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

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

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

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

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

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

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

Volumetric Graph cuts for segmentation Boykov and Jolly ICCV 2001 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

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

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

Volumetric Graph cuts Source Sink

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

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

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

Photo-consistency Occlusion Self occlusion

Photo-consistency Occlusion Self occlusion

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

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

Photo-consistency Score  = 1 - exp( -tan2[(C-1)/4] / 2 ) Average NCC = C Voxel score  = 1 - exp( -tan2[(C-1)/4] / 2 ) Score 0    1  = 0.05 in all experiments

Example

Example - Visual Hull

Example - Slice

Example - Slice with graphcut

Example – 3D

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.

 (x) dS -   dV 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.

Protrusion problem

Protrusion problem

Graph wij = 4/3h2 * (i+j)/2 wb wb = h3 wij i j h SOURCE [Boykov and Kolmogorov ICCV 2001] wb = h3 wij i j h

Results Model House

Results Model House – Visual Hull

Results Model House

Results Stone carving

Results Haniwa

Summary Questions ? 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 ?