Perceptual experiments indicate that corners and curvature are very important features in the process of recognition. This paper presents a new method to detect rotational symmetries, which describes complex curvature such as corners, circles, star, and spiral patterns. It works in two steps: 1) it extracts local orientation from a gray-scale or color image; and 2) it applies normalized convolution on the orientation image with rotational symmetry filters as basis functions. These symmetries can serve as feature points at a high abstraction level for use in hierarchical matching structures for 3D estimation, object recognition, image database retrieval, etc.

Focus of attention mechanisms for robot vision are discussed. A new method for neglecting low level filter responses from already modelled structures is presented. The method is based on a filtering technique termed normalized convolution. In one experiment, the robot is continuously moving its arm in the scene while tracking other objects. It is shown how the arm can be made "invisible" so that only the moving object of interest is detected. This makes tracking of objects much simpler. In another experiment, the attention of the system is shifted between objects by simply cancelling the mask of the object to be attended to. With this strategy the low level processes do not need to know the difference between a new object entering the scene and a mask being cancelled, and thus a complex communication structure between high and low levels is avoided.

The paper discusses the concepts of invariance and equivariance in the context of continuous operator groups, or Lie groups, acting on both the image and a descriptor of some image feature. The theory is illustrated by an example of how a 3D image neighbourhood that contains a linear structure can be mapped to a tensor that represents the orientation of the structure. A second order tensor is defined which represents both local orientation and local phase in a continuous way, the phase is given by the relation between the symmetric and anti-symmetric part of this tensor. By computing a tensor inner product of the tensor, a phase invariant orientations representation is obtained.

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.>

Invariance is a very important property of features that are useful for vision. A great deal of research on this subject is going on at different labs. While invariance mechanisms can be prescribed for certain descriptors, it is our firm belief that this is not feasible for descriptors of higher level properties in general. As a consequence, these invariance mechanisms have to be learned by the vision system. In this paper, such a learning structure is proposed. A major contribution in this paper, as well as a crucial component for a successful operation, is the use of a coordinate-free information representation: the channel representation. Furthermore, each processing unit is a linear perceptron which operates on outer products of input data, implying a complex space of invariance. Two examples of how the representation can be employed are included. The examples shows an excellent separation of invariance modes, good accuracy, as well as a fast convergence.>

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.>

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.>

A number of the issues which arise from the representation of image formation, in particular for 3D volumes and time sequences, are discussed. This includes nonspatially parametric representation of properties, representations in terms of linkage between elements, associative grouping to establish similarity as the criterion for linkage, associative grouping represented as list structures, and ways to take into account the local and global nature of properties.>

The uncertainty principle is recognized as one of the fundamental results in signal processing. Its role in inference is, however, less well known outside of quantum mechanics. It is the aim of this paper to provide a unified approach to the problem of uncertainty in image processing. It is shown that uncertainty can be derived from the fundamental constraints on the process of vision-the requirements for class-defining operations which are both shift-invariant and insensitive to changes in illumination. It is thus shown that uncertainty plays a key role in the language of vision, since it affects the choice of both the alphabet, the elementary signals, and the syntax, the inferential structure, of vision. The report is concluded with a number of practical illustrations of these ideas, taken from such image processing tasks as enhancement, data compression, and segmentation.

A new form of image estimator, which takes account of linear features, is derived using a signal equivalent formulation. The estimator is shown to be a nonstationary linear combination of three stationary estimators. The relation of the estimator to human visual physiology is discussed. A method for estimating the nonstationary control information is described and shown to be effective when the estimation is made from noisy data. A suboptimal approach which is computationally less demanding is presented and used in the restoration of a variety of images corrupted by additive white noise. The results show that the method can improve the quality of noisy images even when the signal-to-noise ratio is very low.

A new predictive coder, based on an estimation method which adapts to line and edge features in images, is described. Quantization of the prediction error is performed by a two-level adaptive scheme: an adaptive transform coder, and threshold coding in both transform and spatial domains. Control information, which determines the behavior of the predictor, is quantized using a simple variable rate technique. The results are improved by pre- and postfiltering using a related noncausal form of the estimator. Acceptable images have been produced in this way at bit rates of less than 0.5 bit/pixel.

Most problems in signal processing have structural aspects which are difficult to solve using general methods. Use of ad hoc methods is limited to cases where structural aspects are easy to re-solve. An approach for hierarchical processing is described whereby structural aspects are resolved simultaneously with the analysis of data values. An effective use of a hierarchical structure puts strong restrictions upon information representation and operations. Information is represented in terms of compatibility and incompatibility of events, combined with a measure of confidence. Operations are of type symmetry operations, which allow data compression, context control and have a good descriptive power. These methods have been tested in various problems in image analysis and image processing with satisfactory results.

A non-stationary predictive image coder is described. The predictor is controlled by a compact representation of the image line and edge content. Quantization of the prediction error is performed in both spatial and transform domains. The control information is transmitted using a simple variable-rate scheme. Acceptable results have been obtained with the coder at rates of .5 bit/pixel and below.

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.