This paper describes a novel method for regional characterization of three-dimensional vector fields using a pattern matching approach. Given a three-dimensional vector field, the goal is to automatically locate, identify, and visualize a selected set of classes of structures or features. Rather than analytically defining the properties that must be fulfilled in a region in order to be classified as a specific structure, a set of idealized patterns for each structure type is constructed. Similarity to these patterns is then defined and calculated. Examples of structures of interest include vortices, swirling flow, diverging or converging flow, and parallel flow. Both medical and aerodynamic applications are presented in this paper.

While many methods exist for visualising scalar and vector data, visualisation of tensor data is still troublesome. We present a method for visualising second order tensors in three dimensions using a hybrid between direct volume rendering and glyph rendering. An overview scalar field is created by using three-dimensional adaptive filtering of a scalar field containing noise. The filtering process is controlled by the tensor field to be visualised, creating patterns that characterise the tensor field. By combining direct volume rendering of the scalar field with standard glyph rendering methods for detailed tensor visualisation, a hybrid solution is created. A combined volume and glyph renderer was implemented and tested with both synthetic tensors and strain-rate tensors from the human heart muscle, calculated from phase contrast magnetic resonance image data. A comprehensible result could be obtained, giving both an overview of the tensor field as well as detailed information on individual tensors.

A four-dimensional mapping (three spatial dimensions + time) of myocardial strain-rate would help to describe the mechanical properties of the myocardium, which affect important physiological factors such as the pumping performance of the ventricles. Strain-rate represents the local instantaneous deformation of the myocardium and can be calculated from the spatial gradients of the velocity field. Strain-rate has previously been calculated using one-dimensional (ultrasound) or two-dimensional (2-D) magnetic resonance imaging) techniques. However, this assumes that myocardial motion only occurs in one direction or in one plane, respectively. This paper presents a method for calculation of the time-resolved three-dimensional (3-D) strain-rate tensor using velocity vector information in a 3-D spatial grid during the whole cardiac cycle. The strain-rate tensor provides full information of both magnitude and direction of the instantaneous deformation of the myocardium. A method for visualization of the full 3-D tensor is also suggested. The tensors are visualized using ellipsoids, which display the principal directions of strain-rate and the ratio between strain-rate magnitude in each direction. The presented method reveals the principal strain-rate directions without a priori knowledge of myocardial motion directions.