A level-set approach to 3D reconstruction from range data

This paper presents a method that uses the level sets of volumes to reconstruct the shapes of 3D objects from range data. The strategy is to formulate 3D reconstruction as a statistical problem: find that surface which is mostly likely, given the data and some prior knowledge about the application domain. The resulting optimization problem is solved by an incremental process of deformation. We represent a deformable surface as the level set of a discretely sampled scalar function of three dimensions, i.e., a volume. Such level-set models have been shown to mimic conventional deformable surface models by encoding surface movements as changes in the greyscale values of the volume. The result is a voxel-based modeling technology that offers several advantages over conventional parametric models, including flexible topology, no need for reparameterization, concise descriptions of differential structure, and a natural scale space for hierarchical representations. This paper builds on previous work in both 3D reconstruction and level-set modeling. It presents a fundamental result in surface estimation from range data: an analytical characterization of the surface that maximizes the posterior probability. It also presents a novel computational technique for level-set modeling, called the sparse-field algorithm, which combines the advantages of a level-set approach with the computational efficiency and accuracy of a parametric representation. The sparse-field algorithm is more efficient than other approaches, and because it assigns the level set to a specific set of grid points, it positions the level-set model more accurately than the grid itself. These properties, computational efficiency and subcell accuracy, are essential when trying to reconstruct the shapes of 3D objects. Results are shown for the reconstruction objects from sets of noisy and overlapping range maps.