Exact Voxel Occupancy with Graph Cuts

Voxel occupancy is one approach for reconstructing the 3-dimensional shape of an object from multiple views. In voxel occupancy, the task is to produce a binary labeling of a set of voxels, that determines which voxels are filled and which are empty. In this paper, we give an energy minimization formulation of the voxel occupancy problem. The global minimum of this energy can be rapidly computed with a single graph cut, using a result due to Greig, Porteous and Seheult [7]. The energy function we minimize contains a data term and a smoothness term. The data term is a sum over the individual voxels, where the penalty for a voxel is based on the observed intensities of the pixels that intersect it. The smoothness term is the number of empty voxels adjacent to filled ones. Our formulation can be viewed as a generalization of silhouette intersection, with two advantages: we do not compute silhouettes, which are a major source of errors; and we can naturally incorporate spatial smoothness. We give experimental results showing reconstructions from both real and synthetic imagery. Reconstruction using this smoothed energy function is not much more time consuming than simple silhouette intersection; it takes about 10 seconds to reconstruct a one million voxel volume.