The reconstruction and analysis of tree-like topological structures in the biomedical images is crucial for biologists and surgeons to understand biomedical conditions and plan surgical procedures. The underlying tree-structure topology reveals how different curvilinear components are anatomically connected to each other. Existing automated topology reconstruction methods have great difficulty in identifying the connectivity when two or more curvilinear components cross or bifurcate, due to their projection ambiguity, imaging noise and low contrast. In this paper, we propose a novel curvilinear structural similarity measure to guide a dominant-set clustering approach to address this indispensable issue. The novel similarity measure takes into account both intensity and geometric properties in representing the curvilinear structure locally and globally, and group curvilinear objects at crossover points into different connected branches by dominant-set clustering. The proposed method is applicable to different imaging modalities, and quantitative and qualitative results on retinal vessel, plant root, and neuronal network datasets show that our methodology is capable of advancing the current state-of-the-art techniques.