The motivation of this paper is the filtering of thin elongated objects, such as veins, fibres etc. In particular, we focus our attention on detecting thin segments and linking them when disconnection is due to noise. A hybrid Hessian-based and morphological linear filtering method is proposed within the framework of scale space theory. For each pixel the second- derivative response kernel is collected and formed into a Hessian matrix which undergoes eigen analysis. From there, the best eigenvalue response along with the corresponding eigenvector is chosen on different scales. Using the resulting principal directions of linear segment pixels, morphological filters are used to track and connect the linears.