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Multi-view Stereo via Volumetric Graph-cuts George Vogiatzis Roberto Cipolla Cambridge Univ. Engineering Dept. Philip H. S. Torr Department of Computing Oxford Brookes University

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Multi-view Dense Stereo Calibrated images of Lambertian scene 3D model of scene

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Multi-view Dense Stereo Volumetric Two main approaches Volumetric Disparity (depth) map

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Dense Stereo reconstruction problem: Disparity-map Two main approaches Volumetric Disparity (depth) map

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Shape representation Disparity-maps 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 representation Volumetric – e.g. Level-sets, Space carving etc. Able to cope with non-functions Levelsets: Local optimization Space carving: no simple way to impose surface smoothness

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Our approach Cast volumetric methods in MRF framework Use approximate surface containing the real scene surface E.g. visual hull Benefits: General surfaces can be represented No depth map merging required Optimisation is tractable (MRF solvers) Smoothness is viewpoint independent

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Volumetric Graph cuts for segmentation Volume is discretized A binary MRF is defined on the voxels Voxels are labelled as OBJECT and BACKGROUND Labelling cost set by OBJECT / BACKGROUND intensity statistics Compatibility cost set by intensity gradient Boykov and Jolly ICCV 2001

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Volumetric Graph cuts for stereo Challenges: What do the two labels represent How to define cost of setting them How to deal with occlusion Interactions between distant voxels

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Volumetric Graph cuts (x) 1. Outer surface 2. Inner surface (at constant offset) 3. Discretize middle volume 4. Assign photoconsistency cost to voxels

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Volumetric Graph cuts Source Sink

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Volumetric Graph cuts Source Sink Cost of a cut (x) dS S S cut 3D Surface S [Boykov and Kolmogorov ICCV 2001]

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Volumetric Graph cuts Source Sink Minimum cut Minimal 3D Surface under photo- consistency metric [Boykov and Kolmogorov ICCV 2001]

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Photo-consistency Occlusion 1. Get nearest point on outer surface 2. Use outer surface for occlusions 2. Discard occluded views

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Photo-consistency Occlusion Self occlusion

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Photo-consistency Occlusion Self occlusion

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Photo-consistency Occlusion N threshold on angle between normal and viewing direction threshold= ~60

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Photo-consistency Score Normalised cross correlation Use all remaining cameras pair wise Average all NCC scores

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Photo-consistency Score Average NCC = C Voxel score = 1 - exp( -tan 2 [ (C-1)/4] / 2 ) 0 1 = 0.05 in all experiments

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Example

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Example - Visual Hull

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Example - Slice

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Example - Slice with graphcut

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Example – 3D

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Protrusion problem Balooning force favouring bigger volumes that fill the visual hull 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 that fill the visual hull 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 (x) dS - dV SV

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Protrusion problem

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w ij SOURCE wbwb wbwb Graph h j i w b = h 3 w ij = 4/3 h 2 * ( i + j )/2 [Boykov and Kolmogorov ICCV 2001]

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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 Occlusions approximately modelled Questions ?

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