The concept of curvature and shape-based rendering is beneficial for medical visualization of CT and MRI image volumes. Color-coding of local shape properties derived from the analysis of the local Hessian can implicitly highlight tubular structures such as vessels and airways, and guide the attention to potentially malignant nodular structures such as tumors, enlarged lymph nodes, or aneurysms. For some clinical applications, however, the evaluation of the Hessian matrix does not yield satisfactory renderings, in particular for hollow structures such as airways, and densely embedded low contrast structures such as lymph nodes. Therefore, as a complement to Hessian-based shape-encoding rendering, this paper introduces a combination of an efficient sparse radial gradient sampling scheme in conjunction with a novel representation, the radial structure tensor (RST). As an extension of the well-known general structure tensor, which has only positive definite eigenvalues, the radial structure tensor correlates position and direction of the gradient vectors in a local neighborhood, and thus yields positive and negative eigenvalues which can be used to discriminate between different shapes. As Hessian-based rendering, also RST-based rendering is ideally suited for GPU implementation. Feedback from clinicians indicates that shape-encoding rendering can be an effective image navigation tool to aid diagnostic workflow and quality assurance.

The paper describes a model of the coronary artery tree. It has been developed for the context of medical image processing and medical reporting. The model combines geometric information with associated medical nomenclature and anatomical relations. Applicability of the model and interindividual geometrical variability has been studied by matching the model to the individual coronary anatomy of 33 patients imaged with a multidetector-row computer tomography scanner.

A diffusion-based approach to surface smoothing is presented. Surfaces are represented as scalar functions defined on the sphere. The approach is equivalent to Gaussian smoothing on the sphere and is computationally efficient since it does not require iterative smoothing. Furthermore, it does not suffer from the well-known shrinkage problem. Evolution of important shape features (parabolic curves) under diffusion is demonstrated. A nonlinear modification of the diffusion process is introduced in order to improve smoothing behavior of elongated and poorly centered objects.

We consider simple digital curves in a 3D orthogonal grid as special polyhedrally bounded sets. These digital curves model digitized curves or arcs in three-dimensional Euclidean space. The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve. So far, no algorithm was known for the calculation of such a shortest polygonal curve. The paper provides an iterative algorithmic solution for approximating the minimum-length polygon of a given simple digital space-curve. The theoretical foundations of this algorithm are presented as well as experimental results.

We consider simple digital curves in a 3D orthogonal grid as special polyhedrally bounded sets. These digital curves model digitized curves or arcs in three-dimensional euclidean space. The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve. So far no algorithm was known for the calculation of such a shortest polygonal curve. The paper provides an iterative algorithmic solution, including a presentation of its foundations and of experimental results.

We introduce quaternionic Gabor filters for the classification of local image structure. These filters are constructed as windowed basis functions of the quaternionic Fourier transform. We show that-in contrast to the 2D complex Gabor filters-the quaternionic Gabor filters are intrinsically 2D filters. A generalized phase concept is introduced and compared to the classical one. It is shown how local image structure can be classified by the value of the local quaternionic phase.