  We propose connectivity-preserving geometry images (CGIMs), which map a
three-dimensional mesh onto a rectangular regular array of an image, such that
the reconstructed mesh produces no sampling errors, but merely round-off
errors. We obtain a V-matrix with respect to the original mesh, whose elements
are vertices of the mesh, which intrinsically preserves the vertex-set and the
connectivity of the original mesh in the sense of allowing round-off errors. We
generate a CGIM array by using the Cartesian coordinates of corresponding
vertices of the V-matrix. To reconstruct a mesh, we obtain a vertex-set and an
edge-set by collecting all the elements with different pixels, and all
different pairwise adjacent elements from the CGIM array respectively. Compared
with traditional geometry images, CGIMs achieve minimum reconstruction errors
with an efficient parametrization-free algorithm via elementary permutation
techniques. We apply CGIMs to lossy compression of meshes, and the experimental
results show that CGIMs perform well in reconstruction precision and detail
preservation.
