Solid shape
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Quasi-Conformally Flat Mapping the Human Cerebellum
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Axioms and variational problems in surface parameterization
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Linear angle based parameterization
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Discrete quadratic curvature energies
Computer Aided Geometric Design
Sampling and Reconstruction of Surfaces and Higher Dimensional Manifolds
Journal of Mathematical Imaging and 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
Quasi-conformal flat representation of triangulated surfaces for computerized tomography
CVAMIA'06 Proceedings of the Second ECCV international conference on Computer Vision Approaches to Medical Image Analysis
| Hi-index | 0.00 |
A method and algorithm of flattening folded surfaces, for two-dimensional representation and analysis of medical images, are presented. The method is based on an application to triangular meshes of classical results of Gehring and Väisälä regarding the existence of quasi-conformal and quasi-isometric mappings.The proposed algorithm is basically local and, therefore, suitable for extensively folded surfaces encountered in medical imaging. The theory and algorithm guarantee minimal distance, angle and area distortion. Yet, the algorithm is relatively simple, robust and computationally efficient, since it does not require computational derivatives. Both random-starting-point and curvature-based versions of the algorithm are presented.We demonstrate the algorithm using medical data obtained from real CT images of the colon and MRI scans of the human cortex. Further applications of the algorithm, for image processing in general are also considered. The globality of this algorithm is also studied, via extreme length methods for which we develop a technique of computing straightest geodesics on polyhedral surfaces.