Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Scale and the differential structure of images
Image and Vision Computing - Special issue: information processing in medical imaging 1991
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
Fields of Experts: A Framework for Learning Image Priors
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Image Sequence Interpolation Using Optimal Control
Journal of Mathematical Imaging and Vision
MMW image reconstruction combined NNSC shrinkage technique and PDEs algorithm
ICIC'11 Proceedings of the 7th international conference on Advanced Intelligent Computing Theories and Applications: with aspects of artificial intelligence
Toward designing intelligent PDEs for computer vision: An optimal control approach
Image and Vision Computing
Low-resolution image restoration using the combination method of sparse representation and PDE model
ICIC'13 Proceedings of the 9th international conference on Intelligent Computing Theories
Hi-index | 0.00 |
Partial differential equations (PDEs) have been successfully applied to many computer vision and image processing problems. However, designing PDEs requires high mathematical skills and good insight into the problems. In this paper, we show that the design of PDEs could be made easier by borrowing the learning strategy from machine learning. In our learning-based PDE (L-PDE) framework for image restoration, there are two terms in our PDE model: (i) a regularizer which encodes the prior knowledge of the image model and (ii) a linear combination of differential invariants, which is data-driven and can effectively adapt to different problems and complex conditions. The L-PDE is learnt from some input/output pairs of training samples via an optimal control technique. The effectiveness of our L-PDE framework for image restoration is demonstrated with two exemplary applications: image denoising and inpainting, where the PDEs are obtained easily and the produced results are comparable to or better than those of traditional PDEs, which were elaborately designed.