Abstract

Thin objects in 3D volumes, for instance vascular networks in medi- cal imaging or various kinds of fibres in materials science, have been of interest for some time to computer vision. Particularly, tubular objects are everywhere elongated in one principal direction – which varies spatially – and are thin in the other two perpendicular directions. Filters for detecting such structures use for instance an analysis of the three principal directions of the Hessian, which is a lo- cal feature. In this article, we present a low-level tubular structure detection filter. This filter relies on paths, which are semi-global features that avoid any blurring effect induced by scale-space convolution. More precisely, our filter is based on recently developed morphological path operators. These require sampling only in a few principal directions, are robust to noise and do not assume feature regu- larity. We show that by ranking the directional response of this operator, we are further able to efficiently distinguish between blob, thin planar and tubular struc- tures. We validate this approach on several applications, both from a qualitative and a quantitative point of view, demonstrating noise robustness and an efficient response on tubular structures.