Regularizing optical-flow computation using tensor theory and complex analysis

Koppel, D.; Tsai, Chuen-Tinn; Wang, Yuan-Fang

doi:10.1109/cvprw.2008.4562971

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…For example, in Ref. 26, a regularization scheme is derived that is the most general regularization not penalizing rigid body motion, making it a natural regularization scheme for flows that are combinations of pure rotations, translations, etc. Mathematically, it means that the computation of the flow takes place in a highly restricted space of affine mappings, but it is more important to analyze the properties of such functions than it is to define and analyze the space rigorously.…”

Section: A Regularization Of the Potential Functionmentioning

confidence: 99%

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A framework for estimating potential fluid flow from digital imagery

Luttman

Bollt

Basnayake

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Given image data of a fluid flow, the flow field, , governing the evolution of the system can be estimated using a variational approach to optical flow. Assuming that the flow field governing the advection is the symplectic gradient of a stream function or the gradient of a potential function-both falling under the category of a potential flow-it is natural to re-frame the optical flow problem to reconstruct the stream or potential function directly rather than the components of the flow individually. There are several advantages to this framework. Minimizing a functional based on the stream or potential function rather than based on the components of the flow will ensure that the computed flow is a potential flow. Next, this approach allows a more natural method for imposing scientific priors on the computed flow, via regularization of the optical flow functional. Also, this paradigm shift gives a framework--rather than an algorithm--and can be applied to nearly any existing variational optical flow technique. In this work, we develop the mathematical formulation of the potential optical flow framework and demonstrate the technique on synthetic flows that represent important dynamics for mass transport in fluid flows, as well as a flow generated by a satellite data-verified ocean model of temperature transport.

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Section: A Regularization Of the Potential Functionmentioning

confidence: 99%

“…The regularization R 4 comes from the "engineering strain tensor" formulation of optical flow, a full description and explanation of which can be found in Ref. 26. Finally, R 5 is the potential and stream function form of the first-order "divcurl" regularization proposed by Suter.…”

Section: A Regularization Of the Potential Functionmentioning

confidence: 99%

A framework for estimating potential fluid flow from digital imagery

Luttman

Bollt

Basnayake

et al. 2013

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The main drawback of these approaches is the smoothing of the optical flow field at motion and object boundaries. Koppel et al [9] have shown, that the regularization terms are only valid for 2d translatory motion and penalize valid changes in the motion field. Matching based approaches can handle arbitrary large motion vectors as long as the image distortion due to perspective effects is small.…”

Section: Introductionmentioning

confidence: 99%

Block-matching based optical flow estimation with reduced search space based on geometric constraints

Kitt

Ranft

Lategahn

2010

13th International IEEE Conference on Intelligent Transportation Systems

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In this paper we propose a new block-matching based approach for the estimation of nearly dense optical flow fields in image sequences. We focus on applications to autonomous vehicles where a dominant movement of the camera along its optical axis is present. The presented algorithm exploits the geometric relations between the two viewpoints induced by the epipolar geometry, hence it is applicable for the static parts of the scene. These relations are used to remap the images so that the resulting virtual images are similar to images captured by an axial stereo camera setup. This alignment dramatically reduces the computational complexity of the correspondence search and avoids false correspondences e.g. caused by repeated patterns. Experiments on challenging realworld sequences show the accuracy of the proposed approach.

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Rapid Optical Flow Computation Based on Multigrid

Xie

Liu

Wang

et al. 2011

AMR

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In order to make optical flow methods suitable for real-time applications, this paper presents a rapid optical flow computation method based on multigrid. Multigrid computation method is well known for being the fastest numerical method when solving elliptic boundary-value problems, so we integrate multigrid into Horn-Schunck algorithm in order to obtain rapid computation. Firstly, we analyze the convergence process of traditional methods for optical flow computation; secondly, we combine the multigrid method with Horn-Schunck method, and in this way optical flow can be calculated efficiently; finally, the experiments show that our rapid optical flow computation method is efficient for target detection and video tracking systems.

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Regularizing optical-flow computation using tensor theory and complex analysis

Abstract: This paper reports a technique that improves the robustness and accuracy in computing dense

Cited by 3 publications

References 14 publications

A framework for estimating potential fluid flow from digital imagery

A framework for estimating potential fluid flow from digital imagery

Block-matching based optical flow estimation with reduced search space based on geometric constraints

Rapid Optical Flow Computation Based on Multigrid

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