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.
Qualitative and Quantitative Behaviour of Geometrical PDEs in Image Processing
Asian Conference on Computer Vision ; 2007 ; Tokyo, Japan November 18, 2007 - November 22, 2007
2007-01-01
10 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Order Derivative , Qualitative Behaviour , Large Time Step , Curvature Motion , Geometrical Evolution Computer Science , Image Processing and Computer Vision , Computer Imaging, Vision, Pattern Recognition and Graphics , Pattern Recognition , Artificial Intelligence , Biometrics , Algorithm Analysis and Problem Complexity
Geometrical PDEs based on second-order derivatives of gauge coordinates in image processing
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