2006-2009 Jean-Marie Favreau
here are several ways to produce 3D acquisitions from a real object (volumic acquisitions, point clouds generated from 3D scanners or cameras) Both of the data structures are usually turned into surfaces described by triangles, using isosurface reconstruction methods . Due to the precision and resolution, the resulting virtual surface may not capture the full topological and/or geometrical details of the original surface, and are prone to artifacts that misrepresent the data.
Wa propose here to tackle the problem of mapping a surface acquired from a real object onto a piece of the plane, taking into account the topological and geometrical properties of the surface, as well as the specificity of low-resolution acquisitions. We introduce a cutting process used to manage the topological constraint of the one-to-one mapping, with some speedup improvements. Specific geometrical constraints linked to the low resolution context can be introduced
In medical imaging, an unfolding approach has been described in a previous work, to produce a flattened map of the region of interest on the cortical surface, using T1-weigthed Magnetic Resonance Imaging scans. After some segmentation steps and a surface reconstruction, a mesh is obtained, modeling the region of interest on the cortical surface. The cutting method used here did not take into account geometry, producing maps with overlaps for high genus original surfaces. The approach described in here was applied to the meshes stemming from the original data. The resulting surface was then unfolded using classical unfolding tools. (a) : A neighbourhood of a central sulcus extracted from the original volumic data. (b), ©, (d) : Cortical maps unfolded by Circle Packing after cutting steps (na-ve, topological, and patching + topological). Dark grey shows regions of overlappings.