How to use Independent set problem for image edge detection?

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Let's say an Image is given, We have to convert the image into a matrix by using grayscale values for each pixel and then convert that matrix into a graph and use independent set problem to detect edges

This is an example of an image converted to a matrix I was able to figure out how to make a graph from an image using this paper https://www.researchgate.net/publication/224737408_A_unified_method_for_segmentation_and_edge_detection_using_graph_theory but I can't figure out how to use independent set problem.