Plane curves of minimal energy
ACM Transactions on Mathematical Software (TOMS)
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
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Fast texture synthesis using tree-structured vector quantization
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
ACM Transactions on Mathematical Software (TOMS)
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: modeling, learning, sampling and computing, Part I
Filtering, Segmentation, and Depth
Filtering, Segmentation, and Depth
Segmentation with Depth but Without Detecting Junctions
Journal of Mathematical Imaging and Vision
Texture Synthesis by Non-Parametric Sampling
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional
International Journal of Computer Vision
Total Variation Wavelet Inpainting
Journal of Mathematical Imaging and Vision
Image Super-Resolution by TV-Regularization and Bregman Iteration
Journal of Scientific Computing
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
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
Method to approximate the space curve of least energy and prescribed length
Computer-Aided Design
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise
SIAM Journal on Scientific Computing
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Removing Multiplicative Noise by Douglas-Rachford Splitting Methods
Journal of Mathematical Imaging and Vision
An axiomatic approach to image interpolation
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Filling-in by joint interpolation of vector fields and gray levels
IEEE Transactions on Image Processing
Disocclusion: a variational approach using level lines
IEEE Transactions on Image Processing
Simultaneous structure and texture image inpainting
IEEE Transactions on Image Processing
Graph Cuts for Curvature Based Image Denoising
IEEE Transactions on Image Processing
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Image Denoising Using Mean Curvature of Image Surface
SIAM Journal on Imaging Sciences
Lagrangian multipliers and split Bregman methods for minimization problems constrained on Sn-1
Journal of Visual Communication and Image Representation
Image Segmentation Using Euler's Elastica as the Regularization
Journal of Scientific Computing
Image Restoration via Tight Frame Regularization and Local Constraints
Journal of Scientific Computing
A Combined First and Second Order Variational Approach for Image Reconstruction
Journal of Mathematical Imaging and Vision
Convex Relaxation of a Class of Vertex Penalizing Functionals
Journal of Mathematical Imaging and Vision
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Minimization of functionals related to Euler's elastica energy has a wide range of applications in computer vision and image processing. A high order nonlinear partial differential equation (PDE) needs to be solved, and the gradient descent method usually takes high computational cost. In this paper, we propose a fast and efficient numerical algorithm to solve minimization problems related to Euler's elastica energy and show applications to variational image denoising, image inpainting, and image zooming. We reformulate the minimization problem as a constrained minimization problem, followed by an operator splitting method and relaxation. The proposed constrained minimization problem is solved by using an augmented Lagrangian approach. Numerical tests on real and synthetic cases are supplied to demonstrate the efficiency of our method.