SIAM Journal on Computing
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Computing Minimal Distances on Polyhedral Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Numerical Solution to the Generalized Mapmaker's Problem: Flattening Nonconvex Polyhedral Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Piecewise surface flattening for non-distorted texture mapping
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Conformal Geometry and Brain Flattening
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Journal of Cognitive Neuroscience
Cortical surface alignment using geometry driven multispectral optical flow
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
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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.