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.

Abstract. Differential methods belong to the most widely used techniques for optic flow computation in image sequences. They can be classified into local methods such as the Lucas–Kanade technique or Bigün’s structure tensor method, and into global methods such as the Horn/Schunck approach and its extensions. Often local methods are more robust under noise, while global techniques yield dense flow fields. The goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways: (i) We juxtapose the role of smoothing/regularisation processes that are required in local and global differential methods for optic flow computation. (ii) This discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches: It yields dense flow fields that are robust against noise. (iii) Spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method. (iv) We propose a simple confidence measure for optic flow methods that minimise energy functionals. It allows to sparsify a dense flow field gradually, depending on the reliability required for the resulting flow. Comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure.

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this paper we formulate a robust statistical framework for representing certain classes of appearance changes. In so doing we have three primary goals. First, we wish to "explain" appearance changes in an image sequence as resulting from a "mixture" of causes. Second, we wish to locate where particular types of appearance change are taking place in an image. And, third, we want to provide a framework that generalizes previous work on motion estimation.

In [10] we presented a new velocity estimation algorithm, using orientation tensors and parametric motion models to provide both fast and accurate results. One of the tradeoffs between accuracy and speed was that no attempts were made to obtain regions of coherent motion when estimating the parametric models. In this paper we show how this can be improved by doing a simultaneous segmentation of the motion field. The resulting algorithm is slower than the previous one, but more accurate. This is shown by evaluation on the well-known Yosemite sequence, where already the previous algorithm showed an accuracy which was substantially better than for earlier published methods. This result has now been improved further.

Motion estimation in image sequences is an important step in many computer vision and image processing applications. Several methods for solving this problem have been proposed, but very few manage to achieve a high level of accuracy without sacrificing processing speed. This paper presents a novel motion estimation algorithm, which gives excellent results on both counts. The algorithm starts by computing 3D orientation tensors from the image sequence. These are combined under the constraints of a parametric motion model to produce velocity estimates. Evaluated on the well-known Yosemite sequence, the algorithm shows an accuracy which is substantially better than for previously published methods. Computationally the algorithm is simple and can be implemented by means of separable convolutions, which also makes it fast. 1 Introduction Motion estimation algorithms always involve a trade-off between speed and accuracy. The method presented here is primarily intended to be accurate but ...

Robust model fitting essentially requires the application of two estimators. The first is an estimator for the values of the model parameters. The second is an estimator for the scale of the noise in the (inlier) data. Indeed, we propose two novel robust techniques: the Two-Step Scale estimator (TSSE) and the Adaptive Scale Sample Consensus (ASSC) estimator. TSSE applies nonparametric density estimation and density gradient estimation techniques, to robustly estimate the scale of the inliers. The ASSC estimator combines Random Sample Consensus (RANSAC) and TSSE: using a modified objective function that depends upon both the number of inliers and the corresponding scale. ASSC is very robust to discontinuous signals and data with multiple structures, being able to tolerate more than 80 % outliers. The main advantage of ASSC over RANSAC is that prior knowledge about the scale of inliers is not needed. ASSC can simultaneously estimate the parameters of a model and the scale of the inliers belonging to that model. Experiments on synthetic data show that ASSC has better robustness to heavily corrupted data than Least Median Squares (LMedS), Residual Consensus (RESC), and Adaptive Least K’th order Squares (ALKS). We also apply ASSC to two fundamental computer vision tasks: range image segmentation and robust fundamental matrix estimation. Experiments show very promising results.

To solve the general point correspondence problem in which the underlying transformation between image patches is represented by a homography, a solution based on extensive use of first order differential techniques is proposed. We integrate in a single robust M-estimation framework the traditional optical flow method and matching of local color distributions. These distributions are computed with spatially oriented kernels in the 5D joint spatial/color space. The estimation process is initiated at the third level of a Gaussian pyramid, uses only local information, and the illumination changes between the two images are also taken into account. Subpixel

In this article, we introduce a new technique for estimating the optical flow field, starting from image sequences. As suggested by Fleet and Jepson, we track contours of constant phase over time, since these are more robust to variations in lighting conditions and deviations from pure translation than contours of constant amplitude. Our phase-based approach proceeds in three stages. First, the image sequence is spatially filtered using a bank of quadrature pairs of Gabor filters, and the temporal phase gradient is computed, yielding estimates of the velocity component in directions orthogonal to the filter pairs' orientations. Second, a component velocity is rejected if the corresponding filter pair's phase information is not linear over a given time span. Third, the remaining component velocities at a single spatial location are combined and a recurrent neural network is used to derive the full velocity. We test our approach on several image sequences, both synthetic and realistic.

The accuracy of optical flow estimation algorithms has been improving steadily as evidenced by results on the Middlebury optical flow benchmark. The typical formulation, however, has changed little since the work of Horn and Schunck. We attempt to uncover what has made recent advances possible through a thorough analysis of how the objective function, the optimization method, and modern implementation practices influence accuracy. We discover that “classical” flow formulations perform surprisingly well when combined with modern optimization and implementation techniques. Moreover, we find that while median filtering of intermediate flow fields during optimization is a key to recent performance gains, it leads to higher energy solutions. To understand the principles behind this phenomenon, we derive a new objective that formalizes the median filtering heuristic. This objective includes a nonlocal term that robustly integrates flow estimates over large spatial neighborhoods. By modifying this new term to include information about flow and image boundaries we develop a method that ranks at the top of the Middlebury benchmark.