In this letter, we present a hierarchical connection graph (HCG) algorithm based on a self-avoiding polygon (SAP) model for detecting and extracting gable roofs from aerial imagery. The SAP model is a deformable shape model that is capable of representing gable roofs of various shapes and appearances. The model is composed of a sequence of roof-corner templates that are connected into a SAP, which serves as a flexible shape prior. An energy function that combines features from three channels (corner, boundary, and interior area) is defined over the sequence to quantify the variability in appearances of gable roofs. To infer the most probable state of the corner sequence for an input image, we use an efficient algorithm-called HCG algorithm. The algorithm converts the solution space of a SAP model into a directed graph (which we call “HCG”) and searches for the best path using dynamic programming (DP). It is efficient for two reasons: 1) By constructing an HCG, the algorithm can quickly prune out a large amount of invalid solutions using only geometric constraints, which are inexpensive to compute, and 2) by employing DP, the algorithm decomposes the searching problem into smaller overlapping subproblems and reuses energy scores, which are expensive to compute. Experimental results on a set of challenging gable roofs show that our algorithm has good performance and is computationally effective.