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Titel
Convex Relaxation of a Class of Vertex Penalizing Functionals
Verfasser/ VerfasserinBredies, Kristian ; Pock, Thomas ; Wirth, Benedikt In der Gemeinsamen Normdatei der DNB nachschlagen
Erschienen in
Journal of mathematical imaging and vision : JMIV, New York, NY : Springer, 1.1992 -, Jg. 47, H. 3, S. 278-302
ErschienenSpringer
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)Variational methods / Convex relaxation / Higher order penalties / Roto-translation space / Vertex counting regularization / Total curvature regularization / Binary image segmentation / Image denoising / Image inpainting
Schlagwörter (GND)Bildverarbeitung / Bildsegmentierung / Variationsrechnung / Online-Publikation
ISSN0924-9907
URNurn:nbn:at:at-ubg:3-392 Persistent Identifier (URN)
DOIdoi:10.1007/s10851-012-0347-x 
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Convex Relaxation of a Class of Vertex Penalizing Functionals [3.24 mb]
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Zusammenfassung (Englisch)

We investigate a class of variational problems that incorporate in some sense curvature information of the level lines. The functionals we consider incorporate metrics defined on the orientations of pairs of line segments that meet in the vertices of the level lines. We discuss two particular instances: One instance that minimizes the total number of vertices of the level lines and another instance that minimizes the total sum of the absolute exterior angles between the line segments. In case of smooth level lines, the latter corresponds to the total absolute curvature. We show that these problems can be solved approximately by means of a tractable convex relaxation in higher dimensions. In our numerical experiments we present preliminary results for image segmentation, image denoising and image inpainting.

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