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19
Reliable Estimation of Dense Optical Flow Fields with Large Displacements
, 2001
"... In this paper we show that a classic optical ow technique by Nagel and Enkelmann (1986) can be regarded as an early anisotropic diusion method with a diusion tensor. We introduce three improvements into the model formulation that (i) avoid inconsistencies caused by centering the brightness term and ..."
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Cited by 97 (11 self)
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In this paper we show that a classic optical ow technique by Nagel and Enkelmann (1986) can be regarded as an early anisotropic diusion method with a diusion tensor. We introduce three improvements into the model formulation that (i) avoid inconsistencies caused by centering the brightness term and the smoothness term in dierent images, (ii) use a linear scalespace focusing strategy from coarse to ne scales for avoiding convergence to physically irrelevant local minima, and (iii) create an energy functional that is invariant under linear brightness changes. Applying a gradient descent method to the resulting energy functional leads to a system of diusion{reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an ecient linear implicit numerical scheme in detail. Our method creates ow elds with 100 % density over the entire image domain, it is robust under a large range of parameter variations, and it c...
A Theoretical Framework for Convex Regularizers in PDEBased Computation of Image Motion
, 2000
"... Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness consta ..."
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Cited by 77 (20 self)
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Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for datadriven and flowdriven, isotropic and anisotropic, as well as spatial and spatiotemporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are wellposed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flowdriven regularizers is identified, and a design criterion is proposed for constructing anisotropic flowdriven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.
Recursive Filters for Optical Flow
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... : Working toward ecient (realtime) implementations of optical ow methods, we have applied simple recursive lters to achieve temporal smoothing and dierentiation of image intensity, and to compute 2d ow from component velocity constraints using spatiotemporal leastsquares minimization. Accuracy in ..."
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Cited by 38 (1 self)
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: Working toward ecient (realtime) implementations of optical ow methods, we have applied simple recursive lters to achieve temporal smoothing and dierentiation of image intensity, and to compute 2d ow from component velocity constraints using spatiotemporal leastsquares minimization. Accuracy in simulation is similar to that obtained in the study by Barron et al. [3], while requiring much less storage, less computation, and shorter delays. 1 Introduction Many methods exist for computing optic ow, but few currently run at frame rates on reasonably priced, conventional hardware. The goal of this paper is to outline simplications to a successful gradientbased approach that reduce computational expense with little degradation in accuracy. Our specic concerns include temporal smoothing and dierentiation of image intensity, and temporal integration of component velocity constraints to solve for 2d velocity. More generally, we are working toward ecient implementations of dierent...
Velocity Likelihoods in Biological and Machine Vision
 In Probabilistic Models of the Brain: Perception and Neural Function
, 2001
"... Recent approaches to estimating twodimensional image motion and to modeling the perception of image motion have achieved success with Bayesian formulations. With a Bayesian approach, the goal is to compute the posterior probability distribution of velocity, which is proportional to a likelihood ..."
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Cited by 35 (4 self)
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Recent approaches to estimating twodimensional image motion and to modeling the perception of image motion have achieved success with Bayesian formulations. With a Bayesian approach, the goal is to compute the posterior probability distribution of velocity, which is proportional to a likelihood function and a prior. The likelihood function describes the probability of observing the image data given the image velocity; surprisingly, there is still disagreement about the right likelihood function to use. Here we derive a likelihood function by starting from a generative model. We assume that the scene translates, conserving image brightness, while the image is equal to the projected scene plus noise. We discuss the connection between the resulting likelihood function and existing models of motion analysis. We show that the likelihood can be calculated by a population of units whose response properties are similar to \motion energy" units. This suggests that a population o...
Match Propagation for ImageBased Modeling and Rendering
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2002
"... This paper presents a quasidense matching algorithm between images based on match propagation principle. The algorithm starts from a set of sparse seed matches, then propagates to the neighboring pixels by the best rst strategy, and produces a quasidense disparity map. The quasidense matching ..."
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Cited by 35 (6 self)
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This paper presents a quasidense matching algorithm between images based on match propagation principle. The algorithm starts from a set of sparse seed matches, then propagates to the neighboring pixels by the best rst strategy, and produces a quasidense disparity map. The quasidense matching aims at broad modeling and visualization applications which rely heavily on matching information. Our algorithm is robust to initial sparse match outliers due to the best rst strategy; It is ecient in time and space as it is only output sensitive; It handles halfoccluded areas because of the simultaneous enforcement of newly introduced discrete 2D gradient disparity limit and the uniqueness constraint. The properties of the algorithm are discussed and empirically demonstrated.
