Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Performance of optical flow techniques
International Journal of Computer Vision
Numerical solution of partial differential equations
Numerical solution of partial differential equations
The robust estimation of multiple motions: parametric and piecewise-smooth flow fields
Computer Vision and Image Understanding
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Introductory Techniques for 3-D Computer Vision
Introductory Techniques for 3-D Computer Vision
Computer Vision: Three-Dimensional Data from Images
Computer Vision: Three-Dimensional Data from Images
SIAM Journal on Scientific Computing
Hierarchical Estimation and Segmentation of Dense Motion Fields
International Journal of Computer Vision
A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms
International Journal of Computer Vision
Advances in Computational Stereo
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Over-Parameterized Variational Optical Flow
International Journal of Computer Vision
Hyperbolic Numerics for Variational Approaches to Correspondence Problems
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
An iterative image registration technique with an application to stereo vision
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 2
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Novel schemes for hyperbolic PDEs using osmosis filters from visual computing
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
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Optic flow and stereo reconstruction are important examples of correspondence problems in computer vision. Correspondence problems have been studied for almost 30 years, and energy-based methods such as variational approaches have become popular for solving this task. However, despite the long history of research in this field, only little attention has been paid to the numerical approximation of derivatives that naturally occur in variational approaches.In this paper we show that strategies from hyperbolic numerics can lead to a significant quality gain in computational results. Starting from a basic formulation of correspondence problems, we take on a novel perspective on the mathematical model. Switching the roles of known and unknown with respect to image data and displacement field, we use the arising hyperbolic colour equation as a basis for a refined numerical approach. For its discretisation, we propose to use one-sided differences in the correct direction identified via a smooth predictor solution. The one-sided differences that are first-order accurate are blended with higher-order central schemes. Thereby the blending mechanism interpolates between the following two situations: The one-sided method is employed at image edges which often coincide with edges in the displacement field. In smooth image parts the higher-order scheme is used. We apply our new scheme to several prototypes of variational models for optic flow and stereo reconstruction, where we achieve significant qualitative improvements compared to standard discretisations.