Left: One of the input images to our algorithm. The grass region contains little texture and therefore, multiple reconstructions satisfy the input images equally well. Right: Volume rendering of the voxel occupancy probabilities obtained using our algorithm. White corresponds to low probability and black to high probability. Voxels on the textured surfaces are assigned high probability, indicating strong image evidence (photo-consistency), whereas voxels in the textureless grass region receive much lower probability, exposing the reconstruction ambiguity.
This paper presents a novel probabilistic foundation for volumetric 3-d reconstruction. We formulate the problem as inference in a Markov random field, which accurately captures the dependencies between the occupancy and appearance of each voxel, given all input images. Our main contribution is an approximate highly parallelized discrete-continuous inference algorithm to compute the marginal distributions of each voxel's occupancy and appearance. In contrast to the MAP solution, marginals encode the underlying uncertainty and ambiguity in the reconstruction. Moreover, the proposed algorithm allows for a Bayes optimal prediction with respect to a natural reconstruction loss. We compare our method to two state-of-the-art volumetric reconstruction algorithms on three challenging aerial datasets with LIDAR ground truth. Our experiments demonstrate that the proposed algorithm compares favorably in terms of reconstruction accuracy and the ability to expose reconstruction uncertainty.
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