Efficient Regularization of Squared Curvature
This work addresses the need for efficient and high-resolution curvature regularization to preserve elongated structures and fine details in computer vision applications, representing an incremental improvement over existing methods.
The paper tackled the problem of inefficient and low-resolution curvature regularization in computer vision by deriving a new model based on integral geometry, resulting in accurate and visually pleasing solutions without strong artifacts at reasonable run times.
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.