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Multi-view Stereo via Volumetric Graph-cuts George Vogiatzis, Philip H. S. Torr Roberto Cipolla

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Shape From Images

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Dense Stereo reconstruction problem: Input Set of images of a scene I={I 1,…,I K } Camera matrices P 1,…,P K Output Surface model

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Shape parametrisation Disparity-map parameterisation MRF formulation – good optimisation techniques exist (Graph-cuts, Loopy BP) MRF smoothness is viewpoint dependent Disparity is unique per pixel – only functions represented

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Shape parametrisation Volumetric parameterisation – e.g. Level- sets, Space carving etc. Able to cope with non-functions Convergence properties not well understood Memory intensive For Space carving, no simple way to impose surface smoothness

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Solution ? Cast volumetric methods in MRF framework Benefits: General surfaces can be represented Optimisation is tractable (MRF solvers) Occlusions can be approximately modelled Smoothness is viewpoint independent

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Graph cuts 40 30 23 12 13 5 5 40 24 1 50 3 4 20 21 13

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Graph cuts 40 30 23 12 13 5 5 40 24 1 50 3 4 20 21 13

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Graph cuts 40 30 23 12 13 5 5 40 24 1 50 3 4 20 21 5+5+1+4+3=18 13

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Volumetric Graph cuts for segmentation Volume is discretized A binary MRF is defined on the voxels Regular grid (6 or 26 neighbourhood) Voxels are labelled as OBJECT and BACKGROUND Labelling cost set by OBJECT / BACKGROUND intensity statistics Compatibility cost set by edge intensities

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Volumetric Graph cuts for stereo How to define Inside and Outside labels How to deal with occlusion

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Volumetric Graph cuts Source Sink Min cut

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Face

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Face - Visual Hull

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Face - Slice

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Face - Slice with graphcut

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Face - Reconstruction

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Protrusion problem Balooning force favouring bigger volumes L.D. Cohen and I. Cohen. Finite-element methods for active contour models and balloons for 2-d and 3-d images. PAMI, 15(11):1131–1147, November 1993.

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Protrusion problem Balooning force favouring bigger volumes L.D. Cohen and I. Cohen. Finite-element methods for active contour models and balloons for 2-d and 3-d images. PAMI, 15(11):1131–1147, November 1993.

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Protrusion problem

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Graph

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Results Model House

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Results Model House – Visual Hull

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Results Model House

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Results Stone carving

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Results Haniwa

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Summary Novel formulation for multiview stereo Volumetric scene representation Computationally tractable global optimisation using Graph-cuts. Visual hull for occlusions and geometric constraint

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Benefits 1.General surfaces and objects can be fully represented and computed as a single surface. 2.The representation and smoothness constraint is image and viewpoint independent. 3.Multiple views of the scene can be used with occlusions approximately modelled. 4.Optimisation is computationally tractable, using existing max-flow algorithms.

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