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
A General Framework for Geometry-Driven Evolution Equations
International Journal of Computer Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Front-End Vision and Multi-Scale Image Analysis: Multi-scale Computer Vision Theory and Applications, written in Mathematica
Modified curvature motion for image smoothing and enhancement
IEEE Transactions on Image Processing
An axiomatic approach to image interpolation
IEEE Transactions on Image Processing
Simultaneous structure and texture image inpainting
IEEE Transactions on Image Processing
Geometrical PDEs based on second-order derivatives of gauge coordinates in image processing
Image and Vision Computing
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We analyse a series of approaches to evolve images. It is motivated by combining Gaussian blurring, the Mean Curvature Motion (used for denoising and edge-preserving), and maximal blurring (used for inpainting). We investigate the generalised method using the combination of second order derivatives in terms of gauge coordinates. For the qualitative behaviour, we derive a solution of the PDE series and mention its properties briefly. Relations with general diffusion equations are discussed. Quantitative results are obtained by a novel implementation whose stability and convergence is analysed. The practical results are visualised on a real-life image, showing the expected qualitative 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.