: This paper describes a method for the enhancement of curvilinear structures such as vessels and bronchi in 3D medical images. A 3D line enhancement filter is developed with the aim of discriminating line structures from other structures and recovering line structures of various widths. The 3D line filter is based on a combination of the eigenvalues of the 3D Hessian matrix. Multi-scale integration is formulated by taking the maximum among single-scale filter responses, and its characteristics are examined to derive criteria for the selection of parameters in the formulation. The resultant multi-scale line-filtered images provide significantly improved segmentation and visualization of curvilinear structures. The usefulness of the method is demonstrated by the segmentation and visualization of brain vessels from MRI (magnetic resonance imaging) and MRA (magnetic resonance angiography), bronchi from a chest CT, and liver vessels (portal veins) from an abdominal CT. Keywords: 3D image ...

In [10] we presented a new velocity estimation algorithm, using orientation tensors and parametric motion models to provide both fast and accurate results. One of the tradeoffs between accuracy and speed was that no attempts were made to obtain regions of coherent motion when estimating the parametric models. In this paper we show how this can be improved by doing a simultaneous segmentation of the motion field. The resulting algorithm is slower than the previous one, but more accurate. This is shown by evaluation on the well-known Yosemite sequence, where already the previous algorithm showed an accuracy which was substantially better than for earlier published methods. This result has now been improved further.

This paper describes 3D image filters for the enhancement of specific local intensity structures such as line and sheet, and its application to tissue classification for volume rendering. Multi-channel classification is performed by combining different 3D image filter outputs. The resulted method significantly enlarges the scope of volume rendering, especially in the medical domain. We show the usefulness of the method for different visualization problems. 1 Introduction Volume rendering is a powerful visualization tool especially for medical application [1],[2],[3],[4]. Basic requirement in medical application is to visualize specific tissues of interest with the relation to surrounding structures. Tissue classification is one of the most important processes in the volume rendering pipeline. Most commonly, this process is done based on the histogram of intensity values in original 3D images. Probabilistic or fuzzy classification has been used instead of binary classification in orde...

Motion estimation in image sequences is an important step in many computer vision and image processing applications. Several methods for solving this problem have been proposed, but very few manage to achieve a high level of accuracy without sacrificing processing speed. This paper presents a novel motion estimation algorithm, which gives excellent results on both counts. The algorithm starts by computing 3D orientation tensors from the image sequence. These are combined under the constraints of a parametric motion model to produce velocity estimates. Evaluated on the well-known Yosemite sequence, the algorithm shows an accuracy which is substantially better than for previously published methods. Computationally the algorithm is simple and can be implemented by means of separable convolutions, which also makes it fast. 1 Introduction Motion estimation algorithms always involve a trade-off between speed and accuracy. The method presented here is primarily intended to be accurate but ...

This thesis presents a new method for detection of complex curvatures such as corners, circles, and star patterns. The method is based on a second degree local polynomial model applied to a local orientation description in double angle representation. The theory of rotational symmetries is used to compute curvature responses from the parameters of the polynomial model. The responses are made more selective using a scheme of inhibition between different symmetry models. 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 search, etc. A very efficient approximative algorithm for single and multiscale polynomial expansion is developed, which is used for detection of the complex curvatures in one or several scales. The algorithm is based on the simple observation that polynomial functions multiplied with a Gaussian function can be described in terms of partial derivatives of the Gaussian. The approximative polynomial expansion

We present an integrated approach to the derivation of scene description from binocular stereo images. Unlike popular stereo approaches, we address both the stereo correspondence problem and the surface reconstruction problem simultaneously by inferring the scene description directly from local measurements of both point and line correspondences. In order to handle the issues of noise, indistinct image features, surface discontinuities, and half occluded regions, we introduce a robust computational technique call tensor voting for the inference of scene description in terms of surfaces, junctions, and region boundaries. The methodology is grounded in two elements: tensor calculus for representation, and non-linear voting for data communication. By efficiently and effectively collecting and analyzing neighborhood information, we are able to handle the tasks of interpolation, discontinuity detection, and outlier identification simultaneously. The proposed method is non-iterative, robust ...

Don’t confuse the moon with the finger that points at it. Zen proverb iii iv In this thesis a new type of representation for medium level vision operations is explored. We focus on representations that are sparse and monopolar. Theword sparse signifies that information in the feature sets used is not necessarily present at all points. On the contrary, most features will be inactive. The word monopolar signifies that all features have the same sign, e.g. are either positive or zero. A zero feature value denotes “no information”, and for non-zero values, the magnitude signifies the relevance. A sparse scale-space representation of local image structure (lines and edges) is developed. A method known as the channel representation is used to generate sparse representations, and its ability to deal with multiple hypotheses is described. It is also shown how these hypotheses can be extracted in a robust manner. The connection of soft histograms (i.e. histograms with overlapping bins) to the channel representation, as well as to the use of dithering in relaxation of quantisation errors is shown. The use of soft histograms for estimation of unknown probability density functions (PDF), and estimation of image rotation are demonstrated. The advantage with the use of sparse, monopolar representations in associative learning is demonstrated. Finally we show how sparse, monopolar representations can be used to speed up and improve template matching. v vi

Abstract. Perceptual experiments indicate that corners and curvature are very important features in the process of recognition. This paper presents a new method to efficiently detect rotational symmetries, which describe complex curvature such as corners, circles, star- and spiral patterns. The method is designed to give selective and sparse responses. It works in three steps; first extract local orientation from a gray-scale or color image, second correlate the orientation image with rotational symmetry filters and third let the filter responses inhibit each other in order to get more selective responses. The correlations can be made efficient by separating the 2D-filters into a small number of 1D-filters. These symmetries can serve as feature points at a high abstraction level for use in hierarchical matching structures for 3D-estimation, object recognition, etc. 1

AbstractÐWe present an integrated approach to the derivation of scene descriptions from a pair of stereo images, where the steps of feature correspondence and surface reconstruction are addressed within the same framework. Special attention is given to the development of a methodology with general applicability. In order to handle the issues of noise, lack of image features, surface discontinuities, and regions visible in one image only, we adopt a tensor representation for the data and introduce a robust computational technique called tensor voting for information propagation. The key contributions of this paper are twofold: First, we introduce ªsaliencyº instead of correlation scores as the criterion to determine the correctness of matches and the integration of feature matching and structure extraction. Second, our tensor representation and voting as a tool enables us to perform the complex computations associated with the formulation of the stereo problem in three dimensions at a reasonable computational cost. We illustrate the steps on an example, then provide results on both random dot stereograms and real stereo pairs, all processed with the same parameter set. Index TermsÐBinocular stereo, tensor voting, perceptual grouping, surface inference. 1

This thesis presents a signal representation in terms of operators. The signal is assumed to be an element of a vector space and subject to transformations of operators. The operators form continuous groups, so-called Lie groups. The representation can be used for signals in general, in particular if spatial relations are undefined, and it does not require a basis of the signal space to be useful. Special attention is given to orthogonal operator groups which are generated by antiHermitian operators by means of the exponential mapping. It is shown that the eigensystem of the group generator is strongly related to properties of the corresponding operator group. For one-parameter orthogonal operator groups, a phase concept is introduced. This phase can for instance be used to distinguish between spatially even and odd signals and, therefore, corresponds to the usual phase for multi-dimensional signals. Given one operator group that represents the variation of the signal and one operator ...