Regression analysis is a powerful tool for the study of changes in a dependent variable as a function of an independent regressor variable, and in particular it is applicable to the study of anatomical growth and shape change. When the underlying process can be modeled by parameters in a Euclidean space, classical regression techniques are applicable and have been studied extensively. However, recent work suggests that attempts to describe anatomical shapes using flat Euclidean spaces undermines our ability to represent natural biological variability. In this paper we develop a method for regression analysis of general, manifold-valued data. Specifically, we extend Nadaraya-Watson kernel regression by recasting the regression problem in terms of Frechet expectation. Although this method is quite general, our driving problem is the study anatomical shape change as a function of age from random design image data. We demonstrate our method by analyzing shape change in the brain from a random design dataset of MR images of 89 healthy adults ranging in age from 22 to 79 years. To study the small scale changes in anatomy, we use the infinite dimensional manifold of diffeomorphic transformations, with an associated metric. We regress a representative anatomical shape, as a function of age, from this population.

The clinical recognition of abnormal vascular tortuosity, or excessive bending, twisting, and winding, is important to the diagnosis of many diseases. Automated detection and quantitation of abnormal vascular tortuosity from three-dimensional (3-D) medical image data would, therefore, be of value. However, previous research has centered primarily upon two-dimensional (2-D) analysis of the special subset of vessels whose paths are normally close to straight. This report provides the first 3-D tortuosity analysis of clusters of vessels within the normally tortuous intracerebral circulation. We define three different clinical patterns of abnormal tortuosity. We extend into 3-D two tortuosity metrics previously reported as useful in analyzing 2-D images and describe a new metric that incorporates counts of minima of total curvature. We extract vessels from MRA data, map corresponding anatomical regions between sets of normal patients and patients with known pathology, and evaluate the three tortuosity metrics for ability to detect each type of abnormality within the region of interest. We conclude that the new tortuosity metric appears to be the most effective in detecting several types of abnormalities. However, one of the other metrics, based on a sum of curvature magnitudes, may be more effective in recognizing tightly coiled, "corkscrew" vessels associated with malignant tumors.

The extraction of the centerlines of tubular objects in two and three-dimensional images is a part of many clinical image analysis tasks. One common approach to tubular object centerline extraction is based on intensity ridge traversal. In this paper, we evaluate the effects of initialization, noise, and singularities on intensity ridge traversal and present multiscale heuristics and optimal-scale measures that minimize these effects. Monte Carlo experiments using simulated and clinical data are used to quantify how these "dynamic-scale" enhancements address clinical needs regarding speed, accuracy, and automation. In particular, we show that dynamic-scale ridge traversal is insensitive to its initial parameter settings, operates with little additional computational overhead, tracks centerlines with subvoxel accuracy, passes branch points, and handles significant image noise. We also illustrate the capabilities of the method for medical applications involving a variety of tubular structures in clinical data from different organs, patients, and imaging modalities.

This paper describes a new method of combining ray-casting with segmentation. Volume rendering is performed at interactive rates on personal computers, and visualizations include both "superficial" ray-casting through a shell at each object's surface and "deep" ray-casting through the confines of each object. A feature of the approach is the option to smoothly and interactively dilate segmentation boundaries along all axes. This ability, when combined with selective "turning off" of extraneous image objects, can help clinicians detect and evaluate segmentation errors that may affect surgical planning. We describe both a method optimized for displaying tubular objects and a more general method applicable to objects of arbitrary geometry. In both cases, select three-dimensional points are projected onto a modified z buffer that records additional information about the projected objects. A subsequent step selectively volume renders only through the object volumes indicated by the z buffer. We describe how our approach differs from other reported methods for combining segmentation with ray-casting, and illustrate how our method can be useful in helping to detect segmentation errors.