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. II
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
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
Understanding and Modeling the Evolution of Critical Points under Gaussian Blurring
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Shape Metamorphism using p-Laplacian Equation
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Exploring and exploiting the structure of saddle points in Gaussian scale space
Computer Vision and Image Understanding
Geometrical PDEs based on second-order derivatives of gauge coordinates in image processing
Image and Vision Computing
Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
A four-pixel scheme for singular differential equations
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
An axiomatic approach to image interpolation
IEEE Transactions on Image Processing
PDE-based image restoration: a hybrid model and color image denoising
IEEE Transactions on Image Processing
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In this work, we take a novel line of approaches to evolve images. It is motivated by the total variation method, known for its denoising and edge-preserving effect. Our approach generalises the TV method by taking a general L p norm of the gradients instead of the L 1 in the TV method. We generalise this method in a series of first and second order derivatives in terms of gauge coordinates. This method also incorporates the well-known blurring by a Gaussian filter and the balanced forward--backward diffusion.The method and its properties are briefly discussed. The practical results are visualised on a real-life image, showing the expected behaviour. When a constraint is added that penalises the distance of the results to the input image, one can vary the desired amount of blurring and denoising.