Introduction

Directional tracking through vector fields has been a widely explored topic in visualization and computer graphics [5,19,20]. The standard streamline technique advects massless particles through the vector field and traces their location as a function of time. Analogously, a hyper-streamlines approach has been proposed to trace changes through tensor fields, following the dominant eigenvector direction [7]. These methods work best on very ``clean'' datasets, which are usually produced as a result of simulations; these methods typically do not handle raw experimental data very well, due to noise and resolution issues. Recently, attention has been given to the visualization of 2D [12] and 3D [10] diffusion tensor fields from DT-MRI data. Although these methods provide nice visual cues, they do not attempt to recover the underlying anatomical structures, which are the white matter fiber tracts (bundles of axons) found within the brain¹. Several previous endeavors have been made for recovering the underlying structure by extracting fibers through the application of modified streamline algorithms. Examples include tensor-lines [21] and stream-tubes [24,6]. Direct fiber tractography method has been developed in [2]. Other work suggests separate regularizaton of eigenvalues and eigenvectors in the tensor fields before fiber tracing [14]. Another method uses level sets for front propagation [16]. These algorithms have had some success in recovering the underlying structures. Some problems remain due to the complexity of the tensor field, voxelization effects and the significant amount of noise that is omnipresent in experimental data. Recent work concentrated on deriving a continuous tensor field approximation [15] and using signal processing techniques (for example, Kalman filtering [8]) for cleaning up the data. The goal of this paper is to develop more stable tensor tracing techniques which allow the extraction of the underlying continuous anatomical structures from experimental diffusion tensor data. The proposed technique uses a moving local regularizing filter that allows the tracing algorithm to cross noisy regions and gaps in the data while preserving directional consistency.