Kai Zhao

Yang Song, Qiyu Kang, Sijie Wang et al.

Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural networks (GNNs), such as the problems of over-smoothing and bottlenecks, has been investigated but not their robustness to adversarial attacks. In this work, we explore the robustness properties of graph neural PDEs. We empirically demonstrate that graph neural PDEs are intrinsically more robust against topology perturbation as compared to other GNNs. We provide insights into this phenomenon by exploiting the stability of the heat semigroup under graph topology perturbations. We discuss various graph diffusion operators and relate them to existing graph neural PDEs. Furthermore, we propose a general graph neural PDE framework based on which a new class of robust GNNs can be defined. We verify that the new model achieves comparable state-of-the-art performance on several benchmark datasets.

Rui She, Qiyu Kang, Sijie Wang et al.

For autonomous vehicles (AVs), visual perception techniques based on sensors like cameras play crucial roles in information acquisition and processing. In various computer perception tasks for AVs, it may be helpful to match landmark patches taken by an onboard camera with other landmark patches captured at a different time or saved in a street scene image database. To perform matching under challenging driving environments caused by changing seasons, weather, and illumination, we utilize the spatial neighborhood information of each patch. We propose an approach, named RobustMat, which derives its robustness to perturbations from neural differential equations. A convolutional neural ODE diffusion module is used to learn the feature representation for the landmark patches. A graph neural PDE diffusion module then aggregates information from neighboring landmark patches in the street scene. Finally, feature similarity learning outputs the final matching score. Our approach is evaluated on several street scene datasets and demonstrated to achieve state-of-the-art matching results under environmental perturbations.

Kai Zhao, Alex Ling Yu Hung, Kaifeng Pang et al.

Denoising diffusion probabilistic models (DDPMs) have achieved impressive performance on various image generation tasks, including image super-resolution. By learning to reverse the process of gradually diffusing the data distribution into Gaussian noise, DDPMs generate new data by iteratively denoising from random noise. Despite their impressive performance, diffusion-based generative models suffer from high computational costs due to the large number of denoising steps.In this paper, we first observed that the intermediate latent states gradually converge and become indistinguishable when diffusing a pair of low- and high-resolution images. This observation inspired us to propose the Partial Diffusion Model (PartDiff), which diffuses the image to an intermediate latent state instead of pure random noise, where the intermediate latent state is approximated by the latent of diffusing the low-resolution image. During generation, Partial Diffusion Models start denoising from the intermediate distribution and perform only a part of the denoising steps. Additionally, to mitigate the error caused by the approximation, we introduce "latent alignment", which aligns the latent between low- and high-resolution images during training. Experiments on both magnetic resonance imaging (MRI) and natural images show that, compared to plain diffusion-based super-resolution methods, Partial Diffusion Models significantly reduce the number of denoising steps without sacrificing the quality of generation.

Rui She, Sijie Wang, Qiyu Kang et al.

Point cloud registration is a crucial technique in 3D computer vision with a wide range of applications. However, this task can be challenging, particularly in large fields of view with dynamic objects, environmental noise, or other perturbations. To address this challenge, we propose a model called PosDiffNet. Our approach performs hierarchical registration based on window-level, patch-level, and point-level correspondence. We leverage a graph neural partial differential equation (PDE) based on Beltrami flow to obtain high-dimensional features and position embeddings for point clouds. We incorporate position embeddings into a Transformer module based on a neural ordinary differential equation (ODE) to efficiently represent patches within points. We employ the multi-level correspondence derived from the high feature similarity scores to facilitate alignment between point clouds. Subsequently, we use registration methods such as SVD-based algorithms to predict the transformation using corresponding point pairs. We evaluate PosDiffNet on several 3D point cloud datasets, verifying that it achieves state-of-the-art (SOTA) performance for point cloud registration in large fields of view with perturbations. The implementation code of experiments is available at https://github.com/AI-IT-AVs/PosDiffNet.

Rui She, Qiyu Kang, Sijie Wang et al.

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.