Novel Clustering Schemes for Full and Compact Polarimetric SAR Data: A Case Study for Rice Phenology Characterization

Information on rice phenological stages from Synthetic Aperture Radar (SAR) images is of prime interest for in-season monitoring. Often, prior in-situ measurements of phenology are not available. In such situations, unsupervised clustering of SAR images might help in discriminating phenological stages of a crop throughout its growing period. Among the existing unsupervised clustering techniques using full-polarimetric (FP) SAR images, the eigenvalue-eigenvector based roll-invariant scattering-type parameter, and the scattering entropy parameter are widely used in the literature. In this study, we utilize a unique target scattering-type parameter, which jointly uses the Barakat degree of polarization and the elements of the polarimetric coherency matrix. In particular, the degree of polarization attributes to scattering randomness from a target. The scattering randomness in crops increases with advancements in its growth stages due to the development of branches and foliage. Hence, the degree of polarization varies with changes in the crop growth stages. Besides, the elements of the coherency matrices are directly related to the crop geometry as well as soil and crop water content. There-fore, this complementarity information captures the scattering randomness at each crop growth stage while taking into account diverse crop morphological characteristics. Likewise, we also utilize an equivalent parameter proposed for compact-polarimetric (CP) SAR data. These scattering-type parameters are analogous to the Cloude-Pottier’s parameter for FP SAR data and the ellipticity parameter for CP SAR data. Besides this, we also introduce new clustering schemes for both FP and CP SAR data for segmenting diverse scattering mechanisms across the phenological stages of rice. In this study, we use the RADARSAT-2 FP and simulated CP SAR data acquired over the Indian test site of Vijayawada under the Joint Experiment for Crop Assessment and Monitoring (JECAM) initiative. The temporal analysis of the scattering-type parameters and the new clustering schemes help us to investigate detailed scattering characteristics from rice across its phenological stages.


169
A total number of 14 in-situ field measurements were considered in this 170 study. We measured soil moisture at each field in two sampling locations, 171 arranged in two parallel transects along the row direction. The separation 172 between each transect was ≈ 80 m. We measured the pointwise soil moisture 173 using theta-probe. Nevertheless, the soil underlying the rice crops was satu-174 rated during the majority of the growth stages due to irrigation and rainfall 175 events. We measured vegetation samples at two points of each field due to 176 the spatial heterogeneity within the field, which is due to the irregular growth 177 pattern of rice. Vegetation sampling included the measurement of PAI, plant height, and phenology through non-destructive methods. The PAI is mea-sured using the notion of hemispherical digital photography. During each 180 measurement day, we took ten photos along two transects which are sepa-181 rated by 2m in each sampling point, using a wide-angle lens mounted on a 182 digital camera. All images were post-processed using the CanEYE software 183 to provide an estimate of PAI. The overall phenology of rice is usually ex-184 pressed with three major stages: vegetative, reproductive, and mature (or 185 ripening). The statistics of bio-physical and soil parameters are given in 186   Table 1.
187 Figure 1: The Google Earth image of the JECAM test site over Vijayawada, India is overlaid with a Pauli RGB image obtained from SAR data acquired on 29 Jul 2018. The samples from region 1 and 2 are used for temporal analysis and clustering. The distribution of five in-situ data points is shown in the sampling unit of region 1 and region 2.
3. Satellite data pre-processing 188 We acquired RADARSAT-2 images in Fine Quad (FQ) wide mode from 189 July to November 2018 over the test site as shown in Table 2. We then 190 apply a multi-look factor of 2 × 3 pixels in the range and azimuth directions,      To reduce the speckle effect in S, the multi-looked Hermitian positive semi-definite 3×3 coherency matrix T is obtained from the averaged outer product of the target vector k P (derived using the Pauli basis matrix, Ψ P ) with its conjugate (Lee and Pottier, 2009).

191
where N denotes the square window size for spatial averaging and Tr is the 219 sum of the diagonal elements of the matrix. two extreme cases, the EM wave is said to be partially polarized, 0 < m < 1.

228
Barakat (Barakat, 1977) provided an expression of m for the N × N 229 coherency matrix. This expression is used in this study to obtain the degree 230 of polarization m FP from the 3 × 3 coherency matrix T for FP SAR data as, where | · | is the determinant of a matrix. where, We define: where γ FP can be related to the average roll-invariant scattering-type pa- to compare the two parameters within the same range, they are suitably 248 modified as, α = 90 • − 2α and θ FP = 2γ FP , which is given as, It can be noticed from equation (6)

254
The eigen-decomposition of T can be expressed as, where Σ is the 3 × 3 diagonal matrix with non-negative elements, λ 1 ≥ λ 2 ≥ 256 λ 3 ≥ 0, which are the eigenvalues of T. The pseudo probabilities, p i obtained 257 from the eigenvalues are defined as, However, in this study, we use the quantity H FP = 1 − H FP to suitably 261 represent the clusters in the H FP /θ FP polar plane.

