Leaf Parameter Estimation Based on Leaf Scale ... - IEEE Xplore

IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 6, NO. 2, APRIL 2013

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Leaf Parameter Estimation Based on Leaf Scale Hyperspectral Imagery Kuniaki Uto, Member, IEEE, and Yukio Kosugi, Member, IEEE

Abstract—Low altitude hyperspectral observation systems provide us with leaf scale optical properties which are not affected by the atmospheric absorption and spectral mixing due to the long distance between the sensors and objects. However, it is difficult to acquire Lambert coefficients as inherent leaf properties because of the shading distribution in leaf scale hyperspectral images. In this paper, we propose an estimation method of Lambert coefficients by making good use of the shading distribution. The surface reflection of a set of leaves is modeled by a combination of dichromatic reflection under direct sunlight and reflection under the shadow of leaves. It is shown that hyperspectral distribution of leaves is composed of three linear clusters, i.e., specular, diffuse and shadowed clusters. Lambert coefficient is derived from the first eigenvector of diffuse cluster. Experimental results show that chlorophyll indices based on the estimated Lambert coefficients are consistent with the growth stages of paddy fields. Index Terms—Dichromatic model, Gaussian mixture model, Lambert coefficient, leaf scale hyperspectral imagery.

I. INTRODUCTION

L

EAF scale hyperspectral properties in the range from visible to near infrared contain useful information related to the leaf-related parameters, e.g., pigment concentrations, water content and leaf mesophyll structure [1]. Chlorophyll content in leaf is highly correlated with nitrogen content which plays an important role in yield and protein content of the crops [2], [3] . Therefore, the appropriate nitrogen fertilizer management based on the accurate estimation of chlorophyll content is indispensable for precision farming [4]. Sugar concentration of some crops, e.g., citrus trees [5] and tomato [6], is increased by appropriate water stress management by means of water content estimation. The leaf scale hyperspectral properties are approximated by models of leaf optical properties [1]. A model of leaf optical properties spectra (PROSPECT) is a radiative transfer model based on scattering parameters, i.e., a spectral refractive index and leaf mesophyll structure value, and absorption parameters, e.g., chlorophyll concentration, water content. The vegetation-related parameters are estimated by the inversion of PROSPECT. On the other hand, spectral vegetation indices

Manuscript received August 31, 2012; revised November 06, 2012; accepted December 14, 2012. Date of publication January 21, 2013; date of current version May 13, 2013. K. Uto is with the Tokyo Institute of Technology, Interdisciplinary Graduate School of Science and Engineering, Midori-ku, Yokohama 226-8502, Japan (corresponding author, e-mail: [email protected]). Y. Kosugi is with Tokyo Institute of Technology, Interdisciplinary Graduate School of Science and Engineering, Midori-ku, Yokohama 226-8502, Japan (e-mail: [email protected]). Digital Object Identifier 10.1109/JSTARS.2012.2236540

based on two or more spectral bands are proposed to estimate pigment contents [7]–[12]. In comparison with close range laboratory observation of leaf surface, the acquisition of leaf scale hyperspectral data from remotely sensed airborne hyperspectral data is difficult because of not only the atmospheric absorption and scattering but also hyperspectral mixing due to the low spatial resolution [13]. Endmember estimations by means of spectral unmixing could provide us with tools to estimate pure optical leaf properties. However, each endmember is generally represented as a single point in the hyperspectral space, whereas detailed subspace structure of the vegetation is needed for the agricultural application. Scattering Arbitrary Inclined Leaves (SAIL) [14]–[17] is a canopy bidirectional reflectance model based on leaf area index (LAI), leaf angle distribution, hot spot parameter, soil reflectance, solar zenith angle, viewing zenith angle, etc. Clevers et al. evaluate the relationship between vegetation indices based on PROSPECT+SAIL (PROSAIL) simulations and the PROSAIL parameters, e.g., chlorophyll and nitrogen contents, as well as the relationship between vegetation indices based on measured spectra and measured chlorophyll and nitrogen contents [18]. The leaf-related parameters estimation based on the inversion of the PROSAIL canopy reflectance model is an ill-posed problem because of the large number of free parameters. In [19], [20], PROSAIL is inverted by means of lookup-table (LUT) approaches to avoid the local minima problem in iterative optimization algorithms. Low altitude hyperspectral observation systems are developed to acquire leaf scale hyperspectral data [21]–[23] by which most of unknown parameters in the remotely sensed airborne hyperspectral data due to the low spatial resolution are identified. However, the spatial distribution of leaf scale hyperspectral image is affected by shading so that the acquisition of consistent optical characteristics is not feasible. In [24], experimental results of the spectral and directional variations of the leaf bidirectional reflectance distribution function (BRDF) are investigated using the dichromatic reflection model. Forward simulations of the leaf scale shading distribution are examined for realistic graphical representation of plants [25], [26]. In [27], the shading distributions based on various leaf angle distribution (LAD) are simulated to confirm the influence of the LAD on the contribution of the specular components of leaf reflectance. However, given the observed shading distribution, inversion methods for retrieval of the leaf model parameters, e.g., inherent optical leaf properties, are not realized. Vigneau et al. [28] estimate nitrogen contents based on leaf scale hyperspectral imageries of wheat obtained by a tractor-mounted hyperspectral image acquisition system. The additive effects, i.e., specular components, and the

