Repairing the cerebral vascular through blending Ball B-Spline curves with G2 continuity

The analysis of cerebrovascular shape is important for the diagnose and pathologic identification. But as the limitation of the segmentation algorithm, the complete cerebrovascular volume data are difficult to obtain. So the triangle mesh of the vessel model generated for the medical images may appear many gaps. In the paper, we present a extension algorithm for Ball B-Spline curve with G2 continuity to repair the cerebrovascular structure from time-of-flight (TOF) magnetic resonance angiography (MRA) data. Ball B-Spline curve has its distinct advantages in representing a 3D tube like organs. A ball Bezier segment is used to construct the extending part and G2-continuity is applied to describe the smoothness at the joints. Fairness of the extending ball Bezier curve segment is achieved by minimizing energy objective functions for the center curve and the radius function separately. New control balls are computed by unclamping algorithm to represent the whole extended ball B-Spline curve. The experimental results demonstrate the effectiveness of our algorithm. The final results show that the proposed method provides good blending result, especially for those blood vessels of small size.