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Zbl 0837.35146
Chambolle, Antonin
A uniqueness result in the theory of stereo vision: Coupling shape from shading and binocular information allows unambiguous depth reconstruction. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 11, No.1, 1-16 (1994). ISSN 0294-1449

Summary: We study here the mathematical consistency of coupling two classical methods in the theory of vision and surface reconstruction, namely the shape from shading theory and the theory of sterio vision. It is known that each of these approaches by itself is incomplete and leads to ill posed problems and multiple solutions, even under drastic simplifying assumptions.\par We show in this paper that, from a mathematical point of view, these ambiguities disappear when both theories are cooperatively implemented. In section 2 we state our assumptions; then part 3 is devoted to the presentation of the binocular vision theory. Section 4 eventually studies, in the one- and two-dimensional case, how introducing the shape from shading tool leads to the uniqueness of the solution. In the annex (section 6), a few mathematical results are explained, and some experiments (in 1D) are presented.

MSC 2000:: *35R25 Improperly posed problems for PDE
35R30 Inverse problems for PDE
78A05 Geometric optics
68U10 Image processing

Keywords: viscosity solution; shape from shading theory; theory of sterio vision; uniqueness

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