Invariance properties of the zero crossings of the Laplacian of Gaussian operator in stereo matching

Given two pictures of an arbitrary scene which are taken from different viewpoints, one can determine the 3-D coordinates of an arbitrary point in the scene, if one can identify its projection in each of the stereopair pictures. This requires the solution of the so-called `correspondence problem´: the matching of a piece of one of the stereo images to a piece of the other one, in order to identify image structures which correspond to the same 3-D part of the scene. The correspondence problem may be subdivided into two parts: the extraction of invariant features from the stereo images and the matching based on these invariants. In this paper, the invariance properties of the zero crossings (ZCs) of the Laplacian of Gaussian operator (LoG) are derived in a mathematical way. The results could be useful to solve the correspondence problem