Mathematics Seminar 11/16/23

Abstract:

Edges in a digital image provide important information about the objects in the image since they constitute boundaries between objects. Most edge detection algorithms are sensitive to noise and attempts to remove noise often weaken not only noise but also the edge strength.This article proposes an innovative denoising method called the reverse-transition weighting (RTW) filter, which can suppress noise without weakening the edge strength. Such a property of preserving the edge strength is unique to the RTW denoising filter. The new filter is analyzed for its stability and convergence and adopted for the denoising step of the Canny edge detection algorithm, replacing the conventional Gaussian smoothing filter. We also compare gradient-fusion methods which combine the RGB gradients into one. Our goal is to formulate a robust edge detection algorithm for color images, particularly for heavily noisy images. Various examples are given to show the effectiveness of the new denoising filter.