Reconstructions from zero crossings in scale space

In computer vision, the one-parameter family of images obtained from the Laplacian-of-a-Gaussian-filtered version of the image, parameterized by the width of the Gaussian, has proved to be a useful data structure for the extraction of feature data. In particular, the zero crossings of this so-called scale-space data are associated with edges and have been proposed by D. Marr (1982) and others as the basis of a representation of the image data. The question arises as to whether the representation is complete and stable. The authors survey some of the studies and results related to these questions as well as several studies that attempt reconstructions based on this or related representations. They formulate a novel method for reconstruction from zero crossings in scale space that is based on minimizing equation error, and they present results showing that the reconstruction is possible but can be unstable. They further show that the method applies when gradient data along the zero crossings are included in the representation, and they demonstrate empirically that the reconstruction is then stable.>