PDE Transforms and Edge Detection

In this paper, we propose the use of partial differential equation (PDE) based novel PDE transforms for determining jump discontinuity locations in piecewise smooth data containting potential isolated jump discontinuities. The PDE transform method involves evolving coupled PDEs under different time scales to extract edge information. Multiscale edge detection is done by varying the parameters and edges of different scales (kinds) are recovered. The focus is on linear PDEs and their implementation using fast fourier transforms (FFTs). We show that PDE tansforms with linear PDEs act as very high order exponential filters. The use of FFTs adapts the PDE transforms for edge detection in spectral data. Experiments are presented in one and two dimensions for detecting edges in signals and images. For giving some background to the use of PDEs in image processing, in general, and edge detection, in particular, we also present a brief discussion of the topic in the beginning sections.