262
The feasible regions for H FP /θ FP clustering plane can be represented by 263 Figure 2: The H FP /θ FP clustering plane displayed in polar plot. Curve I and Curve II represent the azimuthal symmetry lines. No scattering mechanisms exist in the dashed portion of the plane. Two half-circles at 0.5 and 0.7 divide the H F P into high, medium and low entropy regions while −90 • to −10 • represents even bounce scattering, −10 • to 20 • represents multiple bounce scattering and 20 • to 90 • represents odd bounce scattering.
two bounding curves, Curve I and Curve II as shown in Figure 2.
The CP mode measures a projection of the 2 × 2 complex scattering 266 matrix S as, where the subscript C can be either the left-hand circular (L) transmit with 268 a + sign or the right-hand circular (R) transmit with a − sign. The 2 × 2 269 covariance matrix is then obtained from the elements of the scattering vector 270 as, For CP-SAR data, the 4 × 1 Stokes vector g can be written in terms of 272 the elements of the 2 × 2 covariance matrix C 2 as, where ± corresponds to left and right circular polarization respectively. where the total power Span is defined as, Similar to FP, we define: where γ CP can be analogously related to the polarization ellipticity parameter However, in order to compare, the two parameters within 286 the same range, they are suitably scaled as, χ = −2χ and θ CP = 2γ CP which 287 is given as, Similar to θ FP , it can be noticed from (18) that for a pure dihedral scat-

294
The expression for the Barakat degree of polarization for the compact-295 polarimetric case is given as, The eigen-decomposition of C 2 can be expressed as, where Σ is a 2 × 2 diagonal matrix with non-negetive elements, λ 1 ≥ λ 2 ≥ 0, 298 which are the eigenvalues of C 2 . The pseudo probabilities, p i obtained from 299 the eigenvalues are defined as, which are then used to define the scattering entropy (H CP ) for CP-SAR data 301 as,       On 22 Aug, most of the rice fields were at the advanced tillering stage.

395
Therefore, high even-bounce multiple scattering is prominent in these fields. Due to this reason, for high cross-pol components, the difference between SC 410 and OC powers becomes negligible, and θ CP exhibits high diffused scattering.

411
As stated earlier, on 5 Jul, most of the fields were empty. Hence, like θ FP , 412 θ CP also exhibits a high amount of odd-bounce scattering in those fields.

413
On 29 Jul, a notable change in the response of θ FP and θ CP for a few 414 fields must be due to different sowing date. During this period, rice was

449
In Figure 9 and Figure 10, the θ FP and θ CP values are majorly within the 450 odd-bounce scattering region on 05 Jul due to the nearly smooth soil surface 451 condition. Hence, dense clusters are seen in Z10, Z11, and Z12, which corre-452 sponds respectively to low entropy even-bounce scattering, medium entropy even-bounce scattering, and high entropy even-bounce scattering regions.

454
Moreover, a few data points lying in region Z3 is due to the early trans-  The density of the data points in Z6 and Z9 zones has also increased 476 on 29 Jul, while rice transplantation was undergoing in some other fields.

477
Therefore, a moderately high accumulation of data points can also be seen in Z3 (Figure 9 and Figure 10). Moreover, the previously sown rice fields 479 had achieved a higher vegetative stage due to which the areal coverage by However, the orientation, shape, and size of each crop were not the same, 503 and hence there was also a possibility of rough soil surface stretching out 504 from the water surface. Therefore, these phenomena could induce high ran-505 domness in the scattered EM wave. Besides, similar to 29 Jul, some fields 506 progressed to a higher vegetative stage due to which a cluster can be seen in 507 Z2. Furthermore, fields that reached the booting stage display even-bounce 508 multiple scattering with medium entropy characteristics (Z5). However, the 509 even-bounce scattering mechanism is evident throughout the tillering stage.

510
Hence, the even bounce scattering power had decreased by 11.19 %, while 511 multiple bounce scattering had marginally increased by 3.67 %. towards the Z2 and Z5 zones indicates an even-bounce scattering mechanism 520 of the scattered EM wave. Such a response might be due to the extinction of the vertical polarization due to the canopy structure. Also, the amount of 522 odd-bounce scattering reduced during this period, and rice foliage generated 523 moderate odd-bounce multiple scattering due to which dense cluster in the 524 Z8 zone is noticed in Figure 9 and Figure 10.  It is noteworthy that the differences in the characterization capability be-553 tween FP and CP SAR data depends on the type and geometry of the targets.

554
Moreover, the spatial heterogeneity induces the changes in the intensity of 555 the co-pol and cross-pol components. Hence, a change in the scattered EM 556 wave is sometimes evident between FP and CP SAR data.

576
During the initial period of the growing season, both θ FP and θ CP show 577 odd-bounce scattering due to bare ground conditions. Subsequently, changes 578 in the scattering-type from those fields were noticed depending on the sowing 579 time, and morphological characteristics of rice. Changes in the scattering-580 type from odd-bounce to even-bounce at the beginning of the tillering stage 581 from 29 Jul is adequately captured by θ FP , and θ CP values. 582 We observed the saturation in θ FP and θ CP values during the advanced 583 reproductive stage, which was due to weak alteration of crop canopy geome-584 try. Later, close to the senescence stage, the response of θ FP and θ CP became 585 random due to the complex distribution of crop canopy and partial harvest 586 condition. 587 We have introduced novel new clustering schemes, H FP /θ FP and H CP /θ CP