Abstract: Non-rigid object detection is a challenging an open research problem in computer vision. It is a critical part in many applications such as image search, surveillance, human-computer interaction or image auto-annotation. Most successful approaches to non-rigid object detection make use of part-based models. In particular, Conditional Random Fields (CRF) have been successfully embedded into a discriminative parts-based model framework due to its effectiveness for learning and inference (usually based on a tree structure). However, CRF-based approaches do not incorporate global constraints and only model pairwise interactions. This is especially important when modeling object classes that may have complex parts interactions (e.g. facial features or body articulations), because neglecting them yields an oversimplified model with suboptimal performance. To overcome this limitation, this paper proposes a novel hierarchical CRF (HCRF). The main contribution is to build a hierarchy of part combinations by extending the label set to a hierarchy of product label spaces. In order to keep the inference computation tractable, we propose an effective method to reduce the new label set. We test our method on two applications: facial feature detection on the Multi-PIE database and human pose estimation on the Buffy dataset.