Notes on Geometric Measure Theory Applications to Image Processing; De-noising, Segmentation, Pattern, Texture, Lines, Gestalt and Occlusion

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dc.creatorMorgan, Simon P
dc.date2006-05-29
dc.date2006-05-30
dc.date.accessioned2026-07-07T07:09:35Z
dc.date.available2026-07-07T07:09:35Z
dc.descriptionRegularization functionals that lower level set boundary length when used with L^1 fidelity functionals on signal de-noising on images create artifacts. These are (i) rounding of corners, (ii) shrinking of radii, (iii) shrinking of cusps, and (iv) non-smoothing of staircasing. Regularity functionals based upon total curvature of level set boundaries do not create artifacts (i) and (ii). An adjusted fidelity term based on the flat norm on the current (a distributional graph) representing the density of curvature of level sets boundaries can minimize (iii) by weighting the position of a cusp. A regularity term to eliminate staircasing can be based upon the mass of the current representing the graph of an image function or its second derivatives. Densities on the Grassmann bundle of the Grassmann bundle of the ambient space of the graph can be used to identify patterns, textures, occlusion and lines.
dc.description9 pages, no figures. This informal discussion paper will be updated periodically
dc.identifierhttps://arxiv.org/abs/cs/0605131
dc.identifierhttp://arxiv.org/abs/cs/0605131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111123
dc.subjectComputer Vision and Pattern Recognition
dc.titleNotes on Geometric Measure Theory Applications to Image Processing; De-noising, Segmentation, Pattern, Texture, Lines, Gestalt and Occlusion
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