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 6, NO. 2, APRIL 2013

multiplicative effects, i.e., diffuse components, are removed by data centering [29] and data normalization [30], respectively. The data preprocessing and nitrogen estimation are based on manually selected isolated leaves in order to avoid environment effects. Therefore, the methodology is not applicable to the shading distribution of a set of leaves. In our previous paper [31], we proposed an estimation method for Lambert coefficients as inherent leaf property by making good use of the shading distribution. The statistical distribution of leaf reflection is approximated by the direct sunlight illumination on hemiellipsoid surface. The Lambert coefficients are estimated by minimizing the Kullback-Leibler divergence between a probability density of measured data and a probability density of a model with free parameters, e.g., Lambert coefficients, specular parameters and hemiellipsoid parameters. Chlorophyll indices derived from the estimated parameters based on hyperspectral images of rice paddies in early tillering stage, i.e., 49–77 days after transplanting, showed consistent relation with the expected order in chlorophyll content. However, the consistency in the relations between the chlorophyll indices and the expected order were collapsed in case of peak tillering stage, i.e., 70–98 days after transplanting. It is expected that the estimation accuracy in peak tillering stage is declined because the distribution of leaf surface reflection is approximated by dichromatic reflection model under direct sunlight, whereas the ratio of leaf area under leaf shadow is not negligible in peak tillering stage because of the increase of leaf area index (LAI). In this paper, we propose an estimation method for Lambert coefficients based on surface reflection model in which the surface reflection of a set of leaves is modeled by a combination of dichromatic reflection under direct sunlight and reflection under the shadow of leaves. II. REFLECTION MODEL OF LEAF SURFACE

Fig. 1. Illustration of parameters under direct sun illumination.

where the superscript denotes transpose, is a Lambert coefficient of leaf surface, is a viewing direction, and is a normal direction of the local leaf surface. is an intensity of transmitted light by volume scattering at wavelength . , and are Fresnel factor, Beckmann distribution function and a geometry attenuation factor [33], [34], [24]. The apparent reflectance vector, , is derived by the ratio of to [31]. is the number of bands.

(3) (4) (5) (6)

A. Dichromatic Reflection Model of Leaf Surface Under Direct Illumination In peak tillering stage before heading stage of rice, the structure of rice canopies are composed of three layers; leaf and tiller layer as the surface layer, stem layer as the second layer, and water and soil layer as the bottom layer [32]. The top of surface layer in peak tillering stage is covered by rice blades, so that the surface reflection under direct illumination is modeled by dichromatic reflection model. Under illumination with sunlight in the open air (Fig. 1), irradiance of white diffuse reflectance, , is modeled by a sum of specular and diffuse components. (1) and are a normal vector of the reflectance standard where and a directional vector of direct illumination. and are intensities of direct and ambient illuminations at wavelength . Irradiance of leaf surface, , is modeled by a sum of specular, diffuse and transmitted lights.

