on Ground Scene Datasets Both of the two tested real ground scenes images cover the wavelength from 0.4 µm to 0.72 µm, and are sampled at 0.01 µm intervals andimages result cover in 31 bands. For simplicity, selected twoµm, Both of the two tested real ground scenes the wavelength from we 0.4 µm to 0.72 images, Scenes 5 and Scenes 7 as illustrated, because of the following two reasons: First, as shown in and are sampled at 0.01 µm intervals and result in 31 bands. For simplicity, we selected two images, Figure 14, Scenes the spatial resolution is higherofthan the four other datasetsFirst, and as they contain many 14, Scenes 5 and 7 as illustrated, because the following two reasons: shown in Figure man-made objects, thus we know where the edges occur exactly. Therefore, they are rather the spatial resolution is higher than the four other datasets and they contain many man-made objects, appropriate for performance evaluation. Second, there are heavily textured objects in the datasets, thus we know where the edges occur exactly. Therefore, they are rather appropriate for performance such as the objects surrounded by a heavily textured wall in Scene 5 (Figure 14a), and finely evaluation. Second, there are heavily textured objects in the datasets, such as the objects surrounded textured walls and grass in Scene 7 (Figure 14b). Edge detection under these circumstances is still a by a heavily textured wall in Scene 5 (Figure 14a), and finely textured walls and grass in Scene 7 challenge. (Figure 14b). Edge detection under these circumstances is still a challenge.


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Remote Sens. 2017, 9, 592 Remote Sens. 2017, 9, 592

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(a) (a)

(b) (b)

Figure 14. RGB representations of two hyperspectral scene dataset: (a) Scene 5;5;and and (b) Scene 7. Figure14. 14.RGB RGBrepresentations representationsof oftwo twohyperspectral hyperspectralscene scenedataset: dataset:(a) (a)Scene Scene5; and(b) (b)Scene Scene7. 7. Figure

A. Experiment Experiment on the the Scene 55 dataset dataset A. A. Experiment on on the Scene Scene 5 dataset For the Scene Scene555dataset, dataset, Figure 15 illustrates illustrates the binary binary edge generated maps generated generated by methods. the five five For the Figure 15 illustrates the binary edge maps by the five For the Scene dataset, Figure 15 the edge maps by the methods. Obviously, Di Zenzo’s edge image is poor and contains many small and spurious edges, Obviously, Di Zenzo’sDi edge imageedge is poor and is contains many small and spurious and theedges, details methods. Obviously, Zenzo’s image poor and contains many small edges, and spurious and the details of the wall are poorly detected as shown in Figure 15b. Compared to Figure 15b, the of the wall are poorly detected as shown in Figure 15b. Compared to Figure 15b, the RCMG method and the details of the wall are poorly detected as shown in Figure 15b. Compared to Figure 15b, the RCMG method can detect more edges on the wall, while there are still some spurious edges can detect more can edges on the wall,edges while on there still some on theedges chair, RCMG method detect more theare wall, while spurious there areedges still especially some spurious especially on the chair, under the ball and at the bottom right of the wall due to the variance in under the ball and at the bottom right of the wall due to the variance in intensity of the surface as especially on the chair, under the ball and at the bottom right of the wall due to the variance in intensity of the surface as shown in Figure 15c. Drewniok’s method performs better than Di Zenzo’s shown inofFigure 15c. Drewniok’s method better than Di Zenzo’s method theDi wall, but it intensity the surface as shown in Figureperforms 15c. Drewniok’s method performs betteron than Zenzo’s method on the the more wall, spurious but it it has hasand produced more spurious andthe grainy edges than either either the RCMG RCMG or has produced grainy more edgesspurious than either RCMG or GEDHSI. Some fine edges method on wall, but produced and grainy edges than the or GEDHSI. Some fine edges onbag theare wall grid and and racket15d). bag Performance are missing missing (Figure (Figure 15d). Performance of on the wall gridfine andedges racket missing (Figure of SSSDE is Performance better than that GEDHSI. Some on the wall grid racket bag are 15d). of SSSDE is better than that of Di Zenzo’s and Drewniok’s on the left wall, while it misses many edges of Di Zenzo’s on the left while it on misses many edges bluemany and yellow SSSDE is betterand thanDrewniok’s that of Di Zenzo’s andwall, Drewniok’s the left wall, whileonit the misses edges on the blue and yellow boxes as well as the basketball, as shown in Figure 15e. In contrast, almost boxes as well as the basketball, as shown in Figure 15e. In contrast, almost complete edges of most on the blue and yellow boxes as well as the basketball, as shown in Figure 15e. In contrast, almost complete edges of most objects are attained by the proposed method as shown in Figure 15a. The objects are attained by the proposed method as shown in Figure 15a. The details in the circle complete edges of most objects are attained by the proposed method as shown in Figure 15a. from The details in the circle from Figure 15 also illustrate the efficacy of the proposed method, where the Figure 15 illustrate theFigure efficacy the illustrate proposed the method, where the proposed has details in also the circle from 15ofalso efficacy of the proposed GEDHSI method, method where the proposed GEDHSI method has generated the best edge results in keeping the real structure. generated the best edge results in keeping the real structure. proposed GEDHSI method has generated the best edge results in keeping the real structure.

