A finite algorithm for finding the projection of a point onto the Canonical simplex of Rn
Journal of Optimization Theory and Applications
Bayesian modeling of uncertainty in low-level vision
International Journal of Computer Vision
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing Geodesics and Minimal Surfaces via Graph Cuts
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
A Convex Formulation of Continuous Multi-label Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
An Experimental Comparison of Discrete and Continuous Shape Optimization Methods
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Projected Gradient Based Color Image Decomposition
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A duality based approach for realtime TV-L1 optical flow
Proceedings of the 29th DAGM conference on Pattern recognition
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Intermediate flow field filtering in energy based optic flow computations
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Completely Convex Formulation of the Chan-Vese Image Segmentation Model
International Journal of Computer Vision
A Variational Framework for Region-Based Segmentation Incorporating Physical Noise Models
Journal of Mathematical Imaging and Vision
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Convex relaxations for continuous multilabel problems have attracted a lot of interest recently [1,2,3,4,5]. Unfortunately, in previous methods, the runtime and memory requirements scale linearly in the total number of labels, making them very inefficient and often unapplicable for problems with higher dimensional label spaces. In this paper, we propose a reduction technique for the case that the label space is a product space, and introduce proper regularizers. The resulting convex relaxation requires orders of magnitude less memory and computation time than previously, which enables us to apply it to large-scale problems like optic flow, stereo with occlusion detection, and segmentation into a very large number of regions. Despite the drastic gain in performance, we do not arrive at less accurate solutions than the original relaxation. Using the novel method, we can for the first time efficiently compute solutions to the optic flow functional which are within provable bounds of typically 5% of the global optimum.