Magnetic resonance (MR) images lack information about radiation transport-a fact which is problematic in applications such as radiotherapy planning and attenuation correction in combined PET/MR imaging. To remedy this, a crude but common approach is to approximate all tissue properties as equivalent to those of water. We improve upon this using an algorithm that automatically identifies bone tissue in MR. More specifically, we focus on segmenting the skull prior to stereotactic neurosurgery, where it is common that only MR images are available. In the proposed approach, a machine learning algorithm known as a support vector machine is trained on patients for which both a CT and an MR scan are available. As input, a combination of local and global information is used. The latter is needed to distinguish between bone and air as this is not possible based only on the local image intensity. A whole skull segmentation is achievable in minutes. In a comparison with two other methods, one based on mathematical morphology and the other on deformable registration, the proposed method was found to yield consistently better segmentations.

We propose non-local analysis of functional magnetic resonance imaging (fMRI) data in order to detect more brain activity. Our non-local approach combines the ideas of regular fMRI analysis with those of functional connectivity analysis, and was inspired by the non-local means algorithm that commonly is used for image denoising. We extend canonical correlation analysis (CCA) based fMRI analysis to handle more than one activity area, such that information from different parts of the brain can be combined. Our non-local approach is compared to fMRI analysis by the general linear model (GLM) and local CCA, by using simulated as well as real data.

In this paper, we propose a novel algorithm for regularizing displacement fields in image registration. The method uses the local structure tensor and gradients of the displacement field to impose a local metric, which is then used optimizing a global cost function. The method allows for linear operators, such as tensors and differential operators modeling the underlying physical anatomy of the human body in medical images. The algorithm is tested using output from the Morphon image registration algorithm on MRI data as well as synthetic test data and the result is compared to the initial displacement field. The results clearly demonstrate the power of the method and the unique features brought forth through the global optimization approach.

Functional connectivity analysis is a way to investigate how different parts of the brain are connected and interact. A common measure of connectivity is the temporal correlation between a reference voxel time series and all the other time series in a functional MRI data set. An fMRI data set generally contains more than 20,000 within-brain voxels, making a complete correlation analysis between all possible combinations of voxels heavy to compute, store, visualize and explore. In this paper, a GPU-accelerated interactive tool for investigating functional connectivity in fMRI data is presented. A reference voxel can be moved by the user and the correlations to all other voxels are calculated in real-time using the graphics processing unit (GPU). The resulting correlation map is updated in real-time and visualized as a 3D volume rendering together with a high resolution anatomical volume. This tool greatly facilitates the search for interesting connectivity patterns in the brain.

We present a method for fast phase based registration of volume data for medical applications. As the number of different modalities within medical imaging increases, it becomes more and more important with registration that works for a mixture of modalities. For these applications the phase based registration approach has proven to be superior. Today there seem to be two kinds of groups that work with medical image registration, one that works with refining of the registration algorithms and one that works with implementation of more simple algorithms on graphic cards for speeding up the algorithms. We put the work from these groups together and get the best from both worlds. We achieve a speedup of 10-30 compared to our CPU implementation, which makes fast phase based registration possible for large medical volumes.

Image registration is a crucial task in many applications and applied in a variety of different areas. In addition to the primary task of image alignment, the deformation field is valuable when studying structural/volumetric changes in the brain. In most applications a regularizing term is added to achieve a smoothly varying deformation field. This can sometimes cause conflicts in situations of local complex deformations. In this paper we present a new regularizer, which aims at handling local complex deformations while maintaining an overall smooth deformation field. It is based on an adaptive anisotropic regularizer and its usefulness is demonstrated by two examples, one synthetic and one with real MRI data from a pre- and post-op situation with normal pressure hydrocephalus.

We present the first step towards a brain computer interface (BCI) for communication using real-time functional magnetic resonance imaging (fMRI). The subject in the MR scanner sees a virtual keyboard and steers a cursor to select different letters that can be combined to create words. The cursor is moved to the left by activating the left hand, to the right by activating the right hand, down by activating the left toes and up by activating the right toes. To select a letter, the subject simply rests for a number of seconds. We can thus communicate with the subject in the scanner by for example showing questions that the subject can answer. Similar BCI for communication have been made with electroencephalography (EEG). In these implementations the subject for example focuses on a letter while different rows and columns of the virtual keyboard are flashing. The system then tries to detect if the correct letter is flashing or not. In our setup we instead classify the brain activity. Our system is not limited to a communication interface, but can be used for any interface where five degrees of freedom is necessary.

