In this paper, we describe a voxel-based 3-D reconstruction technique from multiple calibrated camera views that makes explicit use of the finite size footprint of a voxel when projected into the image plane. We derive a class of computationally efficient axis-aligned volume traversal orders that ensure that a processed voxel cannot occlude previously processed voxels. For each view, one out of 79 different cases of volume traversal is identified depending on the relative position between camera and voxel volume. Views belonging to the same visibility class can be processed simultaneously. Our voxel coloring strategy is based on a color hypothesis test that ensures the consistency of the projected reconstruction with the original images. A surface voxel list is constantly updated during reconstruction ensuring that only a minimum number of voxels has to be processed. Experimental results that compare the reconstruction quality for voxels with and without spatial extent underscore the conclusion that it is worthwhile taking into account the exact footprint of the projected voxels.