A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion
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
Relations Between Regularization and Diffusion Filtering
Journal of Mathematical Imaging and Vision
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
A Non-Local Algorithm for Image Denoising
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's
International Journal of Computer Vision
Stability Properties of the Perona--Malik Scheme
SIAM Journal on Numerical Analysis
Preserving topological information in the windowed hough transform for rectangle extraction
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Analysis of Superimposed Oriented Patterns
IEEE Transactions on Image Processing
A Short- Time Beltrami Kernel for Smoothing Images and Manifolds
IEEE Transactions on Image Processing
Nonlinear Regularized Reaction-Diffusion Filters for Denoising of Images With Textures
IEEE Transactions on Image Processing
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Image restoration and simplification methods that respect important features such as edges play a fundamental role in digital image processing. However, known edge-preserving methods like common nonlinear diffusion methods tend to round vertices for large diffusion times. In this paper, we adapt the diffusion tensor for anisotropic diffusion to avoid this effects in images containing rotated and sheared rectangles, respectively. In this context, we propose a new method for estimating rotation angles and shear parameters based on the so-called structure tensor. Further, we show how the knowledge of appropriate diffusion tensors can be used in variational models. Numerical examples including orientation estimation, denoising and segmentation demonstrate the good performance of our methods.