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Novel view synthesis of dynamic scenes has been an intriguing yet challenging problem. Despite recent advancements, simultaneously achieving high-resolution photorealistic results, real-time rendering, and compact storage remains a…

High-quality global illumination (GI) in real-time rendering is commonly achieved using precomputed lighting techniques, with lightmap as the standard choice. To support GI for static objects in dynamic lighting environments, multiple…

Photo-realistic novel view synthesis from multi-view images, such as neural radiance field (NeRF) and 3D Gaussian Splatting (3DGS), has gained significant attention for its superior performance. However, most existing methods rely on low…

We present MOSAIC-GS, a novel, fully explicit, and computationally efficient approach for high-fidelity dynamic scene reconstruction from monocular videos using Gaussian Splatting. Monocular reconstruction is inherently ill-posed due to the…

Recently, 3D Gaussian Splatting has emerged as a prominent research direction owing to its ultrarapid training speed and high-fidelity rendering capabilities. However, the unstructured and irregular nature of Gaussian point clouds poses…

Spike cameras, as an innovative neuromorphic camera that captures scenes with the 0-1 bit stream at 40 kHz, are increasingly employed for the 3D reconstruction task via Neural Radiance Fields (NeRF) or 3D Gaussian Splatting (3DGS). Previous…

Stochastic gradient descent (SGD) forms the core optimization method for deep neural networks. While some theoretical progress has been made, it still remains unclear why SGD leads the learning dynamics in overparameterized networks to…

Gaussian Splatting (GS) has emerged as a crucial technique for representing discrete volumetric radiance fields. It leverages unique parametrization to mitigate computational demands in scene optimization. This work introduces…

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being…

We propose a family of high-order local discontinuous Galerkin (LDG) methods, built on a parametric representation and coupled with a semi-implicit backward Euler time discretization, for isotropic and anisotropic curve-shortening flows.…

We present LocoGS, a locality-aware 3D Gaussian Splatting (3DGS) framework that exploits the spatial coherence of 3D Gaussians for compact modeling of volumetric scenes. To this end, we first analyze the local coherence of 3D Gaussian…

3D Gaussian Splatting (3DGS) has demonstrated breakthrough performance in novel view synthesis and real-time rendering. Nevertheless, its practicality is constrained by the high memory cost due to a huge number of Gaussian points. Many…

Computation of high frequency solutions to wave equations is important in many applications, and notoriously difficult in resolving wave oscillations. Gaussian beams are asymptotically valid high frequency solutions concentrated on a single…

Asynchronous stochastic gradient descent (ASGD) is a standard way to exploit heterogeneous compute resources in distributed learning: instead of forcing fast workers to wait for slow ones, the server updates the model whenever a gradient…

While novel view synthesis (NVS) for dynamic scenes has seen significant progress, reconstructing temporally consistent geometric surfaces remains a challenge. Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) offer powerful…

This paper presents Space-Time MultiGrid (STMG) methods which are suitable for performing topology optimisation of transient heat conduction problems. The proposed methods use a pointwise smoother and uniform Cartesian space-time meshes.…

Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion…

3D Gaussian Splatting reconstructs scenes by starting from a sparse Structure-from-Motion initialization and refining under-reconstructed regions. This process is slow, as it requires multiple densification steps where Gaussians are…

Recent accelerated MRI reconstruction models have used Deep Neural Networks (DNNs) to reconstruct relatively high-quality images from highly undersampled k-space data, enabling much faster MRI scanning. However, these techniques sometimes…

Real-world human-built environments are highly dynamic, involving multiple humans and their complex interactions with surrounding objects. While 3D geometry modeling of such scenes is crucial for applications like AR/VR, gaming, and…