Image feature detection and localization.

Abstract

This thesis concerns image feature detection and localization. We use a special kind of nonlinear filter called a quadratic filter to detect various features in images. We also develop a scale-free edge detection algorithm, in which the detected feature locations remain at the true location regardless of the change of the filter scale, and combine with a quadratic filter to obtain better feature localization. The thesis explores the quadratic filter for low-level vision applications. The quadratic filter is the simplest nonlinear time-invariant filter and corresponds to the second term in the Volterra expansion. We will elaborate concepts behind the quadratic filter and show that it can be derived from fundamental properties of regions and the principle of model competition. We present two properties of the filter. First, it is capable of detecting features. Second, it is insensitive to blurred boundaries; it will detect the boundary whether or not the filter size is larger or smaller than the extent of a blurred boundary. The quadratic filter is not restricted to detecting edges and boundaries: it can also detect corners and junctions. Based on the principle of the quadratic filter, an algorithm to detect both sharp and round corners is proposed and analyzed. The algorithm consists of 2-D smoothing, the projection of the smoothed image along two orthogonal directions and the rotation of the coordinate system. We also present a scale-free algorithm for edge localization. When an edge detector is applied to the edge of interest, nearby edges introduce interference into the detection process and cause detected edge locations to differ from the true edge locations. The algorithm recovers the true edge location by removing the edge interference which is estimated by adapting nonparametric methods in statistics and employing robust statistics. It does not make any assumption about the edge profile that is required in a parametric approach. It can even recover those edges which are lost during smoothing because the estimates contain information about the input image, not the smoothed image.