ADAPTIVE DETERMINATION OF FILTER SCALES FOR EDGE-DETECTION

Abstract

This paper suggests a regularization method for determining scales for edge detection adaptively for each site in the image plane. Specifically, we extend the concept of optimal filter by Poggio et al. and scale space by Witkin to an adaptive scale parameter. Conventional methods incorporating multiscale edge detection usually must rely on a scheme for integrating edge maps viewed in various scopes. This integrating scheme itself is, however, an ill-posed problem and has been usually customized by ad hoc or heuristic methods like feature synthesis. To avoid such an ill-posed feature synthesis problem, we introduce an alternative scheme that can automatically find optimal scales adaptively for each pixel before detecting final edge maps. We first introduce an energy function defined as a functional over continuous scale space. Natural constraints for edge detection are incorporated into the energy function. To obtain a set of optimal scales that can minimize the energy function, a parallel relaxation algorithm is introduced. Experiments for synthetic and natural scenes show the advantages of the new algorithm over the edge detectors by Marr and Hildreth or Canny. In particular, it is shown that this system can detect both step and diffuse edges while drastically filtering out the random noise.