In this paper, we present a fully automatic method which identifies every bifurcation in an intravascular ultrasound (IVUS) sequence, the corresponding frames, the angular orientation with respect to the IVUS acquisition, and the extension. This goal is reached using a two-level classification scheme: first, a classifier is applied to a set of textural features extracted from each image of a sequence. A comparison among three state-of-the-art discriminative classifiers (AdaBoost, random forest, and support vector machine) is performed to identify the most suitable method for the branching detection task. Second, the results are improved by exploiting contextual information using a multiscale stacked sequential learning scheme. The results are then successively refined using a-priori information about branching dimensions and geometry. The proposed approach provides a robust tool for the quick review of pullback sequences, facilitating the evaluation of the lesion at bifurcation sites. The proposed method reaches an F-Measure score of 86.35\%, while the F-Measure scores for inter- and intraobserver variability are 71.63\% and 76.18\%, respectively. The obtained results are positive. Especially, considering the branching detection task is very challenging, due to high variability in bifurcation dimensions and appearance.