Several geometric active contour models have been proposed for segmentation in computer vision and image analysis. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) under constraints from image forces so that it clings to features of interest in an intensity image. Recent variations on this theme take into account properties of enclosed regions and allow for multiple curves or surfaces to be simultaneously represented. However, it is still unclear how to apply these techniques to images of narrow elongated structures, such as blood vessels, where intensity contrast may be low and reliable region statistics cannot be computed. To address this problem we derive the gradient flows which maximize the rate of increase of flux of an appropriate vector field through a curve (in 2D) or a surface (in 3D). The key idea is to exploit the direction of the vector field along with its magnitude. The calculations lead to a simple and elegant interpretation which is essentially parameter free and has the same form in both dimensions. We illustrate its advantages with several level-set based segmentations of 2D and 3D angiography images of blood vessels.

Vessel segmentation algorithms are the critical components of circulatory blood vessel analysis systems. We present a survey of vessel extraction techniques and algorithms. We put the various vessel extraction approaches and techniques in perspective by means of a classification of the existing research. While we have mainly targeted the extraction of blood vessels, neurosvascular structure in particular, we have also reviewed some of the segmentation methods for the tubular objects that show similar characteristics to vessels. We have divided vessel segmentation algorithms and techniques into six main categories: (1) pattern recognition techniques, (2) model-based approaches, (3) tracking-based approaches, (4) artificial intelligence-based approaches, (5) neural network-based approaches, and (6) miscellaneous tube-like object detection approaches. Some of these categories are further divided into sub- categories. We have also created tables to compare the papers in each category against such criteria as dimensionality, input type, pre-processing, user interaction, and result type.

The completion of interrupted lines or the enhancement of flow-like structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so-called interest operator (second-moment matrix, structure tensor). An m-dimensional formulation of this method is analysed with respect to its well-posedness and scale-space properties. An efficient scheme is presented which uses a stabilization by a semi-implicit additive operator splitting (AOS), and the scale-space behaviour of this method is illustrated by applying it to both 2-D and 3-D images.

Detection of tubular structures in 3D images is an important issue for vascular detection in medical imaging. We present in this paper a new approach for centerline detection and reconstruction of 3D tubular structures. Several models of vessels are introduced for estimating the sensivity of the image second order derivatives according to elliptical cross-section, to curvature of the axis, or to partial volume e#ects. Our approach uses a multiscale analysis for extracting vessels of di#erent sizes according to the scale. For a given model of vessel, we derive an analytic expression of the relationship between the radius of the structure and the scale at which it is detected. The algorithm gives both centerline extraction and radius estimation of the vessels allowing their reconstruction. The method has been tested on both synthetic and real images, with encouraging results. This work was done in collaboration with GEMS .

Curve evolution schemes for segmentation, implemented with level set methods, have become an important approach in computer vision. Previous work has modeled evolving contours which are curves in 2D or surfaces in 3D. Our objective is to explore recent mathematical work enabling the evolution of manifolds of higher co-dimension. We consider 1D curves in 3D (codimension-two) for the application of automatically segmenting blood vessels in volumetric magnetic resonance angiography (MRA) images. This paper describes the theoretical foundations of our system, CURVES, then provides segmentation results compared against segmentations obtained interactively by a neurosurgeon. Segmentations of bronchi in lung computed tomography (CT) scans are also presented. The new experiments, comparisons to manual segmentations, and sample comparison to the use of a codimension-one regularization force are the primary contributions of this report.

We present a new approach to anisotropic diffusion based on a multi-directional di#usion flux. The diffusion flux is decomposed in an orthogonal basis, e#ectively enabling enhancement of contours as well as di#usion along the contours. To this end, we have selected a 3D basis that depicts the directions of principal curvature and has an interesting interpretation in the context of the vessels. The di#usion function associated to each vector of the basis depends on the first order derivative of the intensity in this direction, instead of the traditional norm of the smoothed gradient. Accordingly, we present the results of a restoration of Computed Tomography data of the liver.

Three-dimensional rotational angiography (3DRA) is a new and promising technique for obtaining high-resolution isotropic 3D images of vascular structures. However, due to the relatively high noise level and the presence of other background structures in clinical 3DRA images, noise reduction is inevitable. In this paper, we evaluate a number of linear and nonlinear diffusion techniques for this purpose. Specifically, we analyze the effects of these techniques on the thresholdbased visualization and quantification of vascular anomalies in 3DRA images. The results of invitro experiments indicate that edge-enhancing anisotropic diffusion filtering is most suitable: the increase in the user-dependency of visualizations and quantifications is considerably less with this technique compared to linear filtering techniques, and it is better at reducing noise near edges than isotropic nonlinear diffusion. However, in view of the memory and computation-time requirements of this technique, the latter scheme may be considered a useful alternative.

A number of geometric active contour and surface models have been proposed for shape segmentation in the literature. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) so that it clings to the features of interest in an intensity image. Several of these models have been derived, using a variational formulation, as gradient flows which minimize or maximize a particular energy functional. However, in practice these models often fail on images of low contrast or narrow structures. To address this problem we have recently proposed the idea of maximizing the rate of increase of flux of an auxiliary vector field through a curve. This has lead to an interpretation as a 2D gradient flow, which is essentially parameter free. In this paper we extend the analysis to 3D and prove that the form of the gradient flow does not change. We illustrate its potential with level-set based segmentations of blood vessels in a large 3D computed rotational angiography (CRA) data set.

Figure 1: In the left three images, an interactive segmentation of a brain tumor with an active surface model given in implicit form is evolving toward the final segmentation using the level set method [Lefohn et al. 2003]. In the right image, the same method is applied to segmentation of a mouse liver. Level set computations and simultaneous visualization are performed entirely on the GPU (graphics processing unit), which performs general floating-point computations in addition to rendering. Recent advances in the computational power of graphics processing units (GPUs) have turned them into a viable platform for general purpose floating-point computations. A very promising application of these new capabilities is interactive segmentation of medical volume data, which usually involves solving a large number of partial differential equations (PDEs) for each iteration of an evolving segmentation that can be viewed and guided by user input while it is being calculated, and is thus computationally very demanding. We give an overview of segmentation algorithms with a focus on leveraging the power of GPUs in order to obtain high-quality segmentations of medical data in an interactive process, with the premise that these algorithms will lead to faster and higher-quality segmentations in clinical practice in the near future. 2

Problem / Background: In order to help hepatic surgical planning we perfected automatic 3D reconstruction of patients from conventional CT-scan, and interactive visualization and virtual resection tools. Tools and Methods: from a conventional abdominal CT-scan, we have developed