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|Title:||Scale space displacement of zero-crossings of del(2)G operated images for convex bodies and convex sets|
|Publisher:||ELSEVIER SCIENCE BV|
|Citation:||SIGNAL PROCESSING, 47(3), 279-285|
|Abstract:||Multi-scale edge detectors are used to detect intensity changes in images at various spatial resolutions. By tracking edge information across scales, it is possible to classify edges according to their underlying physical processes. The tracking process is complicated due to the fact that edges undergo displacement in scale space. In the past, researchers have studied the displacement properties of zero-crossings for different edge models. In this paper, we have presented the results of 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 displaced outside the body and the maximum displacement in a direction normal to the contour is root 2 sigma. As illustrative examples of convex bodies, we have considered a circle and a Bernoulli's lemniscate. Results are also presented for a convex set having parabolic contour. An effective scale-space tracking strategy may be adopted using these results. The information extracted through scale space tracking can be used as a matching parameter in stereo and motion correspondences.|
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