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Hamiltonian neural networks (HNNs) represent a promising class of physics-informed deep learning methods that utilize Hamiltonian theory as foundational knowledge within neural networks. However, their direct application to engineering…

Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the…

Deep Riemannian networks provide a powerful framework for Electroencephalography (EEG) decoding, but their practical applications are severely constrained. Accurately decoding EEG signals requires modeling complex temporal dynamics across…

Deep Convolutional Neural Networks (DCNNs) commonly use generic `max-pooling' (MP) layers to extract deformation-invariant features, but we argue in favor of a more refined treatment. First, we introduce epitomic convolution as a building…

Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…

The data fusion technology aims to aggregate the characteristics of different data and obtain products with multiple data advantages. To solves the problem of reduced resolution of PolSAR images due to system limitations, we propose a fully…

In this paper, we propose a novel, convolutional neural network model to extract highly precise depth maps from missing viewpoints, especially well applicable to generate holographic 3D contents. The depth map is an essential element for…

LiDAR depth maps provide environmental guidance in a variety of applications. However, such depth maps are typically sparse and insufficient for complex tasks such as autonomous navigation. State of the art methods use image guided neural…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

Deep hashing techniques have emerged as the predominant approach for efficient image retrieval. Traditionally, these methods utilize pre-trained convolutional neural networks (CNNs) such as AlexNet and VGG-16 as feature extractors. However,…

In the domain of pattern recognition, using the SPD (Symmetric Positive Definite) matrices to represent data and taking the metrics of resulting Riemannian manifold into account have been widely used for the task of image set…

Recently, deep learning techniques have been extensively studied for pansharpening, which aims to generate a high resolution multispectral (HRMS) image by fusing a low resolution multispectral (LRMS) image with a high resolution…

Constructing HD semantic maps is a central component of autonomous driving. However, traditional pipelines require a vast amount of human efforts and resources in annotating and maintaining the semantics in the map, which limits its…

Recent advances in deep representation learning on Riemannian manifolds extend classical deep learning operations to better capture the geometry of the manifold. One possible extension is the Fr\'echet mean, the generalization of the…

Heterogeneous catalysts possess complex surface and bulk structures, relatively poor intrinsic contrast, and often a sparse distribution of the catalytic nanoparticles (NPs), posing a significant challenge for image segmentation, including…

High-resolution representation learning plays an essential role in many vision problems, e.g., pose estimation and semantic segmentation. The high-resolution network (HRNet)~\cite{SunXLW19}, recently developed for human pose estimation,…

If the training dataset is not very large, image recognition is usually implemented with the transfer learning methods. In these methods the features are extracted using a deep convolutional neural network, which was preliminarily trained…

This work puts forth low-complexity Riemannian subspace descent algorithms for the minimization of functions over the symmetric positive definite (SPD) manifold. Different from the existing Riemannian gradient descent variants, the proposed…

3D shape representation and its processing have substantial effects on 3D shape recognition. The polygon mesh as a 3D shape representation has many advantages in computer graphics and geometry processing. However, there are still some…

Manifold learning-based encoders have been playing important roles in nonlinear dimensionality reduction (NLDR) for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional…