Contour Tracking by Enhancing Corners and Junctions

In a previous paper an approach was presented in which, given an approximated starting contour on the first frame, all the contours of the image sequence could be outlined automatically with the desired resolution. Although such an approach provided satisfactory results, singular isolated points, such as corners and junctions, gave rise to localization errors. The difficulties encountered at corners and junctions were analysed and the edge operator was held to be the main cause of this failure. The gradient of Gaussian, which was used in the previous paper, must be replaced by a filter providing: 1) ridges in correspondence with discontinuities and 2) local maxima at junctions and corners. In this paper such a filter is introduced and its response to a white Gaussian noise is analysed. The filter response is a dispersion index and, in particular, it is a generalization of the absolute central moment, i.e. the mean deviation. The edge map, generated by the filter, can be divided into two maps which represent the "positive mean deviation" and the "negative mean deviation", respectively. Their difference is the mean deviation and provides ridges at the discontinuities (as well as a gradient of Gaussian) and local maxima at junctions and corners. Their sum is a classical DOG (difference of Gaussians). The two single maps provide two half-boundaries which other authors have proposed in order both to achieve maps of the edge points and to improve the procedure of boundary following.