Jeremy S. De Bonet : Poxels: Probabilistic Voxel Reconstruction




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Problem Formulation

The reconstruction problem can be formulated as follows: what is the configuration of the contents of a region of space given a collection observations made from a variety of viewpoints.
dgrm_soccer_capture.jpg
An example of multiview stereo in which the cameras are placed around the perimeter of a volume
A particular subproblem of this is one in which a scene, is observed from various vantage points outside of the volume of interest. For example consider the volume of space filled by the soccer players who are observed by the cameras around the perimeter of the field as in this Figure .
dgrm_flower_capture.jpg
An example of multiview stereo in which a rigid object is rotated in front of a single camera
Another instansiation of the reconstruction problem is one in which a rotating object is observed by a single camera (this Figure ).
dgrm_cat_capture.jpg
An example of a CAT scan, in which xray absorbtion is measured around the perimeter of a volume
A third example is that of a CAT scan, in which a collection observations are made of the radiation absorbed along a 1d ray though a section of body this Figure .
In each instance of the problem, the information provided in each observation (either image or absorbtion measurement) is insufficient to determine the structure of the space. These observations in concert however, provide significant constraint on the structure of the observed space.
One of the significant contributions of this work is that no assumptions are implied about the nature of the space which is not constrained by the observations. Because of this, the uncertainty about the structure of some regions of the reconstructed volume are explicitly represented.
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Jeremy S. De Bonet
jsd@debonet.com
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