Estimation of vector fields in unconstrained and inequality constrained variational problems for segmentation and registration

Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well.We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach

SceneFlowFields: Dense Interpolation of Sparse Scene Flow Correspondences

While most scene flow methods use either variational optimization or a strong rigid motion assumption, we show for the first time that scene flow can also be estimated by dense interpolation of sparse matches. To this end, we find sparse matches across two stereo image pairs that are detected without any prior regularization and perform dense interpolation preserving geometric and motion boundaries by using edge information. A few iterations of variational energy minimization are performed to refine our results, which are thoroughly evaluated on the KITTI benchmark and additionally compared to state-of-the-art on MPI Sintel. For application in an automotive context, we further show that an optional ego-motion model helps to boost performance and blends smoothly into our approach to produce a segmentation of the scene into static and dynamic parts.Comment: IEEE Winter Conference on Applications of Computer Vision (WACV), 201

Colour image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution

We propose a new method for the numerical solution of a PDE-driven model for colour image segmentation and give numerical examples of the results. The method combines the vector-valued Allen-Cahn phase field equation with initial data fitting terms. This method is known to be closely related to the Mumford-Shah problem and the level set segmentation by Chan and Vese. Our numerical solution is performed using a multigrid splitting of a finite element space, thereby producing an efficient and robust method for the segmentation of large images.Comment: 17 pages, 9 figure