Sub-pixel flood inundation mapping from multispectral ...

ISPRS Journal of Photogrammetry and Remote Sensing 101 (2015) 10–21

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Sub-pixel flood inundation mapping from multispectral remotely sensed images based on discrete particle swarm optimization Linyi Li a,b,⇑, Yun Chen b, Xin Yu c, Rui Liu b,d, Chang Huang e a

School of Remote Sensing and Information Engineering, Wuhan University, 129 Luoyu Road, Wuhan 430079, PR China CSIRO Land and Water, Clunies Ross Street, Canberra 2601, Australia c Beijing Institute of Surveying and Mapping, 15 Yangfangdian Road, Beijing 100038, PR China d Key Laboratory of Geographic Information Science (Ministry of Education), East China Normal University, 500 Dongchuan Road, Shanghai 200241, PR China e College of Urban and Environmental Sciences, Northwest University, 1 Xuefu Road, Xi’an 710127, PR China b

a r t i c l e

i n f o

Article history: Received 24 July 2014 Received in revised form 21 November 2014 Accepted 24 November 2014 Available online 13 December 2014 Keywords: Flood inundation Sub-pixel mapping Discrete particle swarm optimization Multispectral remotely sensed images

a b s t r a c t The study of flood inundation is significant to human life and social economy. Remote sensing technology has provided an effective way to study the spatial and temporal characteristics of inundation. Remotely sensed images with high temporal resolutions are widely used in mapping inundation. However, mixed pixels do exist due to their relatively low spatial resolutions. One of the most popular approaches to resolve this issue is sub-pixel mapping. In this paper, a novel discrete particle swarm optimization (DPSO) based sub-pixel flood inundation mapping (DPSO-SFIM) method is proposed to achieve an improved accuracy in mapping inundation at a sub-pixel scale. The evaluation criterion for sub-pixel inundation mapping is formulated. The DPSO-SFIM algorithm is developed, including particle discrete encoding, fitness function designing and swarm search strategy. The accuracy of DPSO-SFIM in mapping inundation at a sub-pixel scale was evaluated using Landsat ETM + images from study areas in Australia and China. The results show that DPSO-SFIM consistently outperformed the four traditional SFIM methods in these study areas. A sensitivity analysis of DPSO-SFIM was also carried out to evaluate its performances. It is hoped that the results of this study will enhance the application of medium-low spatial resolution images in inundation detection and mapping, and thereby support the ecological and environmental studies of river basins. Ó 2014 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.

1. Introduction Flood is one of the most frequently occurring natural disasters, causing great damage, human suffering and economic losses. Changes in global climate and land use have increased the severity and frequency of floods all around the world (Akinci and Erdogan, 2014). Therefore, the study of flood inundation has important significance to human life and social economy (Chen et al., 2014a; Chen et al., 2011; Son et al., 2013; Tralli et al., 2005). Inundation has spatio-temporal distributions. Remote sensing technology has provided an effective way to study these inundation characteristics using multi-spatial, multi-temporal and multispectral remotely sensed images (Chen et al., 2014b; Huang et al., 2012; Huang ⇑ Corresponding author at: School of Remote Sensing and Information Engineering, Wuhan University, 129 Luoyu Road, Wuhan 430079, PR China. Tel.: +86 13545177585. E-mail address: [email protected] (L. Li).

et al., 2013; Huang et al., 2014b; Huang et al., 2014c; Ticehurst et al., 2013). Many remote sensing sensors have been applied to flood inundation detection and mapping (Bryant and Rainey, 2002; Chen et al., 2013; Gan et al., 2012; Huang et al., 2014d; Mason et al., 2014; Thomas et al., 2011), such as the Advanced Very High Resolution Radiometer (AVHRR), Landsat Multispectral Scanner System (MSS), Landsat Thematic Mapper/Enhanced Thematic Mapper Plus (TM/ETM+), the Moderate Resolution Imaging Spectroradiometer (MODIS), Synthetic Aperture Radar (SAR), and Light Detection and Ranging (LIDAR). However, remote sensing sensors generally do not have high temporal and spatial resolutions at the same time. There is usually a trade-off between their temporal and spatial resolutions (Giraldo Osorio and Garcia Galiano, 2012; Huang et al., 2014a). This has limited their ability in inundation mapping. For example, relatively high temporal resolution sensors, such as AVHRR and MODIS, can scan the earth’s surface more than once a day, but usually have relatively coarse spatial resolutions. Mixed pixels do exist when mapping inundation using these

http://dx.doi.org/10.1016/j.isprsjprs.2014.11.006 0924-2716/Ó 2014 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.

