Relaxation methods for liquid crystal problems
SIAM Journal on Numerical Analysis
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
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
International Journal of Computer Vision
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
QAPLIB – A Quadratic Assignment ProblemLibrary
Journal of Global Optimization
Numerical Methods for p-Harmonic Flows and Applications to Image Processing
SIAM Journal on Numerical Analysis
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Convergent Discrete Laplace-Beltrami Operators over Triangular Surfaces
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Applied Numerical Mathematics
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
A Curvilinear Search Method for $p$-Harmonic Flows on Spheres
SIAM Journal on Imaging Sciences
Optimization algorithms exploiting unitary constraints
IEEE Transactions on Signal Processing
IEEE Transactions on Image Processing
Color image enhancement via chromaticity diffusion
IEEE Transactions on Image Processing
Trust, But Verify: Fast and Accurate Signal Recovery From 1-Bit Compressive Measurements
IEEE Transactions on Signal Processing
Fast regularization of matrix-valued images
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Folding-Free Global Conformal Mapping for Genus-0 Surfaces by Harmonic Energy Minimization
Journal of Scientific Computing
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Orthogonality constrained problems are widely used in science and engineering. However, it is challenging to solve these problems efficiently due to the non-convex constraints. In this paper, a splitting method based on Bregman iteration is represented to tackle the optimization problems with orthogonality constraints. With the proposed method, the constrained problems can be iteratively solved by computing the corresponding unconstrained problems and orthogonality constrained quadratic problems with analytic solutions. As applications, we demonstrate the robustness of our method in several problems including direction fields correction, noisy color image restoration and global conformal mapping for genus-0 surfaces construction. Numerical comparisons with existing methods are also conducted to illustrate the efficiency of our algorithms.