TY - JOUR
T1 - Computational surface flattening
T2 - A voxel-based approach
AU - Grossmann, Ruth
AU - Kiryati, Nahum
AU - Kimmel, Ron
N1 - Funding Information:
The authors would like to thank Haim Shvaytser, Gabriele Lohmann, and Nira Dyn for the interesting discussions. The friendly and helpful advice of Gil Zigelman and Sharon Gannot is appreciated. The authors are grateful to the National Research Council of Canada for the 3D digital head model. This research was supported by the Adams Super-Center for Brain Studies at Tel Aviv University and by the German-Israeli Foundation for Scientific Research and Development (GIF).
PY - 2002/4
Y1 - 2002/4
N2 - A voxel-based method for flattening a surface in 3D space into 2D while best preserving distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main parts: Voxel-based calculation of the minimal geodesic distances between points on the surface and finding a configuration of points in 2D that has Euclidean distances as close as possible to these 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 multidimensional scaling (MDS) for finding the 2D point configuration. The proposed algorithm is efficient, simple, and can be applied to surfaces that are not functions. Experimental results are shown.
AB - A voxel-based method for flattening a surface in 3D space into 2D while best preserving distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main parts: Voxel-based calculation of the minimal geodesic distances between points on the surface and finding a configuration of points in 2D that has Euclidean distances as close as possible to these 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 multidimensional scaling (MDS) for finding the 2D point configuration. The proposed algorithm is efficient, simple, and can be applied to surfaces that are not functions. Experimental results are shown.
KW - Geodesic distance estimation
KW - Multidimensional scaling
KW - Surface flattening
KW - Texture mapping
KW - Voxel representation
UR - http://www.scopus.com/inward/record.url?scp=0036537997&partnerID=8YFLogxK
U2 - 10.1109/34.993552
DO - 10.1109/34.993552
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AN - SCOPUS:0036537997
VL - 24
SP - 433
EP - 441
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
SN - 0162-8828
IS - 4
ER -