L. Li et al. / ISPRS Journal of Photogrammetry and Remote Sensing 101 (2015) 10–21

images. One of the most popular approaches to resolve this issue is sub-pixel mapping. Sub-pixel mapping is a method used to obtain the sub-pixel spatial distribution within mixed pixels, which is based on spatial dependence and fraction images (Aplin and Atkinson, 2001; Atkinson, 1997; Atkinson, 2005). Spatial dependence is the likelihood that observations close together are more alike than those that are further apart. The input to sub-pixel mapping is a fraction image, which is commonly derived from soft classification of remotely sensed imagery. Different from hard classification, which assigns one class to each mixed pixel, soft classification derives a fraction value for each mixed pixel in the fraction image. The fraction value only represents the proportion of the class without specifying the location of the class within each mixed pixel. Sub-pixel mapping can be considered as the post processing of soft classification to obtain more information at a sub-pixel scale. It has become one of the hotspots in remote sensing research and applications. There are various existing sub-pixel mapping methods (Ren and Ge, 2011), such as linear optimization model (Verhoeye and De Wulf, 2002), pixel swapping algorithm (Atkinson, 2005; Huang et al., 2014a; Thornton et al., 2007), spatial attraction models (Mertens et al., 2006; Shen et al., 2009), genetic algorithm (Mertens et al., 2003), artificial neural networks (Li et al., 2014; Mertens et al., 2004b; Quang et al., 2011;Tatem et al., 2001; Zhang et al., 2008), Markov random field (Ardila et al., 2011; Kanemura et al., 2009), and artificial immune systems (Zhong and Zhang, 2013). However, sub-pixel mapping is still a difficult task which is under continual development process due to the complexity and uncertainty of remotely sensed images (Datla et al., 2010; Melin et al., 2012; Wu et al., 2009). Attempts to map sub-pixel inundation from remotely sensed images are relatively rare in literatures. Sub-pixel inundation mapping is a combined optimization issue in essence. New methods based on artificial intelligence may provide potential solutions. Particle swarm optimization (PSO) is a relatively new artificial intelligence method that was developed through the simulation of

60%

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(a)

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(b)

60%

60%

40%

40%

0%

0%

(c) flood inundation

100%

60%

40%

0%

0%

(d) non-inundation

Fig. 1. Example of sub-pixel inundation mapping (scale = 5). (a) Fraction image of inundation. (b) Possible distribution 1. (c) Possible distribution 2. (d) Possible distribution 3.

11

simplified social models of bird flocks (Bratton and Kennedy, 2007; Kennedy and Eberhart, 1995, 1997; Shi and Eberhart, 1998). It has a strong ability to search for the optimal solutions for optimization problems because of its intelligent properties, such as adaptation and self-organization. Different from standard PSO, discrete PSO (DPSO) is commonly used to solve combined optimization issues (Kennedy and Eberhart, 1997). PSO has become one of the most well-known methods in artificial intelligence research and has already proven to be useful in solving optimization problems encountered in many fields such as the electricity industry (Azevedo et al., 2007), transportation (Garcia-Nieto et al., 2013), the chemical industry (Lin et al., 2005), and remote sensing (Li 2011, 2013; Li and Li, 2008, 2009; Saeedi and Faez, 2011). In this study, a new DPSO-based sub-pixel flood inundation mapping (DPSO-SFIM) method is proposed to achieve an improved accuracy in mapping inundation at a sub-pixel scale from multispectral remotely sensed images. The main objectives are (1) to formulate an evaluation criterion for sub-pixel inundation mapping and to transform sub-pixel inundation mapping into a combined optimization issue; (2) to develop the DPSO-SFIM algorithm, including particle discrete encoding, fitness function designing and swarm search strategy; and (3) to evaluate the accuracy of the DPSO-SFIM method in mapping inundation at a sub-pixel scale using Landsat ETM + images from study areas in Australia and China. 2. Methodology 2.1. Concept of sub-pixel inundation mapping The intention of sub-pixel inundation mapping is to obtain the sub-pixel spatial distribution of inundation within mixed pixels by maximizing their spatial dependence while maintaining the original proportions of inundation within the mixed pixels. Sub-pixel inundation mapping divides each mixed pixel in fraction images into S ⁄ S sub-pixels, where S represents a scale factor which refers to the scale ratio between a mixed pixel and its sub-pixels. For example, if S equals to 5, then 25 sub-pixels in each mixed pixel will be created. The basic principle of sub-pixel inundation mapping is shown in Fig. 1 which is a simple example with two classes representing inundation and non-inundation respectively. The fraction image is shown in Fig. 1(a), where the fraction value represents the proportion of inundation in a mixed pixel. Fig. 1(b)–(d) describe three possible distributions of sub-pixels in the mixed pixel in the center. The fraction value in the mixed pixel in the center is 20%, so there are 5 inundation sub-pixels and 20 non-inundation sub-pixels in the mixed pixel. The spatial dependence principle can be used to compare different possible distributions of subpixels: the distribution of sub-pixels is more likely if it has higher spatial dependence. Therefore, the most likely distribution of subpixels in the three distributions should be Fig. 1(b). Actually there are far more than three possible distributions of sub-pixels in the above example, so it is usually difficult to find the optimal possible distribution from numerous possible distributions. If ‘1’ represents inundation and ‘0’ represents non-inundation, then sub-pixel inundation mapping is transformed into a combined optimization issue. According to spatial dependence principles (Atkinson, 1997, 2005), sub-pixel inundation mapping can be formulated as a maximum combined optimization issue. Flood inundation spatial dependence index (FISDI) can be calculated for a mixed pixel considering the spatial correlation between its sub-pixels and the neighboring coarse pixels. For each sub-pixel i in a mixed pixel, FISDIi is calculated as a distance-weighted function of its j ¼ 1; 2; . . . ; J neighboring inundation fractions:

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L. Li et al. / ISPRS Journal of Photogrammetry and Remote Sensing 101 (2015) 10–21

FISDIi ¼ C i 

J X

! wj  Fractionj

j¼1

"

are acceleration coefficients; rand() is the random number with uniform distribution U(0, 1); Dt is usually the unit time; vmax is the maximum value of v; and Sðv kim Þ is the Sigmoid function.