Phase-based methods are commonly applied in image registration. When working with phase-difference methods only a single scale is employed, although the algorithms are normally iterated over multiple scales, whereas phase-congruency methods utilize the the phase from multiple scales simultaneously. This paper presents an extension to phase-difference methods employing parallel scales to achieve more accurate displacements. Results are also presented clearly favouring the use of parallel scales over single scale in more than 95% of the 120 tested cases.

Many applications in image analysis include the problem of linear structure detection, e.g. segmentation of blood vessels in medical images, roads in satellite images, etc. A simple and efficient solution is to apply linear filters tuned to the structures of interest and extract line and edge positions from the filter output. However, if the filter is not carefully designed, artifacts such as ringing can distort the results and hinder a robust detection. In this paper, we study the ringing effects using a common Gabor filter for linear structure detection, and suggest a method for generating non-ring filters in 2D and 3D. The benefits of the non-ring design are motivated by results on both synthetic and natural images.

Correlation is often used to measure the similarity between signals and is an important tool in signal and image processing. In some applications it is common that signals are corrupted by local bursts of noise. This adversely affects the performance of signal recognition algorithms. This paper presents a novel correlation estimator, which is robust to locally corrupted signals. The estimator is generalized to multivariate correlation analysis (general linear model, GLM, and canonical correlation analysis, CCA). Synthetic functional MRI data is used to demonstrate the estimator, and its robustness is shown to increase the performance of signal detection.

For data samples in Rn, the mean is a well known estimator. When the data set belongs to an embedded manifold M in Rn, e.g. the unit circle in R2, the definition of a mean can be extended and constrained to M by choosing either the intrinsic Riemannian metric of the manifold or the extrinsic metric of the embedding space. A common view has been that extrinsic means are approximate solutions to the intrinsic mean problem. This paper study both means on the unit circle and reveal how they are related to the ML estimate of independent samples generated from a Brownian distribution. The conclusion is that on the circle, intrinsic and extrinsic means are maximum likelihood estimators in the limits of high SNR and low SNR respectively.

The inverse gradient problem, finding a scalar field f with a gradient near a given vector fieldgon some bounded and connected domain Ω ϵ R𝓃, can be solved by means of a Poisson equation with inhomogeneous Neumann boundary conditions. We present an elementary derivation of this partial differential equation and an efficient multigrid-based method to numerically compute the inverse gradient on non-rectangular domains. The utility of the method is demonstrated by a range of important medical applications such as phase unwrapping, pressure computation, inverse deformation fields, and fiber bundle tracking.

In analysis of fMRI data, it is common to average neighboring voxels in order to obtain robust estimates of the correlations between voxel time-series and the model of the signal expected to be present in activated regions. We have previously proposed a method where only voxels with similar correlation coefficients are averaged. In this paper we extend this idea, and present a novel method for analysis of fMRI data. In the proposed method, only voxels with similar correlation coefficients and similar time-series are averaged. The proposed method is compared to our previous method and to two well-known filtering strategies, and is shown to have superior ability to discriminate between active and inactive voxels

Automatic segmentation of anatomical structures is often performed using model-based non-rigid registration methods. These algorithms work well when the images do not contain any large deviations from the normal anatomy. We have previously used such a method to generate patient specific models of hip bones for surgery simulation. The method that was used, the morphon method, registers two-or three-dimensional images using a multi-resolution deformation scheme. A prototype image is iteratively registered to a target image using quadrature filter phase difference to estimate the local displacement. The morphon method has in this work been extended to deal with automatic segmentation of fractured bones. Two features have been added. First, the method is modified such that multiple prototypes (in this case two) can be used. Second, normalised convolution is utilized for the displacement estimation, to guide the registration of the second prototype, based on the result of the registration of the first one.

It has previously been shown that canonical correlation analysis (CCA) works well for detecting neural activity in fMRI data. This is due to the ability of CCA to perform simultaneous temporal modeling and adaptive spatial filtering of the data. In this paper, we demonstrate that our previously proposed method for CCA-based fMRI data analysis does not provide rotationally invariant detection of activated regions. We propose a modification of the previous method and show that it resolves the rotational invariance issue, thereby further improving the analysis method.

