## Materials and Methods
### Experimental Design
Moreover, using fewer images can reduce the cost and computational burden of image processing and classification. Therefore, it is also worth studying the optimal combination of SAR images that could gain an acceptable classification accuracy. In addition, further investigating optimal combination of both factors, i.e., polarimetric observables and SAR images. will be an interesting topic. Recently, a forward selection procedure was proposed for searching the optimal combination of SAR images that make the best tradeoff between classification and number of images [7]. In this procedure, the SAR images for classification were gradually selected and included in the image set (starting with an empty image set) with an increment step of one acquisition date. The concept of the forward selection procedure can be expanded in search of the optimal combination of polarimetric observables for crop classification, i.e., forward feature selection. In detail, the groups of polarimetric observables for classification were gradually selected and included in the feature set (starting with an empty feature set) with an increment of one group, and the feature combination with the best classification accuracy was chosen at each step. Therefore, we first conducted RF classifications with single groups of polarimetric observables and compared their performances. Then, the classification experiments were focused on investigating optimal combinations. A forward selection procedure was applied for searching the optimal combination of polarimetric observables, SAR images or both aspects. The experiments were designed to make the best tradeoff between classification accuracy and number of parameters, image acquisitions or both factors. First, all SAR images were selected in RF classifications by the forward feature selection procedure. For instance, RF classifications with single groups of polarimetric observables were tested in the first step. The optimal combination of polarimetric observables was obtained. Then, all polarimetric observables were selected in RF classifications by the forward image selection procedure. For instance, RF classifications using single images (one acquisition date) were tested in the first step. Finally, RF classifications were carried out again using the optimal combination of polarimetric observables by the forward image selection procedure. Classification performance was affected by the training and testing samples, including both the number of samples and their distribution. To investigate the impact of the training and testing samples on the overall classification performance, the classification tests for the optimal combination SAR image produced by a forward image selection procedure using all polarimetric observables were carried out again by swapping the training and testing samples in Table 2. Moreover, based on the unique capability of the RF method, the variable importance contributing to crop classification was also quantified. The RF classification with all polarimetric observables using all RADARSAT-2 images was selected to investigate the relative importance of the input variables for crop classification.