While different optical flow techniques continue to appear, there has been a lack of quantitative evaluation of existing methods. For a common set of real and synthetic image sequences, we report the results of a number of regularly cited optical flow techniques, including instances of differential, matching, energy-based and phase-based methods. Our comparisons are primarily empirical, and concentrate on the accuracy, reliability and density of the velocity measurements; they show that performance can differ significantly among the techniques we implemented.

Using known camera motion to estimate depth from image sequences is an important problem in robot vision. Many applications of depth-from-motion, including navigation and manipulation, require algorithms that can estimate depth in an on-line, incremental fashion. This requires a representation that records the uncertainty in depth estimates and a mechanism that integrates new measurements with existing depth estimates to reduce the uncertainty over time. Kalman filtering provides this mechanism. Previous applications of Kalman filtering to depth-from-motion have been limited to estimating depth at the location of a sparse set of features. In this paper, we introduce a new, pixel-based (iconic) algorithm that estimates depth and depth uncertainty at each pixel and incrementally refines these estimates over time. We describe the algorithm and contrast its formulation and performance to that of a feature-based Kalman filtering algorithm. We compare the performance of the two approaches by analyzing their theoretical convergence rates, by conducting quantitative experiments with images of a flat poster, and by conducting qualitative experiments with images of a realistic outdoor-scene model. The results show that the new method is an effective way to extract depth from lateral camera translations. This approach can be extended to incorporate general motion and to integrate other sources of information, such as stereo. The algorithms we have developed, which combine Kalman filtering with iconic descriptions of depth, therefore can serve as a useful and general framework for low-level dynamic vision.

We study an energy functional for computing optical flow that combines three assumptions: a brightness constancy assumption, a gradient constancy assumption, and a discontinuity-preserving spatio-temporal smoothness constraint.

Two-dimensional image motion is the projection of the three-dimensional motion of objects, relative to a visual sensor, onto its image plane. Sequences of time-ordered images allow the estimation of projected two-dimensional image motion as either instantaneous image velocities or discrete image displacements. These are usually called the optical flow field or the image velocity field. Provided that optical flow is a reliable approximation to two-dimensional image motion, it may then be used to recover the three-dimensional motion of the visual sensor (to within a scale factor) and the three-dimensional surface structure (shape or relative depth) through assumptions concerning the structure of the optical flow field, the three-dimensional environment and the motion of the sensor. Optical flow may also be used to perform motion detection, object segmentation, time-to-collision and focus of expansion calculations, motion compensated encoding and stereo disparity measurement. We investiga...

The quantitative evaluation of optical flow algorithms by Barron et al. (1994) led to significant advances in performance. The challenges for optical flow algorithms today go beyond the datasets and evaluation methods proposed in that paper. Instead, they center on problems associated with complex natural scenes, including nonrigid motion, real sensor noise, and motion discontinuities. We propose a new set of benchmarks and evaluation methods for the next generation of optical flow algorithms. To that end, we contribute four types of data to test different aspects of optical flow algorithms: (1) sequences with nonrigid motion where the ground-truth flow is determined by tracking hidden fluorescent texture, (2) realistic synthetic sequences, (3) high frame-rate video used to study interpolation error, and (4) modified stereo sequences of static scenes. In addition to the average angular error used by Barron et al., we compute the absolute flow endpoint error, measures for frame interpolation error, improved statistics, and results at motion discontinuities and in textureless regions. In October 2007, we published the performance of several well-known methods on a preliminary version of our data to establish the current state of the art. We also made the data freely available on the web at

We propose a motion segmentation algorithm that aims to break a scene into its most prominent moving groups. A weighted graph is constructed on the ira. age sequence by connecting pixels that arc in the spatio-temporal neighborhood of each other. At each pizel, we define motion profile vectors which capture the probability distribution of the image veloczty. The distance between motion profiles is used to assign a weight on the graph edges. 5rsmg normalized cuts we find the most salient partitions of the spatiotemporaI graph formed by the image sequence. For swmenting long image sequences,' we have developed a recursire update procedure that incorporates knowledge of segmentation in previous frames for efficiently finding the group correspondence in the new frame.

This paper presents a new approach to the estimation of two-dimensional motion vector fields from time-varying images. The approach is stochastic, both in its formulation and in the solution method. The formulation involves the specification of a deterministic structural model, along with stochastic observation and motion field models. Two motion models are proposed: a globally smooth model based on vector Markov random fields and a piecewise smooth model derived from coupled vector-binary Markov random fields. Two estimation criteria are studied. In the Maximum A Posteriori Probability (MAP) estimation the a posteriori probability of motion given data is maximized, while in the Minimum Expected Cost (MEC) estimation the expectation of a certain cost function is minimized. The MAP estimation is performed via simulated annealing, while the MEC algorithm performs iteration-wise averaging. Both algorithms generate sample fields by means of stochastic relaxation implemented via the Gibbs s...

Absfruet-A new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation that arises from the often used “smoothness constraint” ’yl”. regularization. The interpretation of the smoothness constraint is utilized as a “fractal prior ” to motivate regularization based on a recently introduced class of multiscale stochastic models. The solution of the new problem formulation is computed with an efficient multiscale algorithm. Experiments on several image sequences demonstrate the substantial computational savings that can be achieved due to the fact that the algorithm is noniterative and in fact has a per pixel computational complexity that is independent of image size. The new approach also has a number of other important advantages. Specifically, multiresolution flow field estimates are available, allowing great flexibility in dealing with the tradeoff between resolution and accuracy. Multiscale error covariance information is also available, which is of considerable use in assessing the accuracy of the estimates. In particular, these error statistics can be used as the basis for a rational procedure for determining the spatially-varying optimal reconstruction resolution. Furthermore, if there are compelling reasons to insist upon a standard smoothness constraint, our algorithm provides an excellent initialization for the iterative algorithms associated with the smoothness constraint problem formulation. Finally, the usefulness of our approach should extend to a wide variety of ill-posed inverse problems in which variational techniques seeking a “smooth ” solution are generally Used. I.

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 scale-space 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...

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 data-driven and flow-driven, isotropic and anisotropic, as well as spatial and spatio-temporal 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 well-posed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flow-driven regularizers is identified, and a design criterion is proposed for constructing anisotropic flow-driven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.