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• W1652337965 abstract "This work combines three paradigms of image processing: i) the total variation approach to denoising, ii) the superior structure of hexagonal lattices, and iii) fast and exact graph cut optimization techniques. Although isotropic in theory, numerical implementations of the $BV$ seminorm invariably show anisotropic behaviour. Discretization of the image domain into a hexagonal grid seems perfectly suitable to mitigate this undesirable effect. To this end, we recast the continuous problem as a finite-dimensional one on an arbitrary lattice, before focussing on the comparison of Cartesian and hexagonal structures. Minimization is performed with well-established graph cut algorithms, which are easily adapted to new spatial discretizations. Apart from producing minimizers that are closer in the $ell^1$ sense to the clean image for sufficiently high degrees of regularization, our experiments suggest that the hexagonal lattice also allows for a more effective reduction of two major drawbacks of existing techniques: metrication artefacts and staircasing. For the sake of practical relevance we address the difficulties that naturally arise when dealing with non-standard images." @default.
• W1652337965 created "2016-06-24" @default.
• W1652337965 creator A5046803884 @default.
• W1652337965 date "2012-04-17" @default.
• W1652337965 modified "2023-09-27" @default.
• W1652337965 title "Total Variation Denoising on Hexagonal Grids" @default.
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• W1652337965 hasPublicationYear "2012" @default.
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