This project is intended to explore appropriate higher order models in random fields to better express qualitative and statistical knowledge about the scene, and effective inference methods to simultaneously improve the ability of 3D scene understanding and to complete 3D shapes under a unified framework by integrating 2D images and the corresponding 3D point clouds. In this project, 3D understanding is meant to segment and recognize objects, to determine object’s pose, and to complete incompletely reconstructed object shapes etc. Here design appropriate higher order models and establish effective inference methods for 3D scene understanding are the core issues. The project’s main contents include the following 4 parts: (1): Design appropriate higher order models for 3D scene understanding; (2): establish effective inference methods for higher order energy minimization; (3): investigate the relationship between higher order model and hierarchical networks,such as Deep Neural Networks ( DNN) ;(4): GPU+CPU mixed fast implementation schemes. The expected outcome is a comprehensive theory and method for higher order models design and effective inference in 3D scene understanding, as well as some fast algorithms. In addition, the project’s results are expected to find real applications in some specific domain. Finally, this study will enrich 3D scene understanding research and promote its further development.