  Tubular structure tracking is a crucial task in the fields of computer vision
and medical image analysis. The minimal paths-based approaches have exhibited
their strong ability in tracing tubular structures, by which a tubular
structure can be naturally modeled as a minimal geodesic path computed with a
suitable geodesic metric. However, existing minimal paths-based tracing
approaches still suffer from difficulties such as the shortcuts and short
branches combination problems, especially when dealing with the images
involving complicated tubular tree structures or background. In this paper, we
introduce a new minimal paths-based model for minimally interactive tubular
structure centerline extraction in conjunction with a perceptual grouping
scheme. Basically, we take into account the prescribed tubular trajectories and
curvature-penalized geodesic paths to seek suitable shortest paths. The
proposed approach can benefit from the local smoothness prior on tubular
structures and the global optimality of the used graph-based path searching
scheme. Experimental results on both synthetic and real images prove that the
proposed model indeed obtains outperformance comparing with the
state-of-the-art minimal paths-based tubular structure tracing algorithms.
