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.

Performance of optical flow techniques

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-orderedimages 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 investigate the computation of optical flow in this survey: widely known methods for estimating optical flow are classified and examined by scrutinizing the hypothesis and assumptions they use. The survey concludes with a discussion of current research issues.

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The computation of optical flow

We present an overview of the various uses of the wavelet transform (WT) in medicine and biology. We start by describing the wavelet properties that are the most important for biomedical applications. In particular we provide an interpretation of the the continuous wavelet transform (CWT) as a prewhitening multiscale matched filter. We also briefly indicate the analogy between the WT and some of the the biological processing that occurs in the early components of the auditory and visual system. We then review the uses of the WT for the analysis of 1-D physiological signals obtained by phonocardiography, electrocardiography (ECG), mid electroencephalography (EEG), including evoked response potentials. Next, we provide a survey of wavelet developments in medical imaging. These include biomedical image processing algorithms (e.g., noise reduction, image enhancement, and detection of microcalcifications in mammograms), image reconstruction and acquisition schemes (tomography, and magnetic resonance imaging (MRI)), and multiresolution methods for the registration and statistical analysis of functional images of the brain (positron emission tomography (PET) and functional MRI (fMRI)). In each case, we provide the reader with same general background information and a brief explanation of how the methods work.

A review of wavelets in biomedical applications

The performance of six optical flow techniques is compared, emphasizing measurement accuracy. The most accurate methods are found to be the local differential approaches, where nu is computed explicitly in terms of a locally constant or linear model. Techniques using global smoothness constraints appear to produce visually attractive flow fields, but in general seem to be accurate enough for qualitative use only and insufficient as precursors to the computations of egomotion and 3D structures. It is found that some form of confidence measure/threshold is crucial for all techniques in order to separate the inaccurate from the accurate. Drawbacks of the six techniques are discussed. >

Estimation of local spatial structure has a long history and numerous analysis tools have been developed. A concept that is widely recognized as fundamental in the analysis is the structure tensor. However, precisely what it is taken to mean varies within the research community. We present a new method for structure tensor estimation which is a generalization of many of it's predecessors. The method uses filter sets having Fourier directional responses being monomials of the normalized frequency vector, one odd order sub-set and one even order sub-set. It is shown that such filter sets allow for a particularly simple way of attaining phase invariant, positive semi-definite, local structure tensor estimates. We continue to compare a number of known structure tensor algorithms by formulating them in monomial filter set terms. In conclusion we show how higher order tensors can be estimated using a generalization of the same simple formulation.

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Representing local structure using tensors II

The paper presents a general framework for the analysis of time sequences. Features extracted include speed, acceleration and disparity/depth. The method uses spatio-temporal filtering in a hierarchical structure. Synthetic and real world examples are included. >

Estimation of velocity, acceleration and disparity in time sequences

A framework for computer-aided analysis of mammograms is described. General computer vision algorithms are combined with application specific procedures in a hierarchical fashion. The system is under development and is currently limited to detection of a few types of suspicious areas. The image features are extracted by using feature extraction methods where wavelet techniques are utilized. A low-pass pyramid representation of the image is convolved with a number of quadrature filters. The filter outputs are combined according to simple local Fourier domain models into parameters describing the local neighborhood with respect to the model. This produces estimates for each pixel describing local size, orientation, Fourier phase, and shape with confidence measures associated to each parameter. Tentative object descriptions are then extracted from the pixel-based features by application-specific procedures with knowledge of relevant structures in mammograms. The orientation, relative brightness and shape of the object are obtained by selection of the pixel feature estimates which best describe the object. The list of object descriptions is examined by procedures, where each procedure corresponds to a specific type of suspicious area, e.g. clusters of microcalcifications.

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Feature Extraction for Computer-Aided Analysis of Mammograms

A framework for analysis and adaptive filtering of time sequences and volume is presented. Time sequences and volumes constitute three-dimensional signal spaces (two spatial dimensions and one time dimension or three spatial dimensions). The signal is convolved with a set of 3D quadrature filters. The filter function is separable in orientation and radius and the uncertainty product of the filters exceeds that of Gabor filters by only 15%. The output from the filters is combined to form a 3D tensor field giving a local description of the neighborhood. To increase robustness the field is convolved with a 3D smoothing filter. This field is used to construct a filter adapting to the local situation. Results showing precise and robust performance using both synthetic and real data are presented. >

A framework for anisotropic adaptive filtering and analysis of image sequences and volumes

Robust Orientation Estimation in 2D, 3D and 4D Using Tensors

This paper describes an algorithm for estimation of directionality in 2D and 3D vector fields and how that feature relates to the curvature of curves in 2D images and surfaces in 3D images.

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Håkan Bårman

Papers

Estimation of velocity, acceleration and disparity in time sequences

Feature Extraction for Computer-Aided Analysis of Mammograms

A framework for anisotropic adaptive filtering and analysis of image sequences and volumes

Robust Orientation Estimation in 2D, 3D and 4D Using Tensors

Estimation of Curvature in 3D Images Using Tensor Field Filtering