þ ð1  C i Þ

J X wj  ð1  Fractionj Þ 

# ð1Þ

j¼1

where Ci is the binary class of each sub-pixel i (1 for the flood inundation class and 0 for the non-inundation class), wj is usually calculated as the distance inverse of each sub-pixel i to the j th neighboring coarse pixel center, and Fractionj is the flood inundation fraction value of the j th neighboring coarse pixel. The FISDI of a mixed pixel can be calculated as follows:

FISDI ¼

SS X

FISDIi

ð2Þ

i¼1

where S represents the scale factor which refers to the scale ratio between a mixed pixel and its sub-pixels. The evaluation criterion of sub-pixel inundation mapping can be formulated as: the higher the FISDI value, the higher the possibility of the sub-pixel distribution. Therefore, the intention of sub-pixel inundation mapping is to allocate inundation to the sub-pixels in a mixed pixel while maximizing the FISDI. 2.2. DPSO-SFIM method 2.2.1. Basic principle of DPSO PSO is a relatively new evolutionary computing algorithm based on swarm intelligence (Bratton and Kennedy, 2007; Kennedy and Eberhart, 1995, 1997; Shi and Eberhart, 1998). PSO uses a swarm of individuals to probe the best position in the search space, which represents the best solution of an optimal problem. The individual in the swarm is called a particle. The particle moves stochastically toward its own best previous position and toward the whole swarm’s best previous position in the search space. Suppose the size of the swarm is N and the dimension of the search space is M, then the position of the i th particle is denoted as Xi(xi1, xi2,   , xiM), which represents a possible solution of an optimal problem. Its velocity is denoted as Vi(vi1, vi2,   , viM), its best previous position is denoted as Pi(pi1, pi2,   , piM), and the best previous position discovered by the whole swarm is denoted as Pg(pg1, pg2,   , pgM). Different from standard PSO, the value of xim (1 6 m 6 M) in DPSO is restricted to 0 or 1. The particles in the swarm are manipulated according to the following equations (Bratton and Kennedy, 2007; Kennedy and Eberhart, 1997; Shi and Eberhart, 1998): k k k v kþ1 im ¼ x  v im þ c 1  randðÞ  ðpim  xim Þ=Dt þ c2  randðÞ

 ðpgm  xkim Þ=Dt

xk ¼ xmax  k  ðxmax  xmin Þ=kmax 8 kþ1 > < v im

kþ1 v im ¼ v max > : v max

if

kþ1 v max 6 v im 6 v max

if

v kþ1 im > v max v kþ1 im < v max

if

if ðrandðÞ < Sðv kim ÞÞ xkþ1 im ¼ 1 else

xkþ1 im ¼ 0

1 Sðv kim Þ ¼ 1 þ expðv kim Þ

ð3Þ ð4Þ

ð5Þ

ð6Þ

ð7Þ

where k and kmax are the current iteration time and the maximum iteration time, respectively; x is the inertia weight; xmax and xmin are the maximum and minimum value of x, respectively; c1 and c2

2.2.2. DPSO-SFIM algorithm There are three key problems in the DPSO-SFIM algorithm: (A) particle discrete encoding, (B) fitness function designing and (C) swarm search strategy. (A) Particle discrete encoding The position vector of each particle Xi(xi1, xi2,   , xiM) represents a possible solution of sub-pixel inundation mapping, where M is equal to S ⁄ S. The basic principle of particle discrete encoding for sub-pixel inundation mapping is shown in Fig. 2. A possible distribution of inundation in a mixed pixel is described in Fig. 2(a). Its corresponding discrete binary representation of inundation distribution is shown in Fig. 2(b), where inundation is represented by 1 and non-inundation is represented by 0. Fig. 2(c) shows its corresponding discrete encoding of the particle’s position vector by placing each row in Fig. 2(b) end to end. The velocity vector of each particle has the same dimension as its position vector. Different from its position vector, its velocity vector is composed of real numbers. Position vectors of all particles in the swarm compose a position matrix X and velocity vectors of all particles compose a velocity matrix V as follows:

2

3

x11

x12



x1M

6x 6 21 X¼6 6 .. 4 .

x22 .. .

 .. .

x2M 7 7 .. 7 7 . 5

xN1

xN2

   xNM

2

v 11 v 12 6v 6 21 v 22



v N1 v N2



V ¼6 6 .. 4 .

.. .

