A uniqueness result in the theory of stereo vision: Coupling shape from shading and binocular information allows unambiguous depth reconstruction.

*(English)*Zbl 0837.35146Summary: 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.

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.

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:

35R25 | Ill-posed problems for PDEs |

35R30 | Inverse problems for PDEs |

78A05 | Geometric optics |

68U10 | Computing methodologies for image processing |

##### References:

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