Optimal Structure from Motion: Local Ambiguities and Global Estimates
, 2000
"... “Structure From Motion” (SFM) refers to the problem of estimating spatial properties of a threedimensional scene from the motion of its projection onto a twodimensional surface, such as the retina. We present an analysis of SFM which results in algorithms that are provably convergent and provably o ..."
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Cited by 22 (5 self)
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“Structure From Motion” (SFM) refers to the problem of estimating spatial properties of a threedimensional scene from the motion of its projection onto a twodimensional surface, such as the retina. We present an analysis of SFM which results in algorithms that are provably convergent and provably optimal with respect to a chosen norm. In particular, we cast SFM as the minimization of a highdimensional quadratic cost function, and show how it is possible to reduce it to the minimization of a twodimensional function whose stationary points are in onetoone correspondence with those of the original cost function. As a consequence, we can plot the reduced cost function and characterize the configurations of structure and motion that result in local minima. As an example, we discuss two local minima that are associated with wellknown visual illusions. Knowledge of the topology of the residual in the presence of such local minima allows us to formulate minimization algorithms that, in addition to provably converge to stationary points of the original cost function, can switch between different local extrema in order to converge to the global minimum, under suitable conditions. We also offer an experimental study of the distribution of the estimation error in the presence of noise in the measurements, and characterize the sensitivity of the algorithm using the structure of Fisher’s Information matrix.
Non Uniform Multiresolution Method for Optical Flow and Phase Portrait Models: Environmental Applications
 International Journal of Computer Vision
, 1999
"... . In this paper we dene a complete framework for processing large image sequences for a global monitoring of short range oceanographic and atmospheric processes. This framework is based on the use of a non quadratic regularization technique in optical ow computation that preserves ow discontinuities ..."
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Cited by 13 (2 self)
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. In this paper we dene a complete framework for processing large image sequences for a global monitoring of short range oceanographic and atmospheric processes. This framework is based on the use of a non quadratic regularization technique in optical ow computation that preserves ow discontinuities. We also show that using an appropriate tessellation of the image according to an estimate of the motion eld can improve optical ow accuracy and yields more reliable ows. This method denes a non uniform multiresolution approach for coarse to ne grid generation. It allows to locally increase the resolution of the grid according to the studied problem. Each added node renes the grid in a region of interest and increases the numerical accuracy of the solution in this region. We make use of such a method for solving the optical ow equation with a non quadratic regularization scheme allowing the computation of optical ow eld while preserving its discontinuities. The second part of th...
Motionbased Segmentation and Contourbased Classification of Video Objects
, 2001
"... The segmentation of objects in video sequences constitutes a prerequisite for numerous applications ranging from computer vision tasks to secondgeneration video coding. ..."
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Cited by 8 (0 self)
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The segmentation of objects in video sequences constitutes a prerequisite for numerous applications ranging from computer vision tasks to secondgeneration video coding.
On the Fourier Properties of Discontinuous Motion
 Journal of Mathematical Imaging and Vision
, 2000
"... . Retinal image motion and optical ow as its approximation are fundamental concepts in the eld of vision, perceptual and computational. However, the computation of optical ow remains a challenging problem as image motion includes discontinuities and multiple values mostly due to scene geometry, surf ..."
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Cited by 8 (0 self)
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. Retinal image motion and optical ow as its approximation are fundamental concepts in the eld of vision, perceptual and computational. However, the computation of optical ow remains a challenging problem as image motion includes discontinuities and multiple values mostly due to scene geometry, surface translucency and various photometric eects such as reectance. In this contribution, we analyze image motion in the frequency space with respect to motion discontinuities and translucence. We derive the frequency structure of motion discontinuities due to occlusion and we demonstrate its various geometrical properties. The aperture problem is investigated and we show that the information content of an occlusion almost always disambiguates the velocity of an occluding signal suering from the aperture problem. In addition, the theoretical framework can describe the exact frequency structure of NonFourier motion and bridges the gap between NonFourier visual phenomena and their understanding in the frequency domain. Keywords: Image motion, optical ow, occlusion, aperture problem, nonFourier motion 1.