Omnidirectional (or 360-degree) images are increasingly being used for 3D applications since they allow the rendering of an entire scene with a single image.

Omnidirectional (or 360-degree) images are increasingly being used for 3D applications since they allow the rendering of an entire scene with a single image. Existing works based on neural radiance fields demonstrate successful 3D reconstruction quality on egocentric videos, yet they suffer from long training and rendering times. Recently, 3D Gaussian splatting has gained attention for its fast optimization and real-time rendering.

We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program.

Omnidirectional (or 360-degree) images are increasingly being used for 3D applications since they allow the rendering of an entire scene with a single image.

In this paper, we present a novel geometry-aware RGB-D Gaussian Splatting SLAM system, named G2S-ICP SLAM. The proposed method performs high-fidelity 3D reconstruction and robust camera pose tracking in real-time by representing each scene element using a Gaussian distribution constrained to the local tangent plane. This effectively models the local surface as a 2D Gaussian disk aligned with the underlying geometry, leading to more consistent depth interpretation across multiple viewpoints compared to conventional 3D ellipsoid-based representations with isotropic uncertainty. To integrate this representation into the SLAM pipeline, we embed the surface-aligned Gaussian disks into a Generalized ICP framework by introducing anisotropic covariance prior without altering the underlying registration formulation. Furthermore we propose a geometry-aware loss that supervises photometric, depth, and normal consistency. Our system achieves real-time operation while preserving both visual and geometric fidelity. Extensive experiments on the Replica and TUM-RGBD datasets demonstrate that G2S-ICP SLAM outperforms prior SLAM systems in terms of localization accuracy, reconstruction completeness, while maintaining the rendering quality.

Omnidirectional (or 360-degree) images are increasingly being used for 3D applications since they allow the rendering of an entire scene with a single image. Existing works based on neural radiance fields demonstrate successful 3D reconstruction quality on egocentric videos, yet they suffer from long training and rendering times. Recently, 3D Gaussian splatting has gained attention for its fast optimization and real-time rendering. For each Gaussian, we define a tangent plane that touches the unit sphere and is perpendicular to the ray headed toward the Gaussian center. We then leverage a perspective camera rasterizer to project the Gaussian onto the corresponding tangent plane.

Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the super-exponential scaling of topologies. This scaling challenge limits the efficiency of Euclidean-based approximate inference methods. Motivated by the geometric connections between trees and hyperbolic space, we develop novel hyperbolic extensions of two sequential search algorithms: Combinatorial and Nested Combinatorial Sequential Monte Carlo (\textsc{Csmc} and \textsc{Ncsmc}). Our approach introduces consistent and unbiased estimators, along with variational inference methods (\textsc{H-Vcsmc} and \textsc{H-Vncsmc}), which outperform their Euclidean counterparts. Empirical results demonstrate improved speed, scalability and performance in high-dimensional phylogenetic inference tasks.

This paper describes a method to transform networks learned on perspective images to take spherical images as input. This is an important problem as fisheye and 360-degree sensors become more and more ubiquitous but training data is relatively scarce. The method first transforms the network architecture to adapt the filter sizes and pooling operations to convolutions on a equirectangular representation/projection. Next the filters are learned to match the feature responses of the original network when considering the projections to the tangent plane of the respective feature response. The filters are pre-learned layer-by-layer and fine-tuned to output features as similar as possible to the original network projected to the tangent planes. Detection experiments on Pano2Vid and PASCAL demonstrate that the technique performs slightly below the optimal performance using per-pixel tangent projections (however significantly faster) while outperforming several baselines, including cube map projections.

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.

Contrasts with existing works which all consider nodes as functions and use edges to represent the relationships between different functions. We target at network modeling whose edges are functional data and transform the adjacency matrix into a functional adjacency tensor, introducing an additional dimension dedicated to function representation. Tucker functional decomposition is used for the functional adjacency tensor, and to further consider the community between nodes, we regularize the basis matrices to be symmetrical. Furthermore, to deal with irregular observations of the functional edges, we conduct model inference to solve a tensor completion problem. It is optimized by a Riemann conjugate gradient descent method. Besides these, we also derive several theorems to show the desirable properties of the functional edged network model. Finally, we evaluate the efficacy of our proposed model using simulation data and real metro system data from Hong Kong and Singapore.