Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
SIAM Review
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
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Diffusions and Confusions in Signal and Image Processing
Journal of Mathematical Imaging and Vision
Anisotropic diffusion of surfaces and functions on surfaces
ACM Transactions on Graphics (TOG)
Image Processing via the Beltrami Operator
ACCV '98 Proceedings of the Third Asian Conference on Computer Vision-Volume I - Volume I
The Beltrami Flow over Implicit Manifolds
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Journal of Computational Physics
Efficient Beltrami flow using a short time kernel
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
A general framework for low level vision
IEEE Transactions on Image Processing
Processing textured surfaces via anisotropic geometric diffusion
IEEE Transactions on Image Processing
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The fields of image processing, computer vision and computer graphics have concentrated traditionally on regular 2D images. Recently, images painted on 2D manifolds are becoming more popular and are used in face recognition, volumetric medical image processing, 3D computer graphics, and many other applications. The need has risen to regularize this type of images. Various manifold representations are the input for these applications. Among the main representations are triangulated manifolds and parametric manifolds. We extend the short time image enhancing Beltrami kernel from 2D images to these manifold representations. This approach suits also other manifold representations that can be easily converted to triangulated manifolds, such as implicit manifolds and point clouds. The arbitrary time step enabled by the use of the kernel filtering approach offers a tradeoff between the accuracy of the flow and its execution time. The numerical scheme used to construct the kernel makes the method applicable to all types of manifolds, including open manifolds and self intersecting manifolds. The calculations are done on the 2D manifold itself and are not affected by the complexity of the manifold or the dimension of the space in which it is embedded. The method is demonstrated on images painted on synthetic manifolds and is used to selectively smooth face images. Incorporating the geometrical information of the face manifolds in the regularization process yields improved results.