 .. .

v 1M 3 v 2M 77 .. 7 7 . 5

ð8Þ

ð9Þ

v NM

where N is the number of particles in the swarm and M is the dimension of each particle vector. (B) Fitness function designing Fitness function value is a measure of a particle’s position. The particle is more likely to find the optimal solution if it has a larger fitness function value. The fitness function for sub-pixel flood inundation mapping can be defined as follows:

FitnessFunctioni ¼ FISDIðxi1 ; xi1 ;    ; xiM Þ

ð10Þ

where FitnessFunctioni is the fitness function of the i th particle, and FISDI is its corresponding spatial dependence index when the distribution of inundation in a mixed pixel is represented by (xi1, xi1,  , xiM). (C) Swarm search strategy A flow chart of the swarm search strategy is shown in Fig. 3. For each mixed pixel in the fraction image, the swarm search strategy is described as follows: (1) Initialize particle swarm. Initialize the position matrix X and the velocity matrix V of the particle swarm according to Eqs. (8) and (9), where the elements in the position matrix X and the velocity matrix V are initialized according to the following equations respectively:

xim ¼ rand intðÞ

ð11Þ

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L. Li et al. / ISPRS Journal of Photogrammetry and Remote Sensing 101 (2015) 10–21

0 0 1 0 0

flood inundation non-inundation

(a)

0 0 1 0 0

0 0 1 0 0 (b)

0 0 0 1 0

0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 (c) Fig. 2. Example of particle discrete encoding for sub-pixel inundation mapping (scale = 5). (a) Possible distribution of inundation in a mixed pixel. (b) Corresponding discrete binary representation of inundation distribution. (c) Corresponding discrete encoding of the particle’s position vector.

Fraction image (2)

Initialize particle swarm

(3)

Compute fitness function value of each particle (4)

Update the optimal space position of each particle

Update the optimal space position of the swarm

(5) (6)

Compute the velocity of each particle

(7)

Compute the position of each particle

Maintain original flood inundation proportion

The generation meets the maximum iterative time (8)

All mixed pixels are processed

where 1 6 i 6 N, 1 6 m 6 M, rand int() is the random number with the value of ‘0’ or ‘1’, and Fraction is the flood inundation fraction value of the mixed pixel. Compute fitness function value of each particle in the swarm using Eq. (10). Update the optimal space position of each particle. Compare the computed fitness value of each particle with the fitness value of its best previous position vector. If the current value is better, then set the current position as its best previous position. Update the optimal space position of the swarm. Compare the evaluated fitness value of each particle with the fitness value of the whole swarm’s best previous position vector Pg. If the current value is better, then set the current position as the whole swarm’s best previous position. Compute the velocity of each particle according to Eqs. (3)– (5). Compute the position of each particle according to Eqs. (6) and (7). Maintain the original proportion of inundation in the mixed pixel. The position of each particle represents a distribution P of inundation in the mixed pixel. If M m¼1 xim > Fraction, compare the position of each particle with the current Pg, and retain position elements in common whose value is equal to 1. Then randomly change the value of other position elements whose value is equal to 1 to satisfy PM PM m¼1 xim ¼ Fraction. If m¼1 xim < Fraction, randomly change the value of position elements whose value is equal to 0 to P satisfy M m¼1 xim ¼ Fraction. Exit the loop if the generation meets the maximum iteration time and the output Pg is the optimal possible distribution of inundation in a mixed pixel by the DPSO-SFIM algorithm. Otherwise, go to step (2).

3. Case study

Result image 3.1. Study areas and data Fig. 3. Flow chart of the swarm search strategy.

M X

xim ¼ Fraction

ð12Þ

m¼1

v im ¼ v max þ 2v max  randðÞ

ð13Þ

Two comparative study areas were selected for the case study. The first study area was located in the Chowilla Floodplain of the Murray-Darling Basin of Australia. The second study area was located in the Jianghan Plain of the Changjiang River Basin of China. The remotely sensed images were acquired when there were significant flood events in the study areas. Key characteristics of the two study areas are shown in Table 1. Locations of the

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Table 1 Key characteristics of the two comparative study areas.

Location Date Area Major water body Data

Study area 1

Study area 2

The Chowilla Floodplain of the Murray-Darling Basin of Australia December 13, 2000 225 km2 The main channel of the Murray River and its tributaries A Landsat ETM + image (500  500 pixels) at 30 m resolution

The Jianghan Plain of the Changjiang River Basin of China July 31, 2010 225 km2 The main channel of the Changjiang River and its tributaries A Landsat ETM + image (500  500 pixels) at 30 m resolution

Fig. 4. Locations of the comparative study areas and major water bodies shown in color composite (R5G2B1) Landsat ETM + images at 30 m resolution after image enhancement. (a) The Chowilla Floodplain of the Murray-Darling Basin of Australia (500  500 pixels). (b) The Jianghan Plain of the Changjiang River Basin of China (500  500 pixels). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

comparative study areas and major water bodies are shown in Fig. 4. One large area located in the Chowilla Floodplain of the Murray-Darling Basin of Australia was selected for further experiment. The size of the corresponding Landsat ETM + image is 3000  3000 pixels, which was derived from the Landsat ETM + image acquired on December 13, 2000. The experimental images are the ETM + L1T products, which provide systematic radiometric and geometric accuracy.

