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.

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...

ii About the cover The figure on the cover shows a visualization of a symmetric tensor in three dimensions, G = λ1ê1ê T 1 + λ2ê2ê T 2 + λ3ê3ê T 3 The object in the figure is the sum of a spear, a plate and a sphere. The spear describes the principal direction of the tensor λ1ê1ê T 1, where the length is proportional to the largest eigenvalue, λ1. The plate describes the plane spanned by the eigenvectors corresponding to the two largest eigenvalues, λ2(ê1ê T 1 + ê2ê T 2). The sphere, with a radius proportional to the smallest eigenvalue, shows how isotropic the tensor is, λ3(ê1ê T 1 + ê2ê T 2 + ê3ê T 3). The visualization is done using AVS [WWW94]. I am very grateful to Johan Wiklund for implementing the tensor viewer module used. This thesis deals with filtering of multidimensional signals. A large part of the thesis is devoted to a novel filtering method termed “Normalized convolution”. The method performs local expansion of a signal in a chosen filter basis which

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.

: Working toward ecient (real-time) 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 least-squares 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 gradient-based 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...

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 ...

This paper describes a technique for characterization and segmentation of anisotropic patterns that exhibit a single local orientation. Using Gaussian derivatives we construct a gradient-square tensor at a selected scale. Smoothing of this tensor allows us to combine information in a local neighborhood without canceling vectors pointing in opposite directions. Whereas opposite vectors would cancel, their tensors reinforce. Consequently, the tensor characterizes orientation rather than direction. Usually this local neighborhood is at least a few times larger than the scale parameter of the gradient operators. The eigenvalues yield a measure for anisotropy whereas the eigenvectors indicate the local orientation. In addition to these measures we can detect anomalies in textured patterns. 1.

Abstract. The analytic signal is one of the most capable approaches in onedimensional signal processing. Two-dimensional signal theory suffers from the absence of an isotropic extension of the analytic signal. Accepting the fact that there is no odd filter with isotropic energy in higher dimensions, one tried to circumvent this drawback using the one-dimensional quadrature filters with respect to several preference directions. Disadvantages of these methods are an increased complexity, the loss of linearity and a lot of different heuristic approaches. In this paper we present a filter that is isotropic and odd, which means that the whole theory of local phase and amplitude can directly be applied to images. Additionally, a third local property is obtained which is the local orientation. The advantages of our approach are demonstrated by a stable orientation detection algorithm and an adaption of the phase congruency method which yields a superior edge detector with very low complexity. 1

We propose a new curvature estimator, which operates on the output of an orientation estimator.

Filtering of an image with rotated versions of an orientation selective filter yields a set of images which can be stacked to form an orientation space. Orientation space provides a means of analyzing overlapping and touching anisotropic textures. A set of rotated k order directional derivatives yields a discrete orientation space, which allows interpolation. Next we apply a deconvolution scheme that results in improved orientation selectivity. This scheme allows decomposition of noisy multi-orientation patterns.