Leif Haglund

Estimation of velocity, acceleration and disparity in time sequences

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.<<ETX>>

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

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.<<ETX>>

Feature Extraction for Computer-Aided Analysis of Mammograms

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 neighbourhood 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.

Stable estimation of image orientation

We examine the performance of phase-based and energy-based techniques for estimating image orientation, emphasizing measurement stability under deformations that commonly occur in natural images. We also present a new energy-based technique for estimating multiple orientations in a neighbourhood and for reliably extracting multiple orientations from textured image regions.<<ETX>>

A Tensor Based Approach To Structure Analysis And Enhancement In 2D, 3D And 4D

A theory for the estimation and representation of local structure in terms of orientation has been developed for 2D, 3D and 4D signal spaces. The theory is based upon the representation of local orientation in terms of a symmetric tensor, reminiscent of the familiar inertia tensor in mechanics, and provides the important attributes: uniqueness, uniformity and polar separability. Uniqueness implies that the ma.pping is one to one, uniformity that the representation implicitly carries a definition of distance that is rotation invariant and polar separability means that the norm of the representing tensor is rotation invariant. It is shown that the representaftion can be realized by filtering the signal using a class of symmetrically distributed phase iizvariant quadrature filters. The orientation tensor is then obtained by simply performing a weighted summation of pre calculated, filter specific, tensors, the weights being the quadrakure filter output magnitudes. This situation is satisfying as it implies a simple implementation of the theory and that requirements on computational capacity can be kept within reasonable limits. The algorithm has been tested in a number of different situations and has proven to provide accurate and robust estimates. Unlike other representations th,e properties of this representation makes local averaging a meaningful operation. This makes it possible to obtain good estim,ates of local structure and orientation at very low SNR. These estimates serve as a sound basis for adaptive filtering of noisy data. A steerable Jilter is constructed by a tensor controlled linear summation of a number of fixed filters. The resulting filter adapts to the local situation both in terms of structure, (linelike planelike), and orientation. This enhancement scheme has been tested on still images, image sequences (video, ultrasonic) and volume data (MR, CT) with good results. lThis work is supported by the Swedish board for technical development 9.10

Orientation and Velocity

This chapter introduces the use of tensors in estimation of local structure and orientation. The tensor representation is shown to be crucial to unambiguous and continuous representation of local o ...