Surface reconstruction is a common problem encountered in computer vision, for instance in stereo imaging and visual motion analysis, when a dense depth map of the imaged scene is desirable. It refers to a process in which a piecewise smooth surface is reconstructed from a set of noisy measurements. As identifying and locating discontinuities such as edges and boundaries in the scene are important, the goal of surface reconstruction is not only to reconstruct the surface, but also to identify the location of discontinuous points in the reconstruction.
As in the case of feature-based stereo imaging, the measurements are obtained through the feature correspondence between the left and right images. It thus gives an irregular sampling pattern and the sampling density could be very sparse. It may also happen that some parts in the image have no measurements as there may be no feature detectable in either the right or the left image. The reconstruction problem is therefore ill-posed in nature. Some additional constraints are needed in order to make the problem well-posed.