SIAM Journal on Control and Optimization
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Convex analysis and variational problems
Convex analysis and variational problems
Motion of curves constrained on surfaces using a level-set approach
Journal of Computational Physics
Anisotropic diffusion of surfaces and functions on surfaces
ACM Transactions on Graphics (TOG)
Flows on surfaces of arbitrary topology
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Convergent Discrete Laplace-Beltrami Operators over Triangular Surfaces
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
International Journal of Computer Vision
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Geometric curve flows on parametric manifolds
Journal of Computational Physics
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Active Contour Based Segmentation of 3D Surfaces
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
Finite element approximation of elliptic partial differential equations on implicit surfaces
Computing and Visualization in Science
Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Computational conformal geometry and its applications to human brain mapping
Computational conformal geometry and its applications to human brain mapping
Surface processing methods for point sets using finite elements
Computers and Graphics
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
The piecewise smooth Mumford-Shah functional on an arbitrary graph
IEEE Transactions on Image Processing
Partial differences as tools for filtering data on graphs
Pattern Recognition Letters
SIAM Journal on Imaging Sciences
Regularization on discrete spaces
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
IEEE Transactions on Image Processing
Group-Valued regularization for analysis of articulated motion
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
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After many years of study, the subject of image processing on the plane, or more generally in Euclidean space is well developed. However, more and more practical problems in different areas, such as computer vision, computer graphics, geometric modeling, and medical imaging, inspire us to consider imaging on surfaces beyond imaging on Euclidean domains. Several approaches, such as implicit representation approaches and parameterization approaches, are investigated about image processing on surfaces. Most of these methods require certain preprocessing to convert image problems on surfaces to image problems in Euclidean spaces. In this work, we use differential geometry techniques to directly study image problems on surfaces. By using our approach, all plane image variation models and their algorithms can be naturally adapted to study image problems on surfaces. As examples, we show how to generalize Rudin-Osher-Fatemi (ROF) denoising model [1] and convexified Chan-Vese (CV) [2] segmentation model on surfaces, and then demonstrate how to adapt popular algorithms to solve the total variation related problems on surfaces. This intrinsic approach provides us a robust and efficient method to directly study image processing, in particular, total variation problems on surfaces without requiring any preprocessing.