(a) (a)

(b) (b) Figure 15. Cont.

Remote Remote Sens. Sens. 2017, 2017, 9, 9, 592 592

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(a)

(b)

(c) (d) (e) (c) (d) (e) Figure 15. The binary edge maps generated for the Scene 5 dataset by: (a) GEDHSI; (b) Di Zenzo’s Figure 15. binary edge maps generated for the 5 dataset by: (a) GEDHSI; Figure 15.(c)The The maps formethod the Scene Scene by: (e) (a)SSSDE. GEDHSI; (b) (b) Di Di Zenzo’s Zenzo’s method; thebinary RCMGedge method; (d)generated Drewniok’s ( σ5 dataset = 1.0); and σ = 1.0); and (e) SSSDE. method; (c) the RCMG method; (d) Drewniok’s method ( method; (c) the RCMG method; (d) Drewniok’s method (σ = 1.0); and (e) SSSDE.

B. Experiment on Scene 7 B. Experiment on Scene 7 Figure 16 shows the binary edge maps of Scene 7 produced by the five methods. According to Figure binaryproduces edge maps of Scene 7 produced byperforms the five methods. to Figure 16b, 16 Di shows Zenzo’sthe method many spurious edges and poorly onAccording connectivity. Figure 16b, Di Zenzo’s method produces many spurious edges and performs poorly on connectivity. The RCMG preserves most significant spatial structures, but it also brings many grainy edges The RCMG in preserves most significant spatial butThe it also brings many grainycan edges especially especially the grass region as shown instructures, Figure 16c. Drewniok’s method detect many in the grass region as shown in Figure 16c. The Drewniok’s method can detect many edges on the edges on the wall and grass as depicted in Figure 16d, but the interval between edges onwall the and grass as Figure 16d, but the intervalcaused between on the windows Connectivity is enlarged due windows is depicted enlarged in due to edges displacement by edges Gaussian smoothing. of to edges displacement caused by Gaussian smoothing. Connectivity of edges generated by SSSDE is edges generated by SSSDE is better than that of Di Zenzo’s while some edges between the upper better than that of Di Zenzo’s while some edges between the upper and lower windows are missed, and lower windows are missed, as can be seen in Figure 16e. Comparatively, the better as can be seenofinthe Figure 16e. method Comparatively, the better performance of thestructures proposedsuch method is performance proposed is perceivable. Most of the fine edge as the perceivable. Most of the fine edge structures such as the edges located at the windows are attained edges located at the windows are attained and the edges are clear and connective as shown in and the16a. edges are clear and connective as shown Figure More specifically, as indicated by and the Figure More specifically, as indicated by theincircle at 16a. the bottom of the image, Di Zenzo’s circle at the bottom of produce the image, Di Zenzo’sedges and Drewniok’s methods undesirable edges Drewniok’s methods undesirable for the grass in theproduce circle. The RCMG almost for the grass in the circle. The RCMG almost misses and the SSSDE totally misses the edge structure. misses and the SSSDE totally misses the edge structure. Comparatively, the fine structure is well Comparatively, theproposed fine structure is well preserved byright the proposed GEDHSI method. At the right preserved by the GEDHSI method. At the bottom ellipse, Drewniok’s method has bottom ellipse, Drewniok’s method has missed both the edge of the left sidewalls and the edge between missed both the edge of the left sidewalls and the edge between the middle white door and the dark the middleOn white and the shadow. On the can contrary, proposed GEDHSI can againmissing detect shadow. the door contrary, thedark proposed GEDHSI againthe detect correct edges without correct edges without main structure of that missing region. main structure of that region.