learning rate, and the ratio to decrease learning rate were 1, 0.01, 1.05, and 0.7, respectively. The main configuration for DPSO-SFIM was as follows: the size of the swarm, the maximum iterative time, the maximum inertia weight, and the minimum inertia weight were 20, 30, 0.9, and 0.4, respectively. DPSO-SFIM and four previous algorithms were coded in Matlab. The inputs to these algorithms were the same inundation fraction images. 3.3. Comparative analysis

3.2. Study methods To demonstrate the effectiveness of DPSO-SFIM, comparisons were carried out between DPSO-SFIM and sub-pixel flood inundation mapping (SFIM) based on four previous algorithms. Mertens et al. (2004a) introduced a sub-pixel mapping method directly exploiting spatial dependence (DESD) in a simple and effective manner. Mertens et al. (2006) developed a sub-pixel mapping algorithm based on spatial attraction models (SAM) and the results showed an increased accuracy. Artificial neural networks (ANNs) are classic artificial intelligence methods and have obtained relatively satisfactory results in sub-pixel mapping applications (Li et al., 2014; Mertens et al., 2004b; Quang et al., 2011; Tatem et al., 2001; Zhang et al., 2008). As one of the typical and widely used ANNs, back-propagation neural network (BP) was applied to SFIM for comparison. The four methods for comparison are DESD based SFIM (DESD-SFIM), SAM based SFIM (SAM-SFIM), BP with Bayesian regulation based SFIM (BPBR-SFIM), and BP with gradient descent regulation using momentum and adaptive learning rate based SFIM (BPGDX-SFIM). The same surrounding neighboring type was used for all SFIM methods. The main configuration for BPBR-SFIM was as follows: The number of hidden layers, Marquardt adjustment parameter (MAP), the decrease factor for MAP, and the increase factor for MAP were 1, 0.005, 0.1, and 10, respectively. The main configuration for BPGDX-SFIM was as follows: The number of hidden layers, the learning rate, the ratio to increase

3.3.1. Visual comparisons and analysis Locations of the study areas and major water bodies are shown in color composite (R5G2B1) Landsat ETM + images in Fig. 5(a) and Fig. 6(a) respectively. The reference images (Figs. 5(b), (c) and 6(b), (c)) were derived from the corresponding ETM + images using the modified normalized difference water index (mNDWI; (Xu, 2006)). Fig. 5(b) is a reference image of non-flooding state which was derived from the ETM + image acquired on October 26, 2000. Fig. 6(b) is a reference image of non-flooding state which was derived from the ETM + image acquired on December 16, 2008. The mNDWI is one of the most popular inundation detection indices, and is calculated according to the following equation (Xu, 2006):

mNDWI ¼ ðGreen  SWIRÞ=ðGreen þ SWIRÞ

ð14Þ

where Green is the Green band (band 2 of the Landsat ETM + image), and SWIR is the Short-Wave Infrared band (band 5 of the Landsat ETM + image). The inundation fraction images (Figs. 5(d) and 6(d)) were derived by aggregating the corresponding inundation reference images with a scale factor, and were used as the inputs of sub-pixel inundation mapping respectively. In this case, the scale factor was set to 5. The inundation reference images were aggregated by a 5  5 window and the aggregated pixel value is equal to the proportion of inundation pixels inside this window. Therefore,

L. Li et al. / ISPRS Journal of Photogrammetry and Remote Sensing 101 (2015) 10–21

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Fig. 5. Materials of case study located in the Chowilla Floodplain of the Murray-Darling Basin of Australia (scale = 5). (a) Location of the study area and major water bodies shown in a color composite (R5G2B1) Landsat ETM + image (500  500 pixels) at a resolution of 30 m after image enhancement. (b) Reference image of non-flooding state. (c) Reference image of flooding state. (d) Inundation fraction image (100  100 pixels) at a resolution of 150 m. (e) DESD-SFIM. (f) SAM-SFIM. (g) BPBR-SFIM. (h) BPGDX-SFIM. (i) DPSO-SFIM. (j) Zoom for inundation reference image. (k) Zoom for DESD-SFIM. (l) Zoom for SAM-SFIM. (m) Zoom for BPBR-SFIM. (n) Zoom for BPGDX-SFIM. (o) Zoom for DPSO-SFIM. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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L. Li et al. / ISPRS Journal of Photogrammetry and Remote Sensing 101 (2015) 10–21

