Reconstruction from Range Data: Reconstruction from Real Space Carved Data

We use Steve Seitz's toy dinosaur [Seit 97] as real test data. The set of data was obtained by taking 20 images approximately on a circle around each object, and volumetric surfaces were constructed using the generalized voxel coloring algorithm [Culb 99]. The cameras are calibrated using a grid on which the object sits. The volume is carved by splatting each voxel towards each camera and determining the consistency of the voxel color across the images. If the variance in color intensity is below a specified threshold, the voxel is kept as part of the object surface. Otherwise, it is cast out and assigned a zero value. The data consists of red, green, blue, and alpha channels for each voxel. The surface exists wherever a non-empty voxel is present.

In defining surface constraints, we use the volume as a binary representation and apply the technique described above in Constraint Specificationto define the existence space - surface, exterior, and interior space - of the object. Surface constraints are defined at each non-empty voxel. We do not use the entire set of surface voxels because the system matrix would become too large (19,641 surface voxels for the dinosaur data set), and the reconstructed surface would over fit the data, resulting in overshoots. To obtain a subset of these surface voxels, we uniformly sample the volume by randomly selecting voxels within the bounding box. Positive constraints are obtained by traversing the binary volume along the three principal axis. All points occurring between pairs of non-empty voxels are marked as interior. Only voxels which are marked as interior by all three traversals are kept as interior constraints. Again, only a subset of these are selected by the Poisson disc sampling technique described above. Negative constraints are found by splatting each surface voxel in the volume towards each camera. If the ray from the surface voxel to a camera intersects other surface voxels, then the camera does not have an unobscured view of the voxel. Otherwise, if the camera does have an unobscured view, then a negative constraint can be placed at a small distance away from the surface voxel along the ray towards the camera. Once a specified number of constraints have been collected, they are applied to the reconstruction algorithm. In our research, we have used from 800 to 4500 surface constraints. In practice, we have found that 100 or 200 exterior and interior constraints suffice to define the interior and exterior space.

The constraints used to reconstruct the toy dinosaur model shown in the images throughout this work were obtained using the above technique. The figure below is an example the distribution of surface and exterior constraints for the toy dinosaur data set. The blue squares are surface constraints, while the green squares are negative, exterior constraints.