The high complexity of Transfer Function (TF) design is a major obstacle to widespread routine use of Direct Volume Rendering, particularly in the case of medical imaging. Both manual and automatic TF design schemes would benefit greatly from a fast and simple method for detection of tissue value ranges. To this end, we introduce the a-histogram, an enhancement that amplifies ranges corresponding to spatially coherent materials. The properties of the a-histogram have been explored for synthetic data sets and then successfully used to detect vessels in 20 Magnetic Resonance angiographies, proving the potential of this approach as a fast and simple technique for histogram enhancement in general and for TF construction in particular.

Averaging, filtering and interpolation of 3-D object orientation data is important in both computer vision and computer graphics, for instance to smooth estimates of object orientation and interpolate between keyframes in computer animation. In this paper we present a novel framework in which the non-linear nature of these problems is avoided by embedding the manifold of 3-D orientations into a 16-dimensional Euclidean space. Linear operations performed in the new representation can be shown to be rotation invariant, and defining a projection back to the orientation manifold results in optimal estimates with respect to the Euclidean metric. In other words, standard linear filters, interpolators and estimators may be applied to orientation data, without the need for an additional machinery to handle the non-linear nature of the problems. This novel representation also provides a way to express uncertainty in 3-D orientation, analogous to the well known tensor representation for lines and hyperplanes.

A method for detecting and reducing reverberation artifacts in ultrasound image sequences is described. A reverberation artifact localization map is produced using local Rf-bandwidth estimation. To reduce the artifacts an ideal 3D (2D + time) Wiener filter function is computed by using the reverberation map to interactively produce an estimate of the noise and signal spectra. The Wiener filter kernel is optimized to obtain good locality properties. The optimized filter is then applied to the ultrasound image sequence. The test sequence used is from an open chest pig heart, corrupted by strong reverberation artifacts. The selective power of a 3D filter is far superior to that of ID and 2D filters and the reverberation artifacts are almost completely removed by the developed method.

This paper presents a new robust approach for segmentation. The segmentation is attained by morphing of an TV-dimensional model, the Morphon, onto the TV-dimensional data. The approach is general and can, in fact, be said to encompass much of the deformable model ideas that have evolved over the years. However, in contrast to commonly used models, a distinguishing feature of the Morphon approach is that it allows an intuitive interface for specifying prior information, hence the expression paint on priors. In this way it is simple to design Morphons for specific situations. The priors determine the behavior of the Morphon and can be seen as local data interpreters and response generators. There are three different kinds of priors: material parameter fields (elasticity, viscosity, anisotropy etc.), context fields (brightness, hue, scale, phase, anisotropy, certainly etc.) and global programs (filter banks, estimation procedures, adaptive mechanisms etc.). The morphing is performed using a dense displacement field. Both the material parameter and context fields are addressed via the present displacement field. An example of the performance of is given using 2D ultrasound images of a heart where the purpose is to segment the heart wall.

Linear filtering is a fundamental operation in signal processing, but for multidimensional signals the practical use is severely limited by the computer power available. Decomposition of filters into a layered structure of sparse subfilters, i.e. a filter network, significantly reduces the number of multiplications required for each data sample. A filter network, here used for phase invariant estimation of local 3-D structure, provides a flexible solution for linear filtering, especially suited for applying a set of filters on signals of higher dimensionality. The filter network presented, is twice as efficient as convolution based on the fast Fourier transform (FFT) and outperforms standard convolution by a factor exceeding 50 in terms of multiplications and additions performed.

Tensors and tensor fields are commonly used in multidimensional signal processing to represent the local structure of the signal. This paper focuses on the case where the sampling on the original signal is anisotropic, e.g when the resolution of the multidimensional image varies depending on the direction which is common e.g. in medical imaging devices. To obtain a geometrically correct description of the local structure there are mainly two possibilities. To resample the image prior to the computation of the local structure tensor field or to compute the tensor field on the original grid and transform the result to obtain a correct geometry of the local structure. This paper deals with the latter alternative and contains an in depth theoretical analysis establishing the appropriate rules for tensor transformations induced by changes in space-time geometry with emphasis on velocity and motion estimation.

