Jeremy S. De Bonet : Poxels: Probabilistic Voxel Reconstruction




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Rendering Algorithm

From the collection of poxel-spaces which results from the above iterative algorithm a new of the volume observed from some novel point of view can be synthesized.
The rendering system must combine the pixel estimates from each observation associated with the voxels which are intersected by rays from the rendering plane weighted by PoxelidCDF, the probability of non-occlusion and PoxelPDF the probability of observation.
pxlrender(x,y) = sumd sumi pxli(x,y) (PoxelidCDFi(x,y,d))/(sumjPoxelidCDFj(x,y,d)) PoxelPDFi(x,y,d)
This makes the assumption that objects in the scene are Lambertian, and that the lighting is diffuse, because it will faitfully combine color estimates for a point in space from observations taken from widely differing angles (for an example of this effect, see the results section). In practice however, this assumption rarely holds, so it is often advantageous to weight views from closer viewing angles more heavily. In the examples show here an additional factor of exp(-angle2 / sd2) is used to change the weighting of the contributions of each observation.
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Jeremy S. De Bonet
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