Continuous Conditional Random Field Convolution for Point Cloud Segmentation

Point cloud segmentation is the foundation of 3D environmental perception for modern intelligent systems. To solve this problem and image segmentation, conditional random fields (CRFs) are usually formulated as discrete models in label space to encourage label consistency, which is actually a kind of postprocessing. In this paper, we reconsider the CRF in feature space for point cloud segmentation because it can capture the structure of features well to improve the representation ability of features rather than simply smoothing. Therefore, we first model the point cloud features with a continuous quadratic energy model and formulate its solution process as a message-passing graph convolution, by which it can be easily integrated into a deep network. We theoretically demonstrate that the message passing in the graph convolution is equivalent to the mean-field approximation of a continuous CRF model. Furthermore, we build an encoder-decoder network based on the proposed continuous CRF graph convolution (CRFConv), in which the CRFConv embedded in the decoding layers can restore the details of high-level features that were lost in the encoding stage to enhance the location ability of the network, thereby benefiting segmentation. Analogous to the CRFConv, we show that the classical discrete CRF can also work collaboratively with the proposed network via another graph convolution to further improve the segmentation results. Experiments on various point cloud benchmarks demonstrate the effectiveness and robustness of the proposed method. Compared with the state-of-the-art methods, the proposed method can also achieve competitive segmentation performance.