Organization of Smooth Image Curves at Multiple Scales

While edge detection is an important first step for many vision systems, the linked lists of edge points produced by most existing edge detectors lack the higher level of curve description needed for many visual tasks. For example, they do not specify the tangent direction or curvature of an edge or the locations of tangent discontinuities. In this paper, a method is presented for describing linked edge points at a range of scales by selecting intervals of the curve and scales of smoothing that are most likely to represent the underlying structure of the scene. This multi-scale analysis of curves is complementary to any multi-scale detection of the original edge points. A solution is presented for the problem of shrinkage of curves during Gaussian smoothing, which has been a significant impediment to the use of smoothing for practical curve description. The curve segmentation method is based on a measure of smoothness minimizing the third derivative of Gaussian convolution. The smoothness measure is used to identify discontinuities of curve tangents simultaneously with selecting the appropriate scale of smoothing. The averaging of point locations during smoothing provides for accurate subpixel curve localization. This curve description method can be implemented efficiently and should prove practical for a wide range of applications including correspondence matching, perceptual grouping, and model-based recognition.