Lower semicontinuity of the affine total variation used in image segmentation

Ballester, Coloma; Caselles, Vicente; González Hidalgo, Manuel

Lower semicontinuity of the affine total variation used in image segmentation

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Ballester C, Caselles V, González M. Lower semicontinuity of the affine total variation used in image segmentation. Revista de la Unión Matemática Argentina. 1998 Jan;41(1):41-60.

Abstract

We study the Affine Total Variation, a magnitude measuring the affine complexity of finite unions of continua, in particular, Jordan curves, appearing in an affine invariant analogue of Mumford-Shah energy functional used to segment images. We prove a lower semicontinuity result for the ATV functional.