Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
International Journal of Computer Vision
A Level-Set Approach to 3D Reconstruction from Range Data
International Journal of Computer Vision
Flux Maximizing Geometric Flows
IEEE Transactions on Pattern Analysis and Machine Intelligence
Muliscale Vessel Enhancement Filtering
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Multiscale detection of curvilinear structures in 2-D and 3-D image data
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Eigensnakes for Vessel Segmentation in Angiography
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 4
Three Dimensional Curvilinear Structure Detection Using Optimally Oriented Flux
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part IV
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
IEEE Transactions on Image Processing
Gradient competition anisotropy for centerline extraction and segmentation of spinal cords
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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This paper proposes a novel approach to segment three dimensional curvilinear structures, particularly vessels in angiography, by inspecting the symmetry of image gradients. The proposed method stresses the importance of simultaneously considering both the gradient symmetry with respect to the curvilinear structure center, and the gradient antisymmetry with respect to the object boundary. Measuring the image gradient symmetry remarkably suppresses the disturbance introduced by rapid intensity changes along curvilinear structures. Meanwhile, considering the image gradient antisymmetry helps locate the structure boundary. The gradient symmetry and the gradient antisymmetry are evaluated based on the notion of oriented flux. By utilizing the aforementioned gradient symmetry information, an active contour model is tailored to perform segmentation. On the one hand, by exploiting the symmetric image gradient pattern observed at structure centers, the contours expand along curvilinear structures even through there exists intensity fluctuation along the structures. On the other hand, measuring the antisymmetry of the image gradient conveys strong detection responses to precisely drive contours to the structure boundaries, as well as avoiding contour leakages. The proposed method is capable of delivering promising segmentation results. This is validated in the experiments using synthetic data and real vascular images of different modalities, and through the comparison to two well founded and published methods for curvilinear structure segmentation.