Abstract

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 curvi- linear 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 struc- ture boundary. The gradient symmetry and the gradient antisymmetry are evalu- ated based on the notion of oriented flux. By utilizing the aforementioned gradient symmetry information, an active contour model is tailored to perform segmenta- tion. On the one hand, by exploiting the symmetric image gradient pattern ob- served 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 re- sponses to precisely drive contours to the structure boundaries, as well as avoiding contour leakages. The proposed method is capable of delivering promising seg- mentation 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.