(2)

(7) (8) (9) (10) (11) (12) where and are scalar functions of surface normal and roughness parameter . is a constant bias and the geometry attenuation vector. The Fresnel factor factor are approximately constant because the specular reflection angle of the incidence is small under the condition that the viewing angle is vertical and the directional vector of direct illumination is close to vertical. Equation (3) indicates that, on the assumption that the leaf parameters are homogeneous, the reflectance data of a set of leaves are distributed on two dimensional plane spanned by and in the hyperspectral reflectance space (Fig. 2(a)). Fig. 3(a) shows the distribution of a leaf shading on 2D plane spanned by the first and second principal components based on close-range hyperspectral rice images with spatial resolution of 1 mm at 1 m above the object (data 1 in Table I). The data were

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collected by a linear actuator-mounted hyperspectral array imager containing visible to near-infrared 400–1000 nm, spectral information with spectral resolution of 5 nm and 121 bands, on June 22 in 2010 Tsuruoka, Yamagata, Japan. The high spatial resolution image is observed in order to collect statistically reliable number of data from a leaf. The number of data extracted from the leaf is 487. It is confirmed that specular cluster (highlight reflection) is connected to a narrow part of linear diffuse cluster (matte reflection) [35]. The specular and diffuse clusters are estimated by Gaussian mixture model [36]. Gaussian mixture model is defined in (13) is a Gaussian distribution function of with where and a variance-covariance matrix . is a weight a mean of , and is the number of mixture components, i.e., . The probability density contours of the Gaussian mixture model based on two components are shown in Fig. 3(b), in which the two clusters are successfully classified. B. Reflection Model of Leaf Surface Under the Shadow of Leaves

Fig. 2. (a) Vectors in hyperspectral space, (b) Clusters in hyperspectral space.

The apparent reflectance of leaves under the shadow of leaves is not approximated by (3) because the incident light is not composed of the direct incident . The incident illumination of the shadowed leaves is approximated by a sum of the ambient illumination and isotropic scattered flux caused by multiple scattering based on leaf surface reflection and transmission (Fig. 4). Irradiance of the shadowed leaves is modeled by a sum of the reflection of ambient illumination and isotropic scattered flux, and the transmission of the scattered flux,

(14) (15) is an intensity of isotropic scattered flux at wavewhere is a transmittance of leaves, is a three length , dimensional direction of the ambient illumination based on a zenith angle, , and a azimuth angle, . is an ambient illumination. Apparent reflectances of shadowed leaves are defined in (16).

Fig. 3. (a) Distribution of a leaf shading on 2D space spanned by the first and second principal components, (b) Contour plots of probability density distributions of Gaussian mixture model with two components.

(16) (17) (18)

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 6, NO. 2, APRIL 2013

TABLE I OBSERVATION CONDITION OF A CLOSE-RANGE HYPERSPECTRAL IMAGE

Fig. 4. Illustration of parameters of leaves under the shadow.

(19) (20)

Fig. 5. Simulated fractions of direct and ambient irradiance based on SBDART [37].

(21)

TABLE II SIMULATION CONDITIONS OF SBDART

(22) (23) (24) is decomposed to by assuming the independence between and in . Equation (16) indicates that the reflectance data of shadowed leaves are distributed on one dimensional vector in (21) (Fig. 2(a)). The value of is estimated by the simulation with Santa Barbara Discrete ordinate radiative transfer Atmospheric Radiative Transfer (SBDART) [37] Matlab code [38]. Simulated fractions of direct irradiance and ambient irradiance based on cloudless condition ( ) are shown in Fig. 5. The simulation conditions are listed in Table II. The fraction is higher at shorter wavelengths because the ambient illumination is caused by diffuse sky radiation by Rayleigh scattering. In (16),

III. LEAF PARAMETER ESTIMATION A. Leaf Parameter Estimation Based on Dichromatic Reflection Model Under Direct Illumination In our previous work [31], a virtual cumulative surface model of a set of rice blades under direct illumination is modeled by a hemiellipsoid. By assuming the horizontal homogeneity, the shape of the hemiellipsoid is dependent on one scalar parameter . Under the given observation conditions of the viewing direction and the direction of direct illumination, unknown model

parameters, e.g., , Lambert parameters, Fresnel factor, Beckmann distribution function, Geometry attenuation factor, roughness parameter, are retrieved by fitting the probability density of simulated vertical distribution of apparent reflectance to the observed data in hyperspectral apparent reflectance space. The parameters are optimized in 2D linear subspace spanned by the first and second principal components on the assumption that the reflectance data of a set of rice blades are distributed on two dimensional space as shown in Fig. 2(a). The optimal parameter are estimated in (25) by a lookup-table approach subject to fixed lower-and upperbound constraints of parameters. Note that is a Kullback-Leibler divergence [39] between probability densities and , is a probability density of measured data, and is a probability density of a model with free parameters, e.g., Lambert coefficients, specular parameters and hemiellipsoid parameters. B. Classification of a Set of Leaves The methodology shown in the Section III-A is computationally expensive; besides the model is incomplete because

