Multigrid Interpolation and Discontinuity Detection in Hierarchical Surface Reconstruction

Working within the framework of hierarchical surface reconstruction first introduced by (Schenk et al., 1991), this research focuses on the subsystem of surface interpolation and defines the tasks for interpolation and analysis of a surface. The main objective of this research is to develop an algorithm that produces a dense representation of a surface from a sparse set of observations and, at the same time, facilitates preliminary labeling of discontinuities in the surface. Additionally, this study establishes the instrument and the mechanism for the communication between the levels of the image pyramid as well as the subsystems of the hierarchical surface reconstruction paradigm. The suggested approach is the simultaneous interpolation of the surface and detection of its discontinuities by adopting the weak membrane model. The proposal is a new implementation of the Graduate Non-Convexity (GNC) algorithm based on multigrid techniques. The GNC was originally developed by (Blake and Zisserman, 1987) for a single grid, for applications in computer vision. As it was initially proposed, GNC depends a great deal on the optimal setting of the control parameters. In this work, a specific procedure has been developed that determines the control parameters automatically and less subjectively.