arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1102.3830cs.CVcs.AImath.OC

A linear framework for region-based image segmentation and inpainting involving curvature penalization

Lund University(隆德大学);Center for Mathematical Sciences(数学科学中心);Université de Lyon(里昂大学);Université Lyon 1(里昂第一大学);Institut Camille Jordan(卡米耶·若尔当研究所);TU München(慕尼黑工业大学)

Thomas Schoenemann, Fredrik Kahl, Simon Masnou, Daniel Cremers

英文摘要:

We present the first method to handle curvature regularity in region-based image segmentation and inpainting that is independent of initialization. To this end we start from a new formulation of length-based optimization schemes, based on surface continuation constraints, and discuss the connections to existing schemes. The formulation is based on a \emph{cell complex} and considers basic regions and boundary elements. The corresponding optimization problem is cast as an integer linear program. We then show how the method can be extended to include curvature regularity, again cast as an integer linear program. Here, we are considering pairs of boundary elements to reflect curvature. Moreover, a constraint set is derived to ensure that the boundary variables indeed reflect the boundary of the regions described by the region variables. We show that by solving the linear programming relaxation one gets quite close to the global optimum, and that curvature regularity is indeed much better suited in the presence of long and thin objects compared to standard length regularity.

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