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Exact Voxel Occupancy with Graph Cuts

Exact Voxel Occupancy with Graph Cuts. Dan Snow, Paul Viola and Ramin Zabih CVPR 2000. Volume (silhouette) intersection. Color voxel black if on silhouette in every image. Volume (silhouette) intersection. Color voxel black if on silhouette in every image. hole. Issues.

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Exact Voxel Occupancy with Graph Cuts

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  1. Exact Voxel Occupancy with Graph Cuts Dan Snow, Paul Viola and Ramin Zabih CVPR 2000

  2. Volume (silhouette) intersection • Color voxel black if on silhouette in every image

  3. Volume (silhouette) intersection • Color voxel black if on silhouette in every image hole

  4. Issues • Early hard decisions are a problem • Errors in silhouette identification • Can lead to “holes” • Can we add spatial smoothness with energy minimization? • Can we solve it fast?

  5. Problem statement • Given voxels pP, assigned binary labels fp • filled (1) or empty (0) • Each pixel corresponds to a line of voxels • If pixel is different from background, these voxels prefer 1, else 0

  6. Energy function • Dp(fp) = cost for voxel p to have label fp • Dp(empty) is large if voxel is different from background • Dp(full) = constant • We seek the labeling f that minimizes

  7. What smoothness term? • Here is a natural one where we can efficiently find the global minimum!

  8. Result

  9. Result Conventional Energy minimization

  10. Running time • For 100x100x100 grid, 16 cameras • 9 seconds total, on 500Mhz Intel PIII • 7 sec: graph prep + project • 1 sec: max flow computation • 1 sec: min-cut labeling of voxels from max-flow

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