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
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics
The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics
Pattern-based texturing revisited
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
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
Computational Surface Flattening: A Voxel-Based Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spanning Tree Seams for Reducing Parameterization Distortion of Triangulated Surfaces
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Visualization and Measurement of the Cortical Surface
Journal of Cognitive Neuroscience
Universal multi-dimensional scaling
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Equi-affine invariant geometries of articulated objects
Proceedings of the 15th international conference on Theoretical Foundations of Computer Vision: outdoor and large-scale real-world scene analysis
Composite data mapping for spherical GUI design: clustering of must-watch and no-need TV programs
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part V
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We present a technique for texture mapping arbitrary sphere-like surfaces with minimal distortions by spherical embedding. The embedding is computed using spherical multi-dimensional scaling (MDS). MDS is a family of methods that map a set of points into a finite dimensional domain by minimizing the difference in distances between every pair of points in the original and the new embedding domains. In this paper spherical embedding is derived using geodesic distances on triangulated domains, computed by the fast marching method. The MDS is formulated as a non-linear optimization problem and a fast multi-resolution solution is derived. Finally, we show that the embedding of complex objects which are not sphere-like, can be improved by defining a texture dependent scale factor. This scale is the maximal distance to be preserved by the embedding and can be estimated using spherical harmonics. Experimental results show the benefits of the proposed approach.