Hierarchical stereo correspondence using features of gray connected components

A new feature-based method for the correspondence problem is proposed. The used feature is the boundary of a parameter-dependent connected component ((ε,δ)-component, Wang and Bhattacharya, 1996) of an image. We prove that under certain conditions, there is a one-to-one relationship between the sets of the boundary points in a pair of stereo images. This correspondence may be identified through epipolar geometry. Furthermore, since such connected components may represent some meaningful objects (Wang and Bhattacharya, 1996) in images, we may obtain the corresponding objects directly, instead of only the corresponding points or lines as in some other methods which need the process of feature grouping to conduct further analysis. Also, a hierarchy of the connected components provides us with a coarse-to-fine matching method to recover the surface corresponding to a connected component