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TABLE III OBSERVATION CONDITIONS

the reflection under the shadow of leaves is not embedded. In Section II, it is shown that hyperspectral distribution of a set of leaves is composed of three clusters, i.e., specular, diffuse and shadowed clusters (Fig. 2(b)). In this section, we propose a new method in which the clusters are classified based on Gaussian mixture model of three components, i.e., in (13), by assuming linearities of the cluster structures as shown in Fig. 2(b). The estimated clusters are labeled in order of averaged reflectance levels defined in

where ( ) is a fraction value based on SBDART. The estimated fraction of ambient illumination, , defined in (20) is defined by (31) identical matrix. where is a Estimated Lambert coefficients, and

, are derived by (32) (33)

(26) , 2, 3), is a set of data indices corresponding where , ( to cluster , is an apparent reflectance of data index and wavelength , is the number of data in and is an averaged reflectance level. Clusters , and , defined in (27) are labeled as specular, diffuse and shadowed clusters, respectively, because specular, diffuse and shadowed clusters are corresponding to highlight, shading and dark regions. C. Leaf Parameter Estimation

IV. EXPERIMENTAL RESULTS A. Hyperspectral Images In 2007, hyperspectral paddy images with different days after transplanting, data from 2 to 5 in Table III, were collected by a crane-mounted hyperspectral data acquisition system (spectral range: 400-1000 nm, spectral resolution: 5 nm, bands: 121) [21] on August 7 in Ohsaki, Miyagi, Japan. The spatial resolution of the crane-mounted system is 5 mm at 5.8 m above ground. The swash width is approximately 2.5 m. Hyperspectral images of 200 200 pixel areas, i.e., 1 , are extracted for analysis. B. Leaf Cluster Extraction

By assuming the linear structure of the estimated diffuse and shadowed clusters, it is expected that the first eigenvectors of the clusters corresponds to and . The leaf parameter estimation method is formulated as follows. 1) Leaf Parameter Estimation Method: 1) Extraction of a data set of apparent reflectance of vegetation area, [40], from hyperspectral imagery. 2) Gaussian mixture modeling based on the extracted data set. 3) Labeling of the clusters in accordance with (27), i.e., cluster : specular, : diffuse, : shadowed. 4) Extraction of the first eigenvectors of ( , 3) in and are the hyperspectral space. Estimation of defined in (28) (29) The fraction of direct illumination, , defined in (6) is estimated by SBDART (Fig. 5). The estimation is defined by (30)

Classification results based on data 2 in Table III with spatial resolution of 5 mm/pixel are shown in Fig. 6. Fig. 6(a) is a grayscale image converted from a color image (R: 680 nm, G: 550 nm, B: 450 nm) of data 2. Regions corresponding to specular, diffuse and shadowed clusters are extracted in Fig. 6(b)–(d). Averaged reflectances are shown in Fig. 7. Fig. 8 shows distributions of the classified three clusters on 2D space spanned by the first and second principal components. It is confirmed that the three clusters on 3D space spanned by , and are not separable on 2D space. Normalized spectral profiles of estimated , , and derived by (32), (33), (28) and (29) are plotted on Fig. 9. , and show typical spectral characteristics of Lambert parameter of the BRDF model, i.e., the maximum leaf reflection in green (around 550 nm) domain, minimum reflection in red (around 680 nm) domain, and a high plateau in near-infrared domain, whereas the plateau feature in near-infrared domain is not affirmed in [24]. It is expected that the first eigenvector of the shadowed cluster is not approximated by because in (23) is not spatially homogein (32) is selected as the estimation of neous. Consequently, Lambert coefficients in this paper.

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Fig. 8. Distributions of the classified three clusters on 2D space spanned by the first and second principal components.

Fig. 6. (a) A grayscale image of rice paddy No. 2, (b) Specular cluster, (c) Diffuse cluster, and (d) Shadowed cluster.

