In sketch-based image retrieval (SBIR) systems, representing photo-realistic images by their strong edges is an intuitive and effective way to bridge the appearance gap between sketches and photo-realistic images. However, noisy edges and missing edges usually enlarge the appearance gap and significantly degrade retrieval performance. To alleviate the impact, we formalize the matching task between the sketches and extracted edges of photo-realistic images as a partial matching problem. We treat the sketches and extracted edges as a set of line segments which serve as the basis for better shape description and partial matching. We propose a new descriptor, structure point, to represent sketches and the extracted edges. Based on the structure point, a decompose-and-assemble hierarchical matching algorithm is developed to match sketches and extracted edges. Observing that false matches can degrade performance, we introduce a spatial constraint to filter the false matches. We have tested the proposed framework on public datasets and a new dataset of three million images which we recently collected for the SBIR evaluation purpose. We compared our method with the state-of-the-art methods (SHoG and GF-HOG). The experimental results show that our framework significantly improves retrieval performance.