Multilevel Reconstruction of Visual Surfaces: Variational Principles and Finite-Element Representations View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

1984

AUTHORS

D. Terzopoulos

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 multilevel 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 optimal approximation problem which is posed as a variational principle describing the constrained 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 multilevel algorithm, involving both intralevel relaxation processes and bidirectional interlevel 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. More... »

PAGES

237-310

Book

TITLE

Multiresolution Image Processing and Analysis

ISBN

978-3-642-51592-7
978-3-642-51590-3

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-51590-3_17

DOI

http://dx.doi.org/10.1007/978-3-642-51590-3_17

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1035894838


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