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.

We present a novel method to extract iso-surfaces from distance volumes. It generates high quality semi-regular multiresolution meshes of arbitrary topology. Our technique proceeds in two stages. First, a very coarse mesh with guaranteed topology is extracted. Subsequently an iterative multi-scale force-based solver refines the initial mesh into a semi-regular mesh with geometrically adaptive sampling rate and good aspect ratio triangles. The coarse mesh extraction is performed using a new approach we call surface wavefront propagation. A set of discrete iso-distance ribbons are rapidly built and connected while respecting the topology of the iso-surface implied by the data. Subsequent multi-scale refinement is driven by a simple force-based solver designed to combine good iso-surface fit and high quality sampling through reparameterization. In contrast to the Marching Cubes technique our output meshes adapt gracefully to the iso-surface geometry, have a natural multiresolution structure and good aspect ratio triangles, as demonstrated with a number of examples.

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.

Abstract. In this paper, we propose a new PDE-based methodology for deformable surfaces that is capable of automatically evolving its shape to capture the geometric boundary of the data and simultaneously discover its underlying topological structure. Our model can handle multiple types of data (such as volumetric data, 3D point clouds and 2D image data), using a common mathematical framework. The deformation behavior of the model is governed by partial differential equations (e.g. the weighted minimal surface flow). Unlike the level-set approach, our model always has an explicit representation of geometry and topology. The regularity of the model and the stability of the numerical integration process are ensured by a powerful Laplacian tangential smoothing operator. By allowing local adaptive refinement of the mesh, the model can accurately represent sharp features. We have applied our model for shape reconstruction from volumetric data, unorganized 3D point clouds and multiple view images. The versatility and robustness of our model allow its application to the challenging problem of multiple view reconstruction. Our approach is unique in its combination of simultaneous use of a high number of arbitrary camera views with an explicit mesh that is intuitive and easy-to-interact-with. Our model-based approach automatically selects the best views for reconstruction, allows for visibility checking and progressive refinement of the model as more images become available. The results of our extensive experiments on synthetic and real data demonstrate robustness, high reconstruction accuracy and visual quality. 1

There have been significant efforts to build a probabilistic atlas of the brain and to use it for many common applications, such as segmentation and registration. Though the work related to brain atlases can be applied to nonbrain organs, less attention has been paid to actually building an atlas for organs other than the brain. Motivated by the automatic identification of normal organs for applications in radiation therapy treatment planning, we present a method to construct a probabilistic atlas of an abdomen consisting of four organs (i.e., liver, kidneys, and spinal cord). Using 32 noncontrast abdominal computed tomography (CT) scans, 31 were mapped onto one individual scan using thin plate spline as the warping transform and mutual information (MI) as the similarity measure. Except for an initial coarse placement of four control points by the operators, the MI-based registration was automatic. Additionally, the four organs in each of the 32 CT data sets were manually segmented. The manual segmentations were warped onto the “standard ” patient space using the same transform computed from their gray scale CT data set and a probabilistic atlas was calculated. Then, the atlas was used to aid the segmentation of low-contrast organs in an additional 20 CT data sets not included in the atlas. By incorporating the atlas information into the Bayesian framework, segmentation results clearly showed improvements over a standard unsupervised segmentation method.

A novel, physically motivated deformable model for shape recovery and segmentation is presented. The model, referred to as the charged-particle model (CPM), is inspired by classical electrodynamics and is based on a simulation of charged particles moving in an electrostatic field. The charges are attracted towards the contours of the objects of interest by an electrostatic field, whose sources are computed based on the gradient-magnitude image. The electric field plays the same role as the potential forces in the snake model, while internal interactions are modeled by repulsive Coulomb forces. We demonstrate the flexibility and potential of the model in a wide variety of settings: shape recovery using manual initialization, automatic segmentation, and skeleton computation. We perform a comparative analysis of the proposed model with the active contour model and show that specific problems of the latter are surmounted by our model. The model is easily extendable to 3D and copes well with noisy images.

Abstract. Often in neurosurgical planning a dual echo acquisition is performed that yields proton density (PD) and T2-weighted images to evaluate edema near a tumour or lesion. The development of vessel segmentation algorithms for PD images is of general interest since this type of acquisition is widespread and is entirely noninvasive. Whereas vessels are signaled by black blood contrast in such images, extracting them is a challenge because other anatomical structures also yield similar contrasts at their boundaries. In this paper we present a novel multi-scale geometric flow for segmenting vasculature from PD images which can also be applied to the easier cases of computed tomography (CT) angiography data or Gadolinium enhanced MRI. The key idea is to first apply Frangi’s vesselness measure [4] to find putative centerlines of tubular structures along with their estimated radii. This multi-scale measure is then distributed to create a vector field which is orthogonal to vessel boundaries so that the flux maximizing flow algorithm of [17] can be applied to recover them. We validate the approach qualitatively with PD, angiography and Gadolinium enhanced MRI volumes. 1

This paper is an attempt to review the state-of-the-art cortical segmentation techniques in 2-D and 3-D using brain magnetic resonance imaging (MRI), their applications and new challenges

This paper presents a novel modeling algorithm that is capable of simultaneously recovering correct shape geometry as well as its unknown topology from arbitrarily complicated datasets. Our algorithm starts from a simple seed model (of genus zero) that can be arbitrarily initiated by users within any dataset. The deformable behavior of our model is governed by a locally defined objective function associated with each vertex of the model. Through the numerical computation of function optimization, our algorithm can adaptively subdivide the model geometry, automatically detect self-collision of the model, properly modify its topology (because of the occurrence of self-collision), continuously evolve the model towards the object boundary, and reduce fitting error and improve fitting quality via global subdivision. Commonly used mesh optimization techniques are employed throughout the geometric deformation and topological variation in order to ensure the model both locally smooth and globally well conditioned. We have applied our algorithm to various real/synthetic range data as well as volumetric image data in order to empirically verify and validate its usefulness. Based on our experiments, the new modeling algorithm proves to be very powerful and extremely valuable for shape recovery in computer vision, reverse engineering in computer graphics, and iso-surface extraction in visualization.

We introduce a new method for segmentation of 3D medical data based on geometric variational principles. A minimal variance criterion is coupled with a geometric edge alignment measure and the geodesic active surface model. An efficient numerical scheme is proposed. In order to simultaneously detect a number of different objects in the image, a hierarchal method is presented.