| Abstract | We consider a model of a 3D image obtained bydiscretizing it into a multiresolution tetrahedral mesh
known as a hierarchy of diamonds. This model enables
us to extract crack-free approximations of the 3D image
at any uniform or variable resolution, thus reducing the
size of the data set without reducing the accuracy.
A 3D intensity image is a scalar field (the intensity
field) defined at the vertices of a 3D regular grid and
thus the graph of the image is a hypersurface in R4. We
measure the discrete distortion, a generalization of the
notion of curvature, of the transformation which maps
the tetrahedralized 3D grid onto its graph in R4.
We evaluate the use of a hierarchy of diamonds to
analyze properties of a 3D image, such as its discrete
distortion, directly on lower resolution approximations.
Our results indicate that distortion-guided extractions
focus the resolution of approximated images on the
salient features of the intensity image.
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