© 2015, Springer-Verlag Berlin Heidelberg. Analysis of branching structures represents a very important task in fields such as medical diagnosis, road detection or biometrics. Detecting intersection landmarks becomes crucial when capturing the structure of a branching pattern. We present a very simple geometrical model to describe intersections in branching structures based on two conditions: Bounded Tangency (BT) condition and Shortest Branch (SB) condition. The proposed model precisely sets a geometrical characterization of intersections and allows us to introduce a new unsupervised operator for intersection extraction. We propose an implementation that handles the consequences of digital domain operation that, unlike existing approaches, is not restricted to a particular scale and does not require the computation of the thinned pattern. The new proposal, as well as other existing approaches in the bibliography, are evaluated in a common framework for the first time. The performance analysis is based on two manually segmented image data sets: DRIVE retinal image database and COLON-VESSEL data set, a newly created data set of vascular content in colonoscopy frames. We have created an intersection landmark ground truth for each data set besides comparing our method in the only existing ground truth. Quantitative results confirm that we are able to outperform state-of-the-art performance levels with the advantage that neither training nor parameter tuning is needed.