The paper argues for the use of quadrature filters for local structure tensor and motion estimation. The question of which properties of a local motion estimator are important is discussed. Answers are provided via the introduction of a number of fundamental invariances that are required in object motion estimation. A combination of statistical and deterministic modeling leads to mathematical formulations corresponding to the required invariances. The discussion leads up to the introduction of a new class of filter sets loglets. A number of experiments support the claim that loglets are preferable to other designs. In particular it is demonstrated that the loglet approach outperforms a Gaussian derivative approach in resolution and robustness to variations in object illumination.

The problem of signal estimation for sparsely and irregularly sampled signals is dealt with using continuous normalized convolution. Image values on real-valued positions are estimated using integration of signals and certainties over a neighbourhood employing a local model of both the signal and the used discrete filters. The result of the approach is that an output sample close to signals with high certainty is interpolated using a small neighbourhood. An output sample close to signals with low certainty is spatially predicted from signals in a large neighbourhood.

We present a method for accurate image registration and motion compensation in multidimensional signals, such as two-dimensional (2-D) X-ray images and three-dimensional (3-D) computed tomography/magnetic resonance imaging volumes. The method is based on phase from quadrature filters, which makes it robust to noise and temporal intensity variations. The method is equally applicable to signals of two, three or higher number of dimensions. We use parametric models, e.g., affine models, finite elements or local affine models with global regularization. Experimental results show high accuracy for 2-D and 3-D motion compensation.

We present a method for accurate image registration and motion estimation in multidimensional volumes, such as 3D CT and MR images. The method is based on phase from quadrature filters, which makes it insensitive to variations in luminance and other disturbance in the images. The theory is not restricted to any particular kind of motion model or number of dimensions. Experimental results for affine motions in 3D show high accuracy.

We present a method that finds edges between certain image features, e.g. gray-levels, and disregards edges between other features. The method uses a channel representation of the features and performs normalized convolution using the channel values as certainties. This means that areas with certain features can be disregarded by the edge filter. The method provides an important tool for finding tissue specific edges in medical images, as demonstrated by an MR-image example.

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.

Presents a general strategy for automated generation of efficient representations in vision. The approach is highly task oriented and what constitutes the relevant information is defined by a set of examples. The examples are pairs of situations that are dependent through the chosen feature but are otherwise independent. Particularly important concepts in the work are mutual information and canonical correlation. How visual operators and representation can be generated from examples are presented for a number of features, e.g. local orientation, disparity and motion. Interesting similarities to biological vision functions are observed. The results clearly demonstrates the potential of combining advanced filtering techniques and learning strategies based on canonical correlation analysis.

Conventional gradient methods (optical flow), for motion estimation assume intensity conservation between frames. This assumption is often violated in real applications. The remedy is a novel method that computes constraints on the local motion. These constraint are given on the same form as in conventional methods. Thus, it can directly substitute the gradient method in most applications. Experiments indicate a superior accuracy, even on synthetic images where the intensity conservation assumption is valid. The conventional gradient methods seem obsolete.

This paper presents our general strategy for designing learning machines as well as a number of particular designs. The search for methods allowing a sufficient level of adaptivity are based on two main principles: 1) simple adaptive local models; and 2) adaptive model distribution. Particularly important concepts in our work is mutual information and canonical correlation. Examples are given on learning feature descriptors, modeling disparity, synthesis of a global 3-mode model and a setup for reinforcement learning of online video coder parameter control.

In this paper we focus on using local 3D structure for segmentation. A tensor descriptor is estimated for each neighbourhood, i.e. for each voxel in the data set. The tensors are created from a combination of the outputs form a set of 3D quadrature filters. The shape of the tensors describe locally the structure of the neighbourhood in terms of how much it is like a plane, a line, and a sphere. We apply this to segmentation of bone from Computer Tomography data (CT). Traditional methods are based purely on gray-level value discrimination and have difficulties in recovering thin bone structures due to so called partial voluming, a problem which is present in all such sampled data. We illuminate the partial voluming problem by showing that thresholding creates complicated artifacts even if the signal is densely enough sampled and can be perfectly reconstructed. The unwanted effects of thresholding can be reduced by a change of the signal basis. We show that by using additional local structure information can significantly reduce the degree of sampling artifacts. Evaluation of the method on a clinical case is presented, the segmentation of a human skull from a CT volume. The method shows that many of the thin bone structures which disappear in a pure thresholding can be recovered.

