arXiv subjects

Brian Chao

Publications and source records attributed to Brian Chao.

10 recordsLinked to original sources

arXiv2026

Fast Wave-optics Rendering of Multiplane Images for 3D Holographic Displays

Recent advances in neural rendering have unlocked unprecedented capabilities in 3D reconstruction and novel view synthesis, giving rise to applications such as virtual fly-throughs of a 3D scene reconstructed from a set of sparse, casually captured images. However, these renderings are viewed on a computer screen or conventional VR headsets as 2D images, greatly limiting the perceptual realism and immersiveness of such experiences. The rapid development in novel 3D scene representations calls for dedicated rendering algorithms that convert these readily-available 3D contents into formats that are compatible with emerging 3D display technologies, such as holographic displays. In this paper, we propose a wave-optics rendering pipeline that works with multiplane images (MPIs) for efficient and high-quality hologram synthesis. Our MPI-based computer-generated holography algorithm greatly outperforms state-of-the-art primitive-based CGH algorithms in terms of runtime, achieving speedups up to 250,000x while achieving comparable image quality, and significantly outperforms conventional layer-based CGH algorithms in terms of image quality. We validate our method extensively on a wide variety of 3D scene datasets both in simulation and through experimentally captured results, showing exceptional 3D focal stack and 4D light field reconstruction performance without sacrificing efficiency.

cs.GR↗

arXiv2026

Spectral Progressive Diffusion for Efficient Image and Video Generation

Diffusion models have been shown to implicitly generate visual content autoregressively in the frequency domain, where low-frequency components are generated earlier in the denoising process while high-frequency details emerge only in later timesteps. This structure offers a natural opportunity for efficient generation, as high-resolution computation on noise-dominated frequencies is largely redundant. We propose Spectral Progressive Diffusion, a general framework that progressively grows resolution along the denoising trajectory of pretrained diffusion models. To this end, we develop a spectral noise expansion mechanism and derive an optimal resolution schedule from the model's power spectrum. Our framework supports training-free acceleration and a novel fine-tuning recipe that further improves efficiency and quality. We demonstrate significant speedups on state-of-the-art pretrained image and video generation models while preserving visual quality.

cs.CV↗

arXiv2026

Foveated Diffusion: Efficient Spatially Adaptive Image and Video Generation

Diffusion and flow matching models have unlocked unprecedented capabilities for creative content creation, such as interactive image and streaming video generation. The growing demand for higher resolutions, frame rates, and context lengths, however, makes efficient generation increasingly challenging, as computational complexity grows quadratically with the number of generated tokens. Our work seeks to optimize the efficiency of the generation process in settings where the user's gaze location is known or can be estimated, for example, by using eye tracking. In these settings, we leverage the eccentricity-dependent acuity of human vision: while a user perceives very high-resolution visual information in a small region around their gaze location (the foveal region), the ability to resolve detail quickly degrades in the periphery of the visual field. Our approach starts with a mask modeling the foveated resolution to allocate tokens non-uniformly, assigning higher token density to foveal regions and lower density to peripheral regions. An image or video is generated in a mixed-resolution token setting, yielding results perceptually indistinguishable from full-resolution generation, while drastically reducing the token count and generation time. To this end, we develop a principled mechanism for constructing mixed-resolution tokens directly from high-resolution data, allowing a foveated diffusion model to be post-trained from an existing base model while maintaining content consistency across resolutions. We validate our approach through extensive analysis and a carefully designed user study, demonstrating the efficacy of foveation as a practical and scalable axis for efficient generation.

cs.CV↗

arXiv2025

Dirichlet eigenfunction and heat kernel estimates on annular domains

Motivated by Euclidean boxes, we consider "thin" annular domains of the form $U=(a,b)\times U_0\subseteq \mathbb{R}^n$ in polar coordinates, where the spherical base $U_0\subseteq \mathbb{S}^{n-1}$ is an inner uniform domain. We show that, with respect to the measure $\varphi_U^2$ determined by the principal Dirichlet Laplacian eigenfunction $\varphi_U$, such annular domains satisfy volume doubling and Poincar\'e inequalities uniformly over all locations and scales. This implies sharp Dirichlet heat kernel estimates expressed in terms of $\varphi_U$. Our results hold uniformly over the collection of all annuli in $\mathbb{R}^n$. We also give matching two-sided bounds for the first Dirichlet Laplacian eigenfunction and eigenvalue for some annular domains including annuli in $\mathbb{R}^n$. Moreover, we prove eigenfunction inequalities for $\varphi_U$ under domain perturbations of $U$. The proofs of our main results utilize eigenfunction comparison techniques due to Lierl and the authors (arXiv:1210.4586, arXiv:2504.18783), small scale $\varphi_U^2$-Poincar\'e inequalities, as well as a discretization technique of Coulhon and Saloff-Coste