  Curvature has received increased attention as an important alternative to
length based regularization in computer vision. In contrast to length, it
preserves elongated structures and fine details. Existing approaches are either
inefficient, or have low angular resolution and yield results with strong block
artifacts. We derive a new model for computing squared curvature based on
integral geometry. The model counts responses of straight line triple cliques.
The corresponding energy decomposes into submodular and supermodular pairwise
potentials. We show that this energy can be efficiently minimized even for high
angular resolutions using the trust region framework. Our results confirm that
we obtain accurate and visually pleasing solutions without strong artifacts at
reasonable run times.