Fig. 6. Materials of case study located in the Jianghan Plain of the Changjiang River Basin of China (scale = 5). (a) Location of the study area and major water bodies shown in a color composite (R5G2B1) Landsat ETM + image (500  500 pixels) at a resolution of 30 m after image enhancement. (b) Reference image of non-flooding state. (c) Reference image of flooding state. (d) Inundation fraction image (100  100 pixels) at a resolution of 150 m. (e) DESD-SFIM. (f) SAM-SFIM. (g) BPBR-SFIM. (h) BPGDX-SFIM. (i) DPSOSFIM. (j) Zoom for inundation reference image. (k) Zoom for DESD-SFIM. (l) Zoom for SAM-SFIM. (m) Zoom for BPBR-SFIM. (n) Zoom for BPGDX-SFIM. (o) Zoom for DPSOSFIM. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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L. Li et al. / ISPRS Journal of Photogrammetry and Remote Sensing 101 (2015) 10–21 Table 2 Quantitative comparisons of different method performances. Method

DESD-SFIM SAM-SFIM BPBR-SFIM BPGDX-SFIM DPSO-SFIM

Murray-Darling Basin

Changjiang River Basin

OA (%)

Kappa

APA (%)

AUA (%)

OA (%)

Kappa

APA (%)

AUA (%)

69.9 68.4 74.3 71.3 81.6

0.347 0.299 0.462 0.392 0.620

66.5 63.9 72.7 69.1 81.0

69.9 69.7 73.7 70.5 81.0

75.9 76.4 77.2 76.3 80.2

0.435 0.438 0.475 0.451 0.564

70.3 70.2 72.6 71.3 78.2

74.5 75.7 75.7 74.7 78.2

the resolution of the inundation fraction images is 150 m. Compared with the fraction image commonly derived by image soft classification, the fraction image derived in this way can avoid errors and uncertainties introduced by the classification process (Huang et al., 2014a). The sub-pixel inundation mapping results, using DESD-SFIM, SAM-SFIM, BPBR-SFIM, BPGDX-SFIM, and DPSO-SFIM, are shown in Figs. 5(e)–(i) and 6(e)–(i) respectively. To ensure clarity in comparing these methods, the same small regions from the reference images and result images were zoomed and are shown in Figs. 5(j)–(o) and 6(j)–(o) respectively. As shown in Fig. 5,

especially in Fig. 5(j)–(o), BPBR-SFIM and BPGDX-SFIM performed better than DESD-SFIM and SAM-SFIM, because their results are more similar to the reference image Fig. 5(c) in visualization. DPSO-SFIM obtained the most satisfactory sub-pixel inundation mapping result among the five SFIM methods for the MurrayDarling Basin. DPSO-SFIM mapped the Murray River and its tributaries more continuously and smoothly than other SFIM methods. From Fig. 6, especially from Fig. 6(j)–(o), DPSO-SFIM also obtained the most satisfactory visual sub-pixel inundation mapping result among the five SFIM methods for the Changjiang River Basin.

Fig. 7. Materials of the large area (3000  3000 pixels) located in the Chowilla Floodplain of the Murray-Darling Basin of Australia (scale = 5). (a) Area location and major water bodies shown in a color composite (R5G2B1) Landsat ETM + image at a resolution of 30 m after image enhancement. (b) Reference image of non-flooding state. (c) Reference image of flooding state. (d) Inundation fraction image (600  600 pixels) at a resolution of 150 m. (e) DESD-SFIM. (f) SAM-SFIM. (g) BPBR-SFIM. (h) BPGDX-SFIM. (i) DPSO-SFIM. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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L. Li et al. / ISPRS Journal of Photogrammetry and Remote Sensing 101 (2015) 10–21

representing inundation and non-inundation, respectively. Therefore, the confusion matrix is a 2  2 matrix whose element pi,j represents the proportion of area in the mapped class i and the reference class j. OA, Kappa, APA and AUA were calculated according to the corresponding formulas based on confusion matrices (Foody, 2002; Liu et al., 2007). Table 2 shows the performances in terms of the accuracy derived from the Murray-Darling Basin and the Changjiang River Basin by DESD-SFIM, SAM-SFIM, BPBRSFIM, BPGDX-SFIM, and DPSO-SFIM. From Table 2, we can see that DPSO-SFIM exhibits the highest OA, Kappa, APA and AUA. Therefore, DPSO-SFIM obtained the most accurate sub-pixel inundation mapping results among the five SFIM methods in terms of visual comparisons in Figs. 5 and 6 and quantitative comparisons in Table 2.

Table 3 Quantitative comparisons of different method performances in the large area (3000  3000 pixels). Method

Murray-Darling Basin

DESD-SFIM SAM-SFIM BPBR-SFIM BPGDX-SFIM DPSO-SFIM

OA (%)

Kappa

APA (%)

AUA (%)

71.5 70.0 77.1 73.3 83.4

0.394 0.349 0.525 0.438 0.659

69.0 66.5 76.0 71.4 82.9

71.5 71.2 76.7 73.0 82.9

3.3.2. Quantitative comparisons and analysis For a more detailed verification of the different methods, we compared the mapping results with the reference images using measures of overall accuracy (OA), Kappa coefficient, average producer’s accuracy (APA) and average user’s accuracy (AUA) based on confusion matrices (Foody, 2002; Liu et al., 2007). All pure pixels in the inundation fraction images were excluded when calculating accuracy indicators. There are two classes in the mapping results

