Graphs and algorithms
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
Length Estimation in 3-D Using Cube Quantization
Journal of Mathematical Imaging and Vision
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Texture Mapping Using Surface Flattening via Multidimensional Scaling
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
Three-Dimensional Face Recognition
International Journal of Computer Vision
Topology-Invariant Similarity of Nonrigid Shapes
International Journal of Computer Vision
Expression-invariant 3D face recognition
AVBPA'03 Proceedings of the 4th international conference on Audio- and video-based biometric person authentication
International Journal of Computer Vision
Evaluation of 3d face recognition using registration and PCA
AVBPA'05 Proceedings of the 5th international conference on Audio- and Video-Based Biometric Person Authentication
Texture mapping via spherical multi-dimensional scaling
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Isometric embedding of facial surfaces into S3
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Approximating geodesics on point set surfaces
SPBG'06 Proceedings of the 3rd Eurographics / IEEE VGTC conference on Point-Based Graphics
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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.