Fig. 9. Normalized spectral profiles of

,

,

,

in data 2.

TABLE IV GROWING STAGE.

Fig. 7. Averaged reflectances of specular, diffuse and shadowed clusters in data 2.

C. Leaf Parameter Extraction SPAD readings collected by transparent leave-color monitoring device SPAD (Soil and Plant Analyzer Development) are linearly correlated with the chlorophyll contents [41], so that the relative chlorophyll concentration index is widely used for nitrogen management of rice in Japan. The planting dates, heading dates and observation days of the observation targets (data from 2 to 5 in Table III) are listed in Table IV. At early stage of rice growth, i.e., 0 to 30 days after transplanting, the steady increase in SPAD chlorophyll reading is observed. Subsequently, the trend reverses due to the decrease in nitrogen content in soil

[42], [43]. Therefore, on the observation date 7 August 2007, consistent relation between chlorophyll contents in (34) is a chlorophyll content of data in Table III. are satisfied. Ground truth data of chlorophyll contents in the fields from 2 to 5 in Table III and Table IV are collected by SPAD on 7 August 2007. Ten readings are collected for each field. A box plot of the ground truth data distributions are shown in Fig. 10. The upper and lower edges of the box are 75th and 25th percentiles of the ten data. The line in the box is the 50th percentile, median, of the data. The upper and lower edges of the whiskers

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Fig. 10. Distribution of SPAD readings on 7 August 2007.

Fig. 11. Normalized spectral profiles of

.

Fig. 12. (a) Distribution of

are the maximum and minimum of the data. The inconsistency between the relation (34) and the relation in Fig. 10 suggest that the statistical SPAD values are biased by lack of sufficient number of samples. Fig. 11 shows normalized spectral profiles of the estimation based on four rice paddy images in Table III and Table IV. Fig. 12(a) and (b) are the distributions of chlorophyll content indices and [7] derived from averaged spectra of 1000 vegetation points (dotted line), estimation by the threshold-based specular component reduction (alternate long and short dash line) [44], estimation by hemiellipsoid model (bold dashed line) [31], and estimation by the proposed method (bold solid line, Fig. 11). (35) (36) where , and are wavelength ranges 520–585 nm, 695–710 nm and 800–850 nm respectively. The orders of estimations based on the estimation s in Fig. 12(a), (b) are consistent with the relation (34), whereas the consistency in order of SPAD readings (Fig. 10), averaged spectra, estimation by the

, (b) Distribution of

.

threshold-based specular component reduction, and the hemiellipsoid model are failed. V. CONCLUSION In this paper, a new estimation method for Lambert coefficients is proposed by making good use of shading distribution in leaf scale hyperspectral images of vegetation. It is shown that shading distribution in hyperspectral space is composed of three linear clusters, i.e., specular, diffuse and shadowed clusters, by a combination model of dichromatic reflection under direct sunlight and reflection under the shadow of leaves. The computational cost of the proposed method is relatively low in comparison with previously proposed method [31] in which leaf-related parameters are derived by the inverse optimization based on the lookup-table approach, whereas the Lambert coefficient estimation in the new method is based on Gaussian mixture model. The experimental results show that the chlorophyll indices derived from estimated Lambert coefficient based on proposed method are consistent with the growth stages of paddy fields. Although the proposed method is aiming at the accurate estimation of leaf scale optical properties for the appropriate management in precision farming, it is expected the method provides practical means for model verification of other physical

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING, VOL. 6, NO. 2, APRIL 2013

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UTO AND KOSUGI: LEAF PARAMETER ESTIMATION BASED ON LEAF SCALE HYPERSPECTRAL IMAGERY

Kuniaki Uto received the B.S., M.S. and Dr. Eng. degrees from the Tokyo Institute of Technology, Tokyo, Japan, in 1995, 1997 and 1999, respectively. He is currently an Assistant Professor with the Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology. His current research focuses on multi- and hyper-spectral remote sensing and the development of optical sensing system.

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Yukio Kosugi (S’69–M’75) received the M.S. and Dr.Eng. degrees from the Tokyo Institute of Technology, Tokyo, Japan, in 1972 and 1975, respectively, both in electronics. He is currently a professor at the Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology. His research interests include information processing in the nervous system and neural-network aided image processing in remote sensing and biomedical fields.