3.3.3. Discussion of comparative analysis From the case study, we can see that DPSO-SFIM outperformed the four traditional SFIM methods more significantly in the Australian case study. That is because the inundation distributions in the Murray-Darling Basin are more complicated than those in the

Table 4 Sensitivity of DPSO-SFIM in relation to iteration times. Changjiang River Basin

Kappa

APA (%)

AUA (%)

OA (%)

Kappa

APA (%)

AUA (%)

78.0 79.8 80.7 81.1 81.3 81.6 81.8 82.0 82.2 82.3

0.547 0.583 0.603 0.611 0.614 0.620 0.625 0.630 0.633 0.634

77.3 79.2 80.1 80.5 80.7 81.0 81.2 81.5 81.6 81.7

77.3 79.2 80.1 80.5 80.7 81.0 81.2 81.5 81.6 81.7

77.7 79.0 79.5 79.7 80.1 80.2 80.4 80.5 80.5 80.5

0.510 0.538 0.550 0.555 0.563 0.564 0.569 0.572 0.573 0.573

75.5 76.9 77.5 77.7 78.1 78.2 78.5 78.6 78.6 78.6

75.5 76.9 77.5 77.7 78.1 78.2 78.5 78.6 78.6 78.6

83.0

0.640 Australia China

82.0

0.600

Kappa

80.0 79.0

0.580 0.560 0.540

78.0 77.0

Australia China

0.620

81.0

OA (%)

0.520 0

5

10 15 20 25 30 35 40 45 50

0.500

0

5

10 15 20 25 30 35 40 45 50

ITs

ITs

(a)

(b) 82.0

82.0 Australia China

81.0 80.0

80.0

79.0 78.0

79.0 78.0

77.0

77.0

76.0

76.0

75.0

Australia China

81.0

AUA (%)

5 10 15 20 25 30 35 40 45 50

Murray-Darling Basin OA (%)

APA (%)

ITs

0

5

10 15 20 25 30 35 40 45 50

75.0

0

5

10 15 20 25 30 35 40 45 50

ITs

ITs

(c)

(d)

Fig. 8. Sensitivity of DPSO-SFIM in relation to iteration times. (a) Sensitivity of OA. (b) Sensitivity of Kappa. (c) Sensitivity of APA. (d) Sensitivity of AUA.

19

L. Li et al. / ISPRS Journal of Photogrammetry and Remote Sensing 101 (2015) 10–21 Table 5 Sensitivity of DPSO-SFIM in relation to swarm size. N

5 10 15 20 25 30

Murray-Darling Basin

Changjiang River Basin

OA (%)

Kappa

APA (%)

AUA (%)

OA (%)

Kappa

APA (%)

AUA (%)

79.8 80.9 81.4 81.6 81.9 82.1

0.584 0.605 0.615 0.620 0.626 0.630

79.2 80.3 80.8 81.0 81.3 81.5

79.2 80.3 80.8 81.0 81.3 81.5

79.0 79.7 79.9 80.2 80.2 80.3

0.538 0.554 0.558 0.564 0.565 0.567

76.9 77.7 77.9 78.2 78.3 78.3

76.9 77.7 77.9 78.2 78.3 78.3

Changjiang River Basin. More inundation meanders and confluences exist in the Murray-Darling Basin, so there are much more possible distributions of sub-pixels in each mixed pixel. It is difficult for the four traditional methods to obtain the optimal distribution in this complex situation.

obtains the sub-pixel mapping results for the whole fraction images in a pixel-by-pixel fashion regardless of the total number of pixels searched.

3.3.4. Large area study One large area located in the Chowilla Floodplain of the MurrayDarling Basin of Australia was selected for further experiment. The location is shown in a color composite (R5G2B1) Landsat ETM + image in Fig. 7(a). The reference images (Fig. 7(b) and (c)) were derived from the corresponding ETM + images using mNDWI. Fig. 7(b) is a reference image of non-flooding state which was derived from the ETM + image acquired on October 26, 2000. Table 3 shows the performances of DESD-SFIM, SAM-SFIM, BPBRSFIM, BPGDX-SFIM, and DPSO-SFIM in terms of the accuracy derived from this large area. DPSO-SFIM obtained the optimal sub-pixel inundation mapping results among the five SFIM methods in the large area. It exhibits the highest OA, Kappa, APA and AUA. DPSO-SFIM is suitable for both small and large areas because DPSO-SFIM looks for the most likely distribution of sub-pixels within each mixed pixel and

DPSO-SFIM finds the optimal inundation distribution of subpixels by a swarm of particles through iteration. Therefore, iteration times (ITs) and swarm size N are important parameters for DPSO-SFIM. The sensitivity analysis of DPSO-SFIM in relation to ITs and N was carried out to evaluate their role in the performance of DPSO-SFIM. The Murray-Darling Basin and the Changjiang River Basin Landsat ETM + images were tested using different parameter values.

