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

The authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters, allowing one to adaptively steer a filter to any orientation, and to determine analytically the filter output as a function of orientation. Steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation. The authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase, angularly adaptive filtering, edge detection, and shape from shading. One can also build a self-similar steerable pyramid representation. The same concepts can be generalized to the design of 3-D steerable filters. >

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The design and use of steerable filters

Local image features or interest points provide compact and abstract representations of patterns in an image. In this paper, we extend the notion of spatial interest points into the spatio-temporal domain and show how the resulting features often reflect interesting events that can be used for a compact representation of video data as well as for interpretation of spatio-temporal events.

To detect spatio-temporal events, we build on the idea of the Harris and Forstner interest point operators and detect local structures in space-time where the image values have significant local variations in both space and time. We estimate the spatio-temporal extents of the detected events by maximizing a normalized spatio-temporal Laplacian operator over spatial and temporal scales. To represent the detected events, we then compute local, spatio-temporal, scale-invariant N-jets and classify each event with respect to its jet descriptor. For the problem of human motion analysis, we illustrate how a video representation in terms of local space-time features allows for detection of walking people in scenes with occlusions and dynamic cluttered backgrounds.

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On Space-Time Interest Points

Preface Through many centuries physics has been one of the most fruitful sources of inspiration for mathematics. As a consequence, mathematics has become an economic language providing a few basic principles which allow to explain a large variety of physical phenomena. Many of them are described in terms of partial diierential equations (PDEs). In recent years, however, mathematics also has been stimulated by other novel elds such as image processing. Goals like image segmentation, multiscale image representation, or image restoration cause a lot of challenging mathematical questions. Nevertheless, these problems frequently have been tackled with a pool of heuristical recipes. Since the treatment of digital images requires very much computing power, these methods had to be fairly simple. With the tremendous advances in computer technology in the last decade, it has become possible to apply more sophisticated techniques such as PDE-based methods which have been inspired by physical processes. Among these techniques, parabolic PDEs have found a lot of attention for smoothing and restoration purposes, see e.g. 113]. To restore images these equations frequently arise from gradient descent methods applied to variational problems. Image smoothing by parabolic PDEs is closely related to the scale-space concept where one embeds the original image into a family of subsequently simpler , more global representations of it. This idea plays a fundamental role for extracting semantically important information. The pioneering work of Alvarez, Guichard, Lions and Morel 11] has demonstrated that all scale-spaces fulllling a few fairly natural axioms are governed by parabolic PDEs with the original image as initial condition. Within this framework, two classes can be justiied in a rigorous way as scale-spaces: the linear diiusion equation with constant dif-fusivity and nonlinear so-called morphological PDEs. All these methods satisfy a monotony axiom as smoothing requirement which states that, if one image is brighter than another, then this order is preserved during the entire scale-space evolution. An interesting class of parabolic equations which pursue both scale-space and restoration intentions is given by nonlinear diiusion lters. Methods of this type have been proposed for the rst time by Perona and Malik in 1987 190]. In v vi PREFACE order to smooth the image and to simultaneously enhance semantically important features such as edges, they apply a diiusion process whose diiusivity is steered by local image properties. These lters are diicult to analyse mathematically , as they may act locally like a backward diiusion process. …

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Anisotropic diffusion in image processing

Local image features or interest points provide compact and abstract representations of patterns in an image. We propose to extend the notion of spatial interest points into the spatio-temporal domain and show how the resulting features often reflect interesting events that can be used for a compact representation of video data as well as for its interpretation. To detect spatio-temporal events, we build on the idea of the Harris and Forstner interest point operators and detect local structures in space-time where the image values have significant local variations in both space and time. We then estimate the spatio-temporal extents of the detected events and compute their scale-invariant spatio-temporal descriptors. Using such descriptors, we classify events and construct video representation in terms of labeled space-time points. For the problem of human motion analysis, we illustrate how the proposed method allows for detection of walking people in scenes with occlusions and dynamic backgrounds.

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Space-time interest points

A pattern-recognition method, making use of Fourier transformations to extract features which are significant for a pattern, is described. The ordinary Fourier coefficients are difficult to use as input to categorizers because they contain factors dependent upon size and rotation as well as an arbitrary phase angle. From these Fourier coefficients, however, other more useful features can easily be derived. By using these derived property constants, a distinction can be made between genuine shape constants and constants representing size, location, and orientation. The usefulness of the method has been tested with a computer program that was used to classify 175 samples of handprinted letters, e.g., 7 sets of the 25 letters A to Z. In this test, 98 percent were correctly recognized when a simple nonoptimized decision method was used. The last section contains some considerations of the technical realizability of a fast preprocessing system for reading printed text.

Fourier Preprocessing for Hand Print Character Recognition

The problem of detection of orientation in finite dimensional Euclidean spaces is solved in the least squares sense. The theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n-dimensional Euclidean space. Detection of orientation is shown to correspond to fitting an axis or a plane to the Fourier transform of an n-dimensional structure. The solution of this problem is related to the solution of a well-known matrix eigenvalue problem. The computations can be performed in the spatial domain without actually doing a Fourier transformation. Along with the orientation estimate, a certainty measure, based on the error of the fit, is proposed. Two applications in image analysis are considered: texture segmentation and optical flow. The theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise. The comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow. >

Multidimensional orientation estimation with applications to texture analysis and optical flow

This paper describes a robust algorithm for estimation of local signal frequency and bandwidth. The method is based on combining local estimates of instantaneous frequency over a large number of scales. The filters used are a set of lognormal quadrature wavelets. A novel feature is that an estimate of local frequency bandwidth can be obtained. The bandwidth can be used to produce a measure of certainty for the estimated frequency. The algorithm is applicable to multidimensional data and examples of the performance of the method are demonstrated for one-dimensional and two-dimensional signals. >

Local multiscale frequency and bandwidth estimation

The purpose of this paper is to provide a broad overview of the WITAS Unmanned Aerial Vehicle Project. The WITAS UAV project is an ambitious, long-term basic research project with the goal of developing technologies and functionalities necessary for the successful deployment of a fully autonomous UAV operating over diverse geographical terrain containing road and traffic networks. The project is multi-disciplinary in nature, requiring many different research competences, and covering a broad spectrum of basic research issues, many of which relate to current topics in artificial intelligence. A number of topics considered are knowledge representation issues, active vision systems and their integration with deliberative/reactive architectures, helicopter modeling and control, ground operator dialogue systems, actual physical platforms, and a number of simulation techniques.

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Gösta H. Granlund

Papers

Fourier Preprocessing for Hand Print Character Recognition

Multidimensional orientation estimation with applications to texture analysis and optical flow

Local multiscale frequency and bandwidth estimation

The WITAS Unmanned Aerial Vehicle project

Texture Analysis Using Two-Dimensional Quadrature Filters