SCALE-SPACE DISPLACEMENT OF ZERO-CROSSINGS OF DEL(2)G OPERATED IMAGESFOR CONVEX-BODIES AND CONVEX-SETS

Multi-scale edge detectors are used to detect intensity changes in ima ges at various spatial resolutions. By tracking edge information acros s scales, it is possible to classify edges according to their underlyi ng physical processes. The tracking process is complicated due to the fact that edges undergo displacement in scale space. In the past, rese archers have studied the displacement properties of zero-crossings for different edge models. In this paper, we have presented the results o f our studies on the displacements of zero-crossings of planar convex bodies using the Laplacian of Gaussian filters. It has been shown that for a planar convex body, the zero-crossing contour is always displac ed outside the body and the maximum displacement in a direction normal to the contour is root 2 sigma. As illustrative examples of convex bo dies, we have considered a circle and a Bernoulli's lemniscate. Result s are also presented for a convex set having parabolic contour. An eff ective scale-space tracking strategy may be adopted using these result s. The information extracted through scale space tracking can be used as a matching parameter in stereo and motion correspondences.