Abstract
A voxel-based method for flattening a surface while best preserving the distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main subproblems: Voxel-based calculation of the minimal geodesic distances between the points on the surface, and finding a configuration of points in 2-D that has Euclidean distances as close as possible to the minimal geodesic distances. The method suggested combines an efficient voxel-based hybrid distance estimation method, that takes the continuity of the underlying surface into account, with classical multi-dimensional scaling (MDS) for finding the 2-D point configuration. The proposed algorithm is efficient, simple, and can be applied to surfaces that are not functions. Experimental results are shown.
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Grossmann, R., Kiryati, N., Kimmel, R. (2001). Computational Surface Flattening: A Voxel-Based Approach. In: Arcelli, C., Cordella, L.P., di Baja, G.S. (eds) Visual Form 2001. IWVF 2001. Lecture Notes in Computer Science, vol 2059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45129-3_17
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DOI: https://doi.org/10.1007/3-540-45129-3_17
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