# Automatically Extracted Antarctic Coastline Using Remotely-Sensed Data: An Update
## 3 Method
### The Automated Edge Detection Method  
Three sub-steps were required here: image smoothing, image gradient calculations and selection of threshold to identify edge pixels. The image smoothing step deals with bad strips commonly found in the Landsat-7 images and speckle noise common in radar data. Therefore, a smoothing filter was applied to suppress noise. Practical experiences have shown that the Gaussian filter can provide an acceptable compromise between noise immunity and accurate edge detection [23]. The larger the size of the kernel, the lower the detector's sensitivity to noise. In order to maintain a good balance, we chose a kernel size of 5 and the standard deviation of 1.4. In the image gradient calculations step, four filters were used to calculate image gradients along the horizontal, vertical, and the two diagonal directions, centered at each pixel in the image. This produced gradients in eight cardinal and ordinal directions at each pixel (\(0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\), \(135^{\circ}\), \(180^{\circ}\), \(225^{\circ}\), \(270^{\circ}\), \(315^{\circ}\)). The gradient was calculated using the finite difference of the first-order partial derivative. The maximum of the eight gradients was selected to represent the edge strength, and the direction associated with this represented the direction perpendicular to the edge, which usually coincides with the highest gradient. The pixel was then identified as a possible edge pixel if the edge strength (gradient magnitude) was higher than a selected threshold. However, if we base the definition of the edge pixel on a single threshold of gradient values applied to all pixels, then the resulting edge may likely be blurred, noisy, and disconnected. In the threshold selection step, to identify the potential edge pixel, we followed the Canny algorithm again but with a modification. In the original algorithm, two fixed global thresholds (high and low) on the gradient of the pixel value are manually set to filter out the false edges. If the gradient exceeds the high threshold, then the pixel is considered an edge pixel. If the gradient is less than the low threshold, then the pixel is not part of an edge and the DN will be set to zero. If the magnitude is between the high and low thresholds, then the pixel is considered as a \"potential\" edge pixel and the neighboring pixels are examined to confirm whether the edge is identified. If at least one pixel among the neighboring pixels exceeds the high threshold, then the pixel is identified as an edge pixel. Based on experiments of extracting coastline with the original Canny algorithm, we found that the application of a fixed pair of thresholds to a sequence of spatially different images (around the Antarctica) yielded noisy images, as shown in Figure 1b. This is caused by the different contrast when the ice is subjected to surface deformation, metamorphosed snow cover, or when the water surface roughness varies due to varying surface wind field. Therefore, we introduced an adaptive threshold method to generate a pair of thresholds for each image. For each image, we examined the bimodality of the histogram of the pixel gradient and automatically identified the two clusters of edge and non-edge pixels with their different gradient magnitudes. This eventually led to improvement of the edge identification, as shown in Figure 1c. The selection of the adaptive thresholds (a pair representing the maximum and minimum associated with an image) is explained in Figure 2. For the three Landsat-8 images shown in panels a1a2, b1b2, and c1c2 (locations are marked in Figure 2d), the histograms of the gradients from all pixels of the images are presented in Figure 2e-g. All histograms feature tri-modal distribution (some feature bi-modal distribution but not shown). The two thresholds, which are selected automatically within the algorithm, are marked for each histogram. This is the added component to [PERSON]'s method in this study.