Refining edges detected by a LoG operator

The Laplacian-of-Gaussian (LoG) operator is one of the most popular operators used in edge detection. This operator, however, has some problems: zero-crossings do not always correspond to edges, and edges with an asymmetric profile introduce a symmetric bias between edge and zero-crossing locations. In this paper, we offer solutions to these two problems. First, for one-dimensional signals, such as slices from images, we propose a simple test to detect “true” edges, and, for the problem of bias, we propose different techniques: the first one combines the results of the convultion of two LoG operators of different standard deviations, whereas the others sample the convolution with a single LoG filter at two points besides the zero-crossing. In addition to localization, these methods allow us to further characterize the shape of the edge. We then present an implementation of these techniques for edges in 2D images, in which we apply the refining process to linear segments approximating the detected contours. The methods are illustrated on several examples.