## 3 Methodology
### Object Extraction  
Pixel-based classification is commonly adopted when moderate-to-coarse resolution data is used but rarely adopted when finer resolution data is used due to the salt-and-pepper effect resulting from increased pixel heterogeneity. To alleviate such effect, super-pixel or object-based classification can be adopted [32; 33; 34; 35], in which basic classification units approximate parcels or fields. Finding edges of a field using single-date imagery is challenging when different crop types have similar spectral and structural properties at certain stages of their phenological growth cycle. This challenge is compounded when a single crop is grown on adjacent fields. Therefore, it is necessary to use multiple images throughout the year to accurately detect spatial transitions (edges) between different crop types as well as crops of the same type. Edges in imagery can be defined as a sharp change or discontinuity in the gray-scale values. Various edge detectors have been proposed, such as Sobel, Prewitt, Robert, Scharr, and Canny, to generate the edge layer, which can be described as a gray-scale image that represents object edges. High gray values indicate a sharp discontinuity with adjacent pixels. The Canny operator was used in this study due to its superior performance compared with other edge detection algorithms [24]. We applied the Canny edge operator to image grids from Section 2.2 to extract the edge layers (Figure 3). Figure 2: Schematic diagram of the processing chain for the proposed algorithm. The first three modules are implemented in GEE while the fourth module, validation, is implemented on a local computer. Single edge layers have false edges as caused by noise and true edges from fields. A simple equal weight summation of the edge layers was used to combine the images into single, composite, multi-temporal edge images where false edges were faded and true edges were strengthened (Figure 3). The aggregate gradient edge images were divided into edge pixels and non-edge pixels using a threshold. Edge pixels have greater values than the threshold while non-edge pixels have lesser values. As the number of images used in each grid varies (see Figure 1), the thresholds for each grid can change. Generally, a greater number of superimposed images gives a higher threshold. The threshold is set as the product of the image count and a factor, which is determined from trial-and-error experiments. An appropriate factor should keep the integrity of individual plots (assuming the plot grows the same crop) while dividing different plots. A higher (lower) factor causes over- (under)-segmentation. Figure 4 showcases the procedure of multi-temporal edge detection analysis. The edge layer for each date (Figure 4 column b) is the equal-weight aggregation of four edge layers generated from the red, green, blue, and NIR bands. This example qualitatively illustrates how multi-temporal composites of edge layers capture and accentuate persistent field boundaries. Some faint field boundaries (low intensities) on specific dates become more pronounced as images from various dates are combined. Edge pixels are excluded from subsequent operations and non-edge pixels are retained. These non-edge pixels come from different classes, such as forests, wetlands, built-up areas, and cropland. Although flooding signals in paddy rice transplanting periods give unique characteristics for paddy rice, flooding signals from other land cover types could also exist during the paddy rice transplanting phase, which mainly includes water bodies (e.g., rivers and lakes) and natural wetlands. In addition, some noise could be caused by miscellaneous non-cropland covers, such as natural vegetation and built-up lands due to some unexpected weather effects. The generation of these non-cropland masks helps reduce sporadic commission errors in the resultant paddy rice maps [11]. We generated several masks by refining the rules used in a previous study [11].