Deep Semantic Graph Matching for Large-scale Outdoor Point Clouds Registration

The current point cloud registration methods are mainly based on geometric information and usually ignore the semantic information in the point clouds. In this paper, we treat the point cloud registration problem as semantic instance matching and registration task, and propose a deep semantic graph matching method for large-scale outdoor point cloud registration. Firstly, the semantic category labels of 3D point clouds are obtained by utilizing large-scale point cloud semantic segmentation network. The adjacent points with the same category labels are then clustered together by using Euclidean clustering algorithm to obtain the semantic instances. Secondly, the semantic adjacency graph is constructed based on the spatial adjacency relation of semantic instances. Three kinds of high-dimensional features including geometric shape features, semantic categorical features and spatial distribution features are learned through graph convolutional network, and enhanced based on attention mechanism. Thirdly, the semantic instance matching problem is modeled as an optimal transport problem, and solved through an optimal matching layer. Finally, according to the matched semantic instances, the geometric transformation matrix between two point clouds is first obtained by SVD algorithm and then refined by ICP algorithm. The experiments are cconducted on the KITTI Odometry dataset, and the average relative translation error and average relative rotation error of the proposed method are 6.6cm and 0.229{\deg} respectively.

Neural Gaussian Mirror for Controlled Feature Selection in Neural Networks

Deep neural networks (DNNs) have become increasingly popular and achieved outstanding performance in predictive tasks. However, the DNN framework itself cannot inform the user which features are more or less relevant for making the prediction, which limits its applicability in many scientific fields. We introduce neural Gaussian mirrors (NGMs), in which mirrored features are created, via a structured perturbation based on a kernel-based conditional dependence measure, to help evaluate feature importance. We design two modifications of the DNN architecture for incorporating mirrored features and providing mirror statistics to measure feature importance. As shown in simulated and real data examples, the proposed method controls the feature selection error rate at a predefined level and maintains a high selection power even with the presence of highly correlated features.

The Wang-Landau Algorithm as Stochastic Optimization and its Acceleration

We show that the Wang-Landau algorithm can be formulated as a stochastic gradient descent algorithm minimizing a smooth and convex objective function, of which the gradient is estimated using Markov Chain Monte Carlo iterations. The optimization formulation provides a new perspective for improving the efficiency of the Wang-Landau algorithm using optimization tools. We propose one possible improvement, based on the momentum method and the adaptive learning rate idea, and demonstrate it on a two-dimensional Ising model and a two-dimensional ten-state Potts model.