Edge preserving smoothing is a locally adaptive process, where the size of the blurkernel, applied to suppress the noise, is a local function of the edge strength [2, 3]. Blurring is described by a partial differential equation, the diffusion equation. At strong edges, the 'conductivity' of the diffusion is reduced.This was first introduced into the realm of computer vision by Perona and Malik  in 1991. It was a huge success, as it also enhanced the remaining edges. But at strong edges, the noise remained, and there was a parameter k that had to be set. Alvarez  came up with an elegant solution for both issues, by proposing a new nonlinear image evolution scheme, where the local edge direction was taken into account. This solution is known as Euclidean Shortening Flow.We first give the theory and implementation of Perona & Malik nonlinear diffusion, then we focus on Euclidean shortening flow. The last section discusses an implementation on a noise ultrasound image. This paper is based on Chapter 21 of the book "Front-End Vision & Multi-Scale Image Analysis" (ter Haar Romeny, 2003).
|Title of host publication||Proceedings of the international mathematica symposium 2005 (IMS2005), 5-8 August 2005 Perth, Australia|
|Publication status||Published - 2005|