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.

It is shown how estimates of local structure and orientation can be obtained using a set of spherically separable quadrature filters. The method is applicable to signals of any dimensionality the only requirement being that the filter set spans the corresponding orientation space. The estimates produced are second order tensors, the size of the tensors corresponding to the dimensionality of the input signal. A central part of the algorithm is an operation termed 'tensor whitening' reminiscent of classical whitening procedures. This operation compensates exactly for any biases introduced by non-uniform filter orientation distributions and/or non-uniform filter output certainties. Examples of processing of 2D-images, 3D-volumes and 2D-image sequences are given. Sensitivity to noise and missing filter outputs are analyzed in different situations. Estimation accuracy as a function of filter orientation distributions are studied. The studies provide evidence that the algorithm is robust and preferable to other algorithms in a wide range of situations.>

This paper establishes an algebraic relation between two methods recently reported; normalized convolution and normalized differential convolution. These are general methods for filtering incomplete or uncertain data and are based on the separation of both data and operator into a signal part and a certainty part. General filtering can be performed without preprocessing input data with an interpolation step. The methods allow both data and operators to be scalars, vectors or tensors of higher order. Normalized differential convolution has been used in a wide range of applications. Examples are estimation of gradient estimation in irregularly sampled data, estimation of differential invariants in sparse image flow fields and image edge effect reduction. It was previously shown that normalized convolution produces a description of the neighbourhood which is optimal in a least square sense. The algebraic relation to normalized differential convolution presented in this paper proves that the latter method is also optimal in the same sense as well.>

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.>

This paper presents a method for computation of two-dimensional motion vector fields from an image sequence. The magnitudes from a set of spatio-temporal quadrature filters are combined into a tensor description. The shape of the tensors describe locally the structure of the spatio-temporal neighbourhood and provides information about local velocity and if true flow or only normal flow is present. It is shown how normal flow estimates are combined into a true flow using linear filtering on this tensor field description.>

An approach for processing incomplete or uncertain data based on subspace methods is presented in this paper. The paper addresses the problem of how a subset of a parameter vector describing a signal can be estimated. The term parameter vector refers to the coefficients in the linear combination of basis functions describing a local image neighbourhood. Images are normally described locally using simple basis functions. Low order local momentums such as order 0 (the local DC component), 1 and 2 are commonly used. Low order differentiations are also useful descriptors. In densely regularly sampled images, these descriptors are easily computed using standard convolution. However, when working with irregularly sampled data or incomplete data the signal model has to be of higher order than the signal variations of interest. This is the case where only a part of the parameter vector is to be estimated. If possible, only this part of the parameter should be calculated explicitly as opposed to calculating the whole parameter vector. This paper describes such a method based on partitioning the model subspace into two parts.

It is shown how false operator responses due to missing or uncertain data can be significantly reduced or eliminated. It is shown how operators having a higher degree of selectivity and higher tolerance against noise can be constructed using simple combinations of appropriately chosen convolutions. The theory is based on linear operations and is general in that it allows for both data and operators to be scalars, vectors or tensors of higher order. Three new methods are represented: normalized convolution, differential convolution and normalized differential convolution. All three methods are examples of the power of the signal/certainty-philosophy, i.e., the separation of both data and operator into a signal part and a certainty part. Missing data are handled simply by setting the certainty to zero. In the case of uncertain data, an estimate of the certainty must accompany the data. Localization or windowing of operators is done using an applicability function, the operator equivalent to certainty, not by changing the actual operator coefficients. Spatially or temporally limited operators are handled by setting the applicability function to zero outside the window.>

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 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.>

Recent physiological research has indicated that the visual system makes use of units responsive to Gabor signals in the analysis of visual stimuli. Such functions effect a tradeoff between pure spatial- and frequency-domain descriptions. The authors explain the use of such representations in vision, considered as a process in inference from the retinal signals to a symbolic description. The appropriate mathematical structure for the inference is that of the subspaces of the signal vector space, a feature which it shares with quantum mechanics. The theory is derived directly from the fundamental constraints on visual inference. It is then shown to be consistent with many of the known properties of the visual system. In particular, a major feature of the inference system-the occurrence of interference effects-has already been observed in visual system operation.>

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.