1 (a)

(b)

(c)

(d)

(e)

Figure 16. 16. The The binary binary edge edge maps maps generated generated for for the the Scene Scene 77 by: by: (a) (a) GEDHSI; GEDHSI; (b) (b) Di Di Zenzo’s Zenzo’s method; method; Figure σ (c) the RCMG method; (d) Drewniok’s method ( = 1.0); and (e) SSSDE. (c) the RCMG method; (d) Drewniok’s method (σ = 1.0); and (e) SSSDE.

Overall, the comparative experiments above have validated the superiority of the proposed Overall, the comparative experiments above have validated the superiority of the proposed GEDHSI for edge detection in HSIs. The proposed method is more robust to background clusters GEDHSI for edge detection in HSIs. The proposed method is more robust to background clusters and weak edges, as illustrated by the experiments on artificial images. For real-world images, it is and weak edges, as illustrated by the experiments on artificial images. For real-world images, it is robust to noisy bands in keeping complete and reasonable spatial structures and performs well on


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robust to noisy bands in keeping complete and reasonable spatial structures and performs well on edge localization and resolution. As a result, GEDHSI is more suitable for HSI edge detection than other state-of-the-art multi-band approaches. 4.5. Comparison of Runtime In this section, we compare the computational efficiency of the above five algorithms. The mean computational time (in seconds) required by each algorithm for five independent runs in solving the two tested images, the Farmland and Washington DC Mall, are presented for comparison. As seen in Table 2, RCMG takes the least time, and one main reason is its C++ based implementation in comparison to the MATLAB-based implementation for the other four methods. The proposed GEDHSI, unfortunately, consumes the longest runtime as a whole. The long time consumption is largely caused by the iterative computation in traveling procedure. For each particle, the repeating calculation of gravitational force for all particles in dataset D leads to heavy burden of runtime. How to speed up the process and improve the efficiency of GEDHSI will be investigated in the future. Table 2. The time efficiency evaluation. Image

GEDHSI 1

Di Zenzo

RCMG 2

Drewniok

SSSDE 3

Farmland Washington DC Mall

32.17s 36.56s

15.65s 22.45s

4.04s 4.81s

13.55s 14.28s

21.53s 26.75s

1

GEDHSI (Gravitation-Based Edge Detection in Hyperspectral Image); 2 RCMG (Robust Color Morphological Gradient); 3 SSSDE (modified Simultaneous Spectral/Spatial Detection of Edges).

5. Conclusions In recent years, various heuristic and physically inspired image-understanding methods have been developed. To extract the edges from HSIs, a novel edge-detection method, namely Gravitation-based Edge Detection on HSIs (GEDHSI), is presented in this paper. In GEDHSI, each pixel is modeled as a movable celestial object in the joined spatial-spectral feature space where all objects travel in the feature space under the gravitational field force. Due to the relative positions, the edge pixels and non-edge pixels can be separated by computing their potential energy fields. In addition to its simplicity and generality, GEDHSI has promising theoretical properties that make it a solid tool for edge detection. The performance of the proposed algorithm has been benchmarked with four state-of-the-art methods, including Di Zenzo’s, Drewniok’s, RCMG, and SSSD detectors. Experiments on a variety of datasets have validated the efficacy of the proposed algorithm in edge-detection for HSIs under various levels of noise. The future work will focus on further improving the efficiency of the approach and investigating the relationship between the edge scale and the parameter settings for edge results in the multiscale space. Acknowledgments: This work was supported by Chinese Natural Science Foundation Projects (41471353) and National Key Research and Development Program of China (2016YFB0501501). Author Contributions: Genyun Sun, Aizhu Zhang, and Peng Wang conceived, designed and performed the experiments, analyzed the data, and wrote the paper. Jinchang Ren, Jingsheng Ma, and Yuanzhi Zhang help organize and revise the paper. Xiuping Jia helps analyze the experimental data and improve the presentation of the second version. Conflicts of Interest: The authors declare no conflict of interest.

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Gravitation-Based Edge Detection in Hyperspectral Images - MDPI

Gravitation-Based Edge Detection in Hyperspectral Images - MDPI

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