# Multi-Level Reconstruction of Visual Surfaces: Variational Principles and Finite Element Representations

 dc.date.accessioned 2004-10-01T20:30:47Z dc.date.accessioned 2018-11-24T10:10:05Z dc.date.available 2004-10-01T20:30:47Z dc.date.available 2018-11-24T10:10:05Z dc.date.issued 1982-04-01 en_US dc.identifier.uri http://hdl.handle.net/1721.1/5678 dc.identifier.uri http://repository.aust.edu.ng/xmlui/handle/1721.1/5678 dc.description.abstract Computational modules early in the human vision system typically generate sparse information about the shapes of visible surfaces in the scene. Moreover, visual processes such as stereopsis can provide such information at a number of levels spanning a range of resolutions. In this paper, we extend this multi-level structure to encompass the subsequent task of reconstructing full surface descriptions from the sparse information. The mathematical development proceeds in three steps. First, the surface most consistent with the sparse constraints is characterized as the solution to an equilibrium state of a thin flexible plate. Second, local, finite element representations of surfaces are introduced and, by applying the finite element method, the continuous variational principle is transformed into a discrete problem in the form of a large system of linear algebraic equations whose solution is computable by local-support, cooperative mechanisms. Third, to exploit the information available at each level of resolution, a hierarchy of discrete problems is formulated and a highly efficient multi-level algorithm, involving both intra-level relaxation processes and bi-directional inter-level algorithm, involving both intra-level relaxation processes and bidirectional inter-level local interpolation processes is applied to their simultaneous solution.. Examples of the generation of hierarchies of surface representations from stereo constraints are given. Finally, the basic surface approximation problem is revisited in a broader mathematical context whose implications are of relevance to vision. en_US dc.format.extent 91 p. en_US dc.format.extent 9352085 bytes dc.format.extent 6703080 bytes dc.language.iso en_US dc.subject computer vision en_US dc.subject hierarchical representations en_US dc.subject svariational principles en_US dc.subject stereo en_US dc.subject surface reconstruction en_US dc.subject finite elements en_US dc.subject smulti-level relaxation en_US dc.subject interpolation en_US dc.title Multi-Level Reconstruction of Visual Surfaces: Variational Principles and Finite Element Representations en_US
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