diff --git a/help/Functions_description.md b/help/Functions_description.md index 0fdbe18..f6b3738 100644 --- a/help/Functions_description.md +++ b/help/Functions_description.md @@ -247,7 +247,7 @@ Compact-pol functionalities require the SAR data in the form of 2x2 covariance m - * Compact-pol Radar Vegetation Index (CpRVI) This functionality computes the compact-pol radar vegetation index for compact polarimetric SAR data. The required input and the computed output are as follows: + * CpRVI (Compact-pol Radar Vegetation Index): This functionality computes the compact-pol radar vegetation index for compact polarimetric SAR data. The required input and the computed output are as follows: ````python input : input_C2_folder, window_size @@ -317,7 +317,7 @@ Compact-pol functionalities require the SAR data in the form of 2x2 covariance m - * DOP (Degree of Polarization) This functionality computes the degree of polarization for compact polarimetric SAR data. The required input and the computed output are as follows: + * DOP (Degree of Polarization): This functionality computes the degree of polarization for compact polarimetric SAR data. The required input and the computed output are as follows: ````python @@ -383,58 +383,78 @@ Dual-pol functionalities require the SAR data in the form of 2x2 covariance matr
- * Dual-pol Radar Vegetation Index (DpRVI) + * DpRVI (Dual-pol Radar Vegetation Index): This functionality computes the dual polarimetric radar vegetation index for dual polarimetric (HH | HV), (VV | VH) SAR data. The required input and the computed output are as follows: + + ````python + input : input_C2_folder, window_size + output: DpRVI.bin + ```` + + The formulation of DpRVI is as follows: +
- ![grvi](https://latex.codecogs.com/svg.latex?\Large&space;\text{DpRVI}=1-\Big(\frac{\lambda_1}{\lambda_1+\lambda_2}\Big)\sqrt{1-\frac{4\times\text{det([C2])}}{\text{(Trace[C2])}^2}}) + ![dprvi](https://latex.codecogs.com/svg.latex?\Large&space;\text{DpRVI}=1-\Big(\frac{\lambda_1}{\lambda_1+\lambda_2}\Big)\sqrt{1-\frac{4\times\text{det([C2])}}{\text{(Trace[C2])}^2}})
-where, C2 is co-variance matrix, and λ1 and λ2 are the eigen values of C2 matrix in descending order. + where, C2 is co-variance matrix, and λ1 and λ2 are the eigen values of C2 matrix in descending order (λ1 > λ2). Further details on DpRVI can be obtained from [[5]](#5) -````python - input : input_C2_folder, window_size - output: DpRVI.bin -```` - * Radar Vegetation Index (RVIdp) -
-![grvi](https://latex.codecogs.com/svg.latex?\Large&space;\text{RVI}_{dp}=\frac{4\sigma^\circ_{\text{XY}}}{\sigma^\circ_{\text{XX}}+\sigma^\circ_{\text{XY}}}) - -
+ * RVI (Radar Vegetation Index): This functionality computes the radar vegetation index for dual polarimetric (HH | HV), (VV | VH) SAR data. The required input and the computed output are as follows: + + ````python + input : input_c2_folder, window_size + output: RVI_dp.bin + ```` + The formulatin of RVI is as follows: -````python - input : input_c2_folder, window_size - output: RVI_dp.bin -```` +
- * Polarimetric Radar Vegetation Index (PRVIdp) -
+ ![rvidp](https://latex.codecogs.com/svg.latex?\Large&space;\text{RVI}_{dp}=\frac{4\sigma^\circ_{\text{XY}}}{\sigma^\circ_{\text{XX}}+\sigma^\circ_{\text{XY}}}) + +
+ + where, σoXX and σoXY co- and cross-pol backscatter intensities. -![grvi](https://latex.codecogs.com/svg.latex?\Large&space;\text{PRVI}_{dp}=(1-\text{DOP}_{dp})\sigma^\circ_{\text{XY}}) + * PRVI (Polarimetric Radar Vegetation Index): This functionality computes the polarimetric radar vegetation index for dual polarimetric (HH | HV), (VV | VH) SAR data. The required input and the computed output are as follows: + + ````python + input : input_c2_folder, window_size + output: PRVI_dp.bin + ```` -
+ The formulation of PRVI is as follows: +
+
+ + ![prvidp](https://latex.codecogs.com/svg.latex?\Large&space;\text{PRVI}_{dp}=\Big(1-\sqrt{1-\frac{4\times\text{det([C2])}}{\text{(Trace[C2])}^2}}\Big)\sigma^\circ_{\text{XY}}) + +
-````python - input : input_c2_folder, window_size - output: PRVI_dp.bin -```` - * Degree of Polarization (DOPdp) -
-![grvi](https://latex.codecogs.com/svg.latex?\Large&space;\text{DOP}_{dp}=\sqrt{1-\frac{4\times\text{det([C2])}}{\text{(Trace[C2])}^2}}) + + * DOP (Degree of Polarization): This functionality computes the 2D Barakat degree of polarization for dual polarimetric (HH | HV), (VV | VH) SAR data. The required input and the computed output are as follows: -
+ ````python + input : input_c2_folder, window_size + output: dop_dp.bin + ```` + +
+ + ![dopdp](https://latex.codecogs.com/svg.latex?\Large&space;\text{DOP}_{dp}=\sqrt{1-\frac{4\times\text{det([C2])}}{\text{(Trace[C2])}^2}}) + +
+ + Further details on the Barakat Degree of polarization can be found in [[10]](#10) + -````python - input : input_c2_folder, window_size - output: dop_dp.bin -```` ## References