Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Toward a computational theory of shape: an overview
ECCV 90 Proceedings of the first european conference on Computer vision
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Segmentation of Cerebral Vessels and Aneurysms from MR Angiography Data
IPMI '97 Proceedings of the 15th International Conference on Information Processing in Medical Imaging
IPMI '99 Proceedings of the 16th International Conference on Information Processing in Medical Imaging
Muliscale Vessel Enhancement Filtering
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Directional Anisotropic Diffusion Applied to Segmentation of Vessels in 3D Images
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Model-Based Multiscale Detection of 3D Vessels
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Multiscale detection of curvilinear structures in 2-D and 3-D image data
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Gradient flows and geometric active contour models
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A Statistical Approach to Snakes for Bimodal and Trimodal Imagery
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Geodesic Active Regions for Supervised Texture Segmentation
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
Area and length minimizing flows for shape segmentation
IEEE Transactions on Image Processing
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
Tubular Structure Segmentation Based on Minimal Path Method and Anisotropic Enhancement
International Journal of Computer Vision
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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.