A Computational Theory of Visual Surface Interpolation.
Abstract
Computational theories of structure from motion (Ullman, 1979) and stereo vision (Marr and Poggio, 1979) only specify the computation of three-dimensional surface information at special points in the image. Yet, the visual perception is clearly of complete surfaces. In order to account for this, a computational theory of the interpolation of surfaces from visual information is presented. The problem is constrained by the fact that the surface must agree with the information from stereo or motion correspondence, and not vary radically between these points. Using the image irradiance equation (Horn, 1977), an explicit form of this surface consistency constraints can be derived (Grimson, 1981c). To determine which of two possible surfaces is more consistent with the surface consistency constraint, one must be able to compare the two surfaces. To do this, a functional from the space of functions to the real numbers is required. In this way, the surface most consistent with the visual information will be that which minimizes the functional. To ensure that the functional has a unique minimal surface, conditions on the form of the functional. To ensure that the functional has a unique minimal surface, conditions on the form of the functional are derived. In particular, if the functional is a complete semi-norm which satisfies the parallelogram law, or the space of functions is a semi-Hilbert space and the functional is a semi-inner product, then there is a unique (to within an element of the null space of the functional) surface which is most consistent with the visual information.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1981
- Accession Number
- ADA103921
Entities
People
- W. E. L. Grimson
Organizations
- Massachusetts Institute of Technology