Tubular Curvature Filter: Implicit Pointwise Curvature Calculation Method for Tubular Objects

Curvature estimation methods are important as they capture salient features for various applications in image processing, especially within medical domains where tortuosity of vascular structures is of significant interest. Existing methods based on centerline or skeleton curvature fail to capture curvature gradients across a rotating tubular structure. This paper presents a Tubular Curvature Filter method that locally calculates the acceleration of bundles of curves that traverse along the tubular object parallel to the centerline. This is achieved by examining the directional rate of change in the eigenvectors of the Hessian matrix of a tubular intensity function in space. This method implicitly calculates the local tubular curvature without the need to explicitly segment the tubular object. Experimental results demonstrate that the Tubular Curvature Filter method provides accurate estimates of local curvature at any point inside tubular structures.