Non uniform multiresolution method for optical flow computation

Cohen, Isaac; Herlin, Isabelle

doi:10.1007/3-540-76076-8_144

Cited by 40 publications

(63 citation statements)

References 9 publications

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“…• the Horn and Schunck (HS) model (Horn and Schunck 1981), • a discontinuity preserving optical flow model (Black and Anandan 1991;Cohen 1993;Weickert 1998), and • the combined local global (CLG) model (Bruhn et al 2002;Bruhn et al 2005). …”

Section: Optical Flow Computationsmentioning

confidence: 99%

“…Sect. 4.1) on the velocity components u and v. Discontinuity-preserving optical flow (Black and Anandan 1993;Cohen 1993;Weickert 1998) contains the same data term as in E HS , but it uses a nonlinear regularization term instead of a linear one. This nonlinear regularization boils down to Perona Malik nonlinear diffusion as in Sect.…”

Section: Discontinuity-preserving Optical Flow Computationmentioning

confidence: 99%

“…We demonstrate the usage of the formalism by exemplary implementations of very well known and thus well understood algorithms: Gaussian smoothing via isotropic diffusion, Perona-Malik isotropic nonlinear diffusion (Perona and Malik 1990), variational optical flow estimation by Horn-Schunck (1981), a version with a robust smoothing term (Black and Anandan 1991;Cohen 1993;Weickert 1998) and optical flow computation with a regularized data term (Bruhn et al 2005). These algorithms are prototypes of linear and nonlinear, energy-based computer vision approaches for regularization, noise suppression, and parameter estimation with a wealth of practical applications.…”

Section: Introductionmentioning

confidence: 99%

“…4 the stochastic generalization of some well known PDEs used in computer vision is presented and discretized with help of the building blocks. We consider a linear and a nonlinear diffusion (Perona and Malik 1990) model, the optical flow extraction with the Horn and Schunck approach (Horn and Schunck 1981), a robust smoothing term for the optical flow field (Black and Anandan 1993;Cohen 1993;Weickert 1998), and finally a combined local global (CLG) approach (Bruhn et al 2005). An investigation of the bias of the CLG model further underlines the usefulness of our framework.…”

Section: Introductionmentioning

confidence: 99%

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Building Blocks for Computer Vision with Stochastic Partial Differential Equations

et al. 2008

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We discuss the basic concepts of computer vision with stochastic partial differential equations (SPDEs). In typical approaches based on partial differential equations (PDEs), the end result in the best case is usually one value per pixel, the "expected" value. Error estimates or even full probability density functions PDFs are usually not available. This paper provides a framework allowing one to derive such PDFs, rendering computer vision approaches into measurements fulfilling scientific standards due to full error propagation. We identify the image data with random fields in order to model images and image sequences which carry uncertainty in their gray values, e.g. due to noise in the acquisition process. The noisy behaviors of gray values is modeled as stochastic processes which are approximated with the method of generalized polynomial chaos (Wiener-Askey-Chaos). The Wiener-Askey polynomial chaos is combined with a standard spatial approxi- We present the basic building blocks needed for computer vision and image processing in this stochastic setting, i.e. we discuss the computation of stochastic moments, projections, gradient magnitudes, edge indicators, structure tensors, etc. Finally we show applications of our framework to derive stochastic analogs of well known PDEs for denoising and optical flow extraction. These models are discretized with the stochastic Galerkin method. Our selection of SPDE models allows us to draw connections to the classical deterministic models as well as to stochastic image processing not based on PDEs. Several examples guide the reader through the presentation and show the usefulness of the framework.

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Section: Optical Flow Computationsmentioning

confidence: 99%

Section: Discontinuity-preserving Optical Flow Computationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Building Blocks for Computer Vision with Stochastic Partial Differential Equations

et al. 2008

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“…While the development of better matching and regularization criteria as well as more effective optimization techniques has significantly advanced the state of the art [1][2][3][4][5][6][7][8][9], the parameters of these methods are generally set by hand on the same data that is used for evaluation. Although there has recently been some work on learning for optical flow, such as [10], the relative lack of investigation of learning techniques stands in sharp contrast with higher-level vision such as object recognition, where learning techniques are ubiquitous.…”

Section: Introductionmentioning

confidence: 99%

Learning for Optical Flow Using Stochastic Optimization

Liu

Huttenlocher

2008

Lecture Notes in Computer Science

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Abstract. We present a technique for learning the parameters of a continuousstate Markov random field (MRF) model of optical flow, by minimizing the training loss for a set of ground-truth images using simultaneous perturbation stochastic approximation (SPSA). The use of SPSA to directly minimize the training loss offers several advantages over most previous work on learning MRF models for low-level vision, which instead seek to maximize the likelihood of the data given the model parameters. In particular, our approach explicitly optimizes the error criterion used to evaluate the quality of the flow field, naturally handles missing data values in the ground truth, and does not require the kinds of approximations that current methods use to address the intractable nature of maximum-likelihood estimation for such problems. We show that our method achieves state-of-the-art results and requires only a very small number of training images. We also find that our method generalizes well to unseen data, including data with quite different characteristics than the training set.

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Adaptive vs. non-adaptive strategies for the computation of optical flow

Condell

Scotney²,

Morrow³

2006

Int. J. Imaging Syst. Technol.

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Confident adaptive algorithms are described, evaluated, and compared with other algorithms that implement the estimation of motion. A Galerkin finite element adaptive approach is described for computing optical flow, which uses an adaptive triangular mesh in which the resolution increases where motion is found to occur. The mesh facilitates a reduction in computational effort by enabling processing to focus on particular objects of interest in a scene. Compared with other state-of-the-art methods in the literature our adaptive methods show only motion where main movement is known to occur, indicating a methodological improvement. The mesh refinement, based on detected motion, gives an alternative to methods reported in the literature, where the adaptation is usually based on a gradient intensity measure. A confidence is calculated for the detected motion and if this measure passes the threshold then the motion is used in the adaptive mesh refinement process. The idea of using the reliability hypothesis test is straightforward. The incorporation of the confidence serves the purpose of increasing the optical flow determination reliability. Generally, the confident flow seems most consistent, accurate and efficient, and focuses on the main moving objects within the image.

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Non uniform multiresolution method for optical flow computation

Cited by 40 publications

References 9 publications

Building Blocks for Computer Vision with Stochastic Partial Differential Equations

Building Blocks for Computer Vision with Stochastic Partial Differential Equations

Learning for Optical Flow Using Stochastic Optimization

Adaptive vs. non-adaptive strategies for the computation of optical flow

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