Citation Context

...important to use a data term which matches the expected noise model. 4.3 Variational models with possibly nonconvex data terms The approach in this section is described with more details in the paper =-=[64]-=-. Let us consider the problem of finding the minimizer of an energy functional F : L 1 (Ω) → [0, ∞] of the form { ∫ } min F(u) = f(x,u(x), ∇u(x))dx , (64) u Ω where Ω is a d-dimensional bounded open s...

Citation Context

...ture of light field data and much more robust than traditional stereo matching methods to non-Lambertian objects. 1 • We introduce a labeling scheme based on state-of-theart convex relaxation methods =-=[17, 21]-=-, which allows to estimate globally consistent depth maps which satisfy visibility constraints for all (possibly hundreds of) views simultaneously. The robustness of our method is demonstrated on a la...

Citation Context

...e associated saddle point problem [PCBC09a]. By lifting the objective to a higher dimensional space, it turns out that the same method can be used to solve many problems also with nonlinear data term =-=[PCBC09b]-=-. Our approach is a generalization of [ZGFN08, LKY+09], where a similar linearization is used with the regularizer restricted to the Potts distance, and with less strong convergence results. These met...

Citation Context

...on techniques for energy minimization in computer vision. Particular efforts were directed towards multilabel problems, as they lie at the heart of fundamental problems like segmentation [15], stereo =-=[17]-=-, 3D reconstruction [7] and optic flow [9]. In multilabel problems, we are looking for a pointwise labeling u : Ω → Γ of a domain Ω ⊂ R n which is optimal in the following sense. Assigning the label γ...

Citation Context

...ccess in optical flowRobust Trajectory-Space TV-L1 Optical Flow for Non-rigid Sequences 3 computation, this optimization scheme has since been successfully applied to motion and disparity estimation =-=[17]-=- and real time dense 3D reconstruction [18]. Non-rigid image registration, is a long standing field that has recently seen important progress in its robust estimation in the case of severe deformation...

Citation Context

...lelized using graphics hardware (Zach et al. 2007). Following its success in optical flow computation, this optimization scheme has since been successfully applied to motion and disparity estimation (=-=Pock et al. 2010-=-) and real time dense 3D reconstruction (Newcombe et al. 2011; Stuehmer et al. 2010). In this work we adopt this efficient duality based TV-L 1 optimization scheme (Zach et al. 2007) and extend it to ...

Citation Context

.... These bilinear saddle point problems are very useful in the context of labeling [4, 12, 14], and – using a “lifting” technique – can be used to minimize a large class of common variational problems =-=[18]-=-. As these problems are generally convex, they do not suffer from local minima, which allows to clearly separate modelling from optimization aspects. The inner problem turns out to be a convenient way...

Citation Context

...ll pairs of neighboring pixels. One important practical advantage of this basic energy is that there are efficient methods for their global minimization using graph cuts [4] or continuous relaxations =-=[5, 18]-=-. In many applications the appearance models may not be known a priori. Some well-known approaches to segmentation [25, 19, 6] consider model parameters as extra optimization variables in their segmen...

Citation Context

...for the homogeneous case. Non-homogeneous regularizers constitute an interesting direction for future work. In particular, such regularizers naturally occur when applying convex relaxation techniques =-=[1,25]-=- in order to solve nonconvex variational problems. With the increasing computational power, such techniques have become quite popular recently. For problems where the convexity is confined to the data...