4. Sensitivity analysis of DPSO-SFIM

4.1. Sensitivity in relation to iterative times To analyze the DPSO-SFIM sensitivity in relation to ITs, other parameters were kept the same as those in the case study. The values of ITs were assumed as follows: ITs ¼ f5; 10; 15; 20; 25; 30; 35; 40; 45; 50g. Sensitivity of DPSO-SFIM in relation to ITs is shown in Table 4 and Fig. 8. It can be revealed

83.0

0.650

Australia China

Australia China

0.630 0.610

81.0

Kappa

OA (%)

82.0

80.0

0.590 0.570

79.0 78.0

0.550 0

5

10

15

20

25

0.530

30

N

0

5

10

25

30

20

25

30

(b)

82.0

82.0

Australia China

81.0

Australia China

81.0

80.0

AUA (%)

APA (%)

20

N

(a)

79.0 78.0 77.0 76.0

15

80.0 79.0 78.0 77.0

0

5

10

15

N

(c)

20

25

30

76.0

0

5

10

15

N

(d)

Fig. 9. Sensitivity of DPSO-SFIM in relation to swarm size. (a) Sensitivity of OA. (b) Sensitivity of Kappa. (c) Sensitivity of APA. (d) Sensitivity of AUA.

20

L. Li et al. / ISPRS Journal of Photogrammetry and Remote Sensing 101 (2015) 10–21

that the higher the value of ITs, the higher the value of OA. That is because the particles in the swarm get closer to the optimal solution through the iterative optimization process. For the Murray-Darling Basin, the value of OA increases from 78.0% to 82.3% when the value of ITs is from 5 to 50. We can also see that the value of OA has a relatively large increase when the value of ITs is relatively low. For the Murray-Darling Basin, the value of OA increases from 78.0% to 80.7% when the value of ITs is from 5 to 15. The values of Kappa, APA and AUA have the similar increasing trend as that of OA. Similar trends were derived from the Changjiang River Basin.

4.2. Sensitivity in relation to swarm size To analyze the DPSO-SFIM sensitivity in relation to swarm size N, other parameters were kept the same as those in the case study. The values of N were assumed as follows: N ¼ f5; 10; 15; 20; 25; 30g. Sensitivity of DPSO-SFIM in relation to N is shown in Table 5 and Fig. 9. It can be observed that the higher the value of N, the higher the value of OA. That is because the swarm size N represents the diversity of the swarm and determines the number of particles used to search for the optimal solution. For the Murray-Darling Basin, the value of OA increases from 79.8% to 82.1% when the value of N is from 5 to 30. We can also see that the value of OA has a relatively large increase when the value of N is relatively low. For the Murray-Darling Basin, the value of OA increases from 79.8% to 81.4% when the value of N is from 5 to 15. The values of Kappa, APA and AUA have the similar increasing trend as that of OA. Similar trends were derived from the Changjiang River Basin.

5. Conclusions This study proposed a new method called DPSO-SFIM to achieve an improved accuracy in mapping inundation at a sub-pixel scale from multispectral remotely sensed images. The evaluation criterion for sub-pixel inundation mapping was formulated and sub-pixel inundation mapping was transformed into a combined optimization issue, which allocated inundation to the sub-pixels in mixed pixels while maximizing the FISDI. The DPSO-SFIM algorithm was developed, including particle discrete encoding, fitness function designing and swarm search strategy. We assessed the accuracy of DPSO-SFIM in mapping inundation at a sub-pixel scale using Landsat ETM + images from the study areas in Australia and China. Compared with traditional DESDSFIM, SAM-SFIM, BPBR-SFIM, and BPGDX-SFIM methods, DPSOSFIM consistently achieves more accurate sub-pixel mapping results in terms of visual and quantitative evaluations. DPSO-SFIM outperforms the four traditional SFIM methods, which can be more significantly observed in the Australian case study. More inundation meanders and confluences exist in the Murray-Darling Basin, so there are much more possible distributions of sub-pixels in each mixed pixel. Therefore it is difficult for the four traditional methods to obtain the optimal distribution in this complex situation. DPSO-SFIM is suitable for both small and large areas because DPSO-SFIM looks for the most likely distribution of sub-pixels within each mixed pixel and obtains the results for the whole fraction images in a pixel-by-pixel fashion regardless of the total number of pixels searched. The sensitivity analysis of DPSO-SFIM in relation to iteration times and swarm size was carried out to evaluate the performances of DPSO-SFIM. Within the selected parameter range in this study, the higher the values of iteration times and swarm size, the higher the values of sub-pixel mapping accuracy, because the particles in the swarm get closer to the optimal solution through the iterative optimization process,

and the swarm size determines the particle quantity and swarm diversity in searching the optimal solution. The study of inundation has important significance to human life and social economy. It is hoped that the results of this study will enhance the application of median-low resolution remotely sensed images in inundation detection and mapping, and ultimately benefit the ecological and environmental studies of river basins.

Acknowledgements This paper was supported by the National Natural Science Foundation of China (Grant No. 41371343 and Grant No. 41001255) and the scholarship provided by the China Scholarship Council. The authors would like to thank the Editor-in-Chief, the Associate Editor, and anonymous reviewers for the helpful comments and suggestions that improved this paper. The authors also wish to thank their colleagues Susan Cuddy and Catherine Ticehurst for their helpful discussions and constructive suggestions.

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