Point cloud registration is a fundamental technique in 3-D computer vision with applications in graphics, autonomous driving, and robotics. However, registration tasks under challenging conditions, under which noise or perturbations are prevalent, can be difficult. We propose a robust point cloud registration approach that leverages graph neural partial differential equations (PDEs) and heat kernel signatures. Our method first uses graph neural PDE modules to extract high-dimensional features from point clouds by aggregating information from the 3-D point neighborhood, thereby enhancing the robustness of the feature representations. Then, we incorporate heat kernel signatures into an attention mechanism to efficiently obtain corresponding keypoints. Finally, a singular value decomposition (SVD) module with learnable weights is used to predict the transformation between two point clouds. Empirical experiments on a 3-D point cloud dataset demonstrate that our approach not only achieves state-of-the-art performance for point cloud registration but also exhibits better robustness to additive noise or 3-D shape perturbations.

Camera relocalization has various applications in autonomous driving. Previous camera pose regression models consider only ideal scenarios where there is little environmental perturbation. To deal with challenging driving environments that may have changing seasons, weather, illumination, and the presence of unstable objects, we propose RobustLoc, which derives its robustness against perturbations from neural differential equations. Our model uses a convolutional neural network to extract feature maps from multi-view images, a robust neural differential equation diffusion block module to diffuse information interactively, and a branched pose decoder with multi-layer training to estimate the vehicle poses. Experiments demonstrate that RobustLoc surpasses current state-of-the-art camera pose regression models and achieves robust performance in various environments. Our code is released at: https://github.com/sijieaaa/RobustLoc

Image matching identifies matching street landmark patches between the images captured by a vehicular camera and those stored in a database. Applications include autonomous driving perception and localization. However, in practical scenarios, challenging conditions such as changing weather, illumination, and dynamic objects result in perturbations of the captured images, leading to inaccurate matching. To achieve robust landmark patch matching, we present a method, named GRAND-Mat, which leverages a neural diffusion over graph embeddings to counteract perturbations. We first extract high-dimensional features of landmark patches using a ResNet. Then, we utilize graph neural diffusion models to aggregate the self and cross-graph information from these features. Furthermore, we apply feature similarity learning to acquire the final matching score. We evaluate the performance of our model on a street scene dataset, which demonstrates state-of-the-art matching performance under additive perturbations.

Matching landmark patches from a real-time image captured by an on-vehicle camera with landmark patches in an image database plays an important role in various computer perception tasks for autonomous driving. Current methods focus on local matching for regions of interest and do not take into account spatial neighborhood relationships among the image patches, which typically correspond to objects in the environment. In this paper, we construct a spatial graph with the graph vertices corresponding to patches and edges capturing the spatial neighborhood information. We propose a joint feature and metric learning model with graph-based learning. We provide a theoretical basis for the graph-based loss by showing that the information distance between the distributions conditioned on matched and unmatched pairs is maximized under our framework. We evaluate our model using several street-scene datasets and demonstrate that our approach achieves state-of-the-art matching results.