Invariant reconstruction of visual surfaces

This study addresses a problem that arises in the early stages of visual processing. Low-level vision processing tasks generate information describing distances and orientations at sparse locations of visible surfaces in a scene. The information from these various low-level tasks need to be combined to form an estimate of the visual surface for all points in the scene. This step is commonly referred to as the surface reconstruction problem. The problem is cast as an ill-posed inverse problem, which must be stabilized using a priori information relative to image and constraint formation. A desirable property of any reconstruction algorithm is invariance with respect to rigid transformations of the surface in three-dimensional space. Two surface reconstruction algorithms that are based on invariant surface characteristics are proposed. These algorithms are studied in detail, and an example is presented to demonstrate their effectiveness. The discrete realization of the algorithms is also briefly discussed