This work proposes a novel and efficient surface matching and
visualization framework through the geodesic distance-weighted shape
vector image diffusion. Based on conformal geometry, our approach
can uniquely map a 3D surface to a canonical rectangular domain and
encode the shape characteristics (e.g., mean curvatures and
conformal factors) of the surface in the 2D domain to construct a
geodesic distance-weighted shape vector image, where the distances
between sampling pixels are not uniform but the actual geodesic
distances on the manifold. Through the novel geodesic
distance-weighted shape vector image diffusion, we can create a
multiscale diffusion space, in which the cross-scale extrema can be
detected as the robust geometric features for the matching and
registration of surfaces. Therefore, statistical analysis and
visualization of surface properties across subjects become readily
available. The experiments on scanned surface models show that our
method is very robust for feature extraction and surface matching
even under noise and resolution change. We have also applied the
framework on the real 3D human neocortical surfaces, and
demonstrated the excellent performance of our approach in
statistical analysis and integrated visualization of the
multimodality volumetric data over the shape vector image.
Further details of this work are available
here.
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