Efficient Maximum Euclidean Distance Transform Computation in Component Trees Using the Differential Image Foresting Transform

Abstract The distance transform is a crucial technique in binary image processing, assigning the distance to the nearest contour to each foreground pixel. In this extended version of our previous work, we enhance our method for computing the maximum distance transform (DT) value, now utilizing the optimized differential image foresting transform (DIFT) and improved contour extraction processes. These advancements enable more efficient computation of the maximum DT value across all connected components of a grayscale image, significantly reducing computational time by intelligently reusing DIFT trees rooted at contour points (DIFT seeds). Our optimized algorithm now achieves processing speeds that are twice as fast as our previous differential method. The proposed attribute, maximum distance, which measures the thickness of objects within the image, has proven pivotal in different image processing approaches. We showcase this through detailed illustrations of attribute opening, extinction value filters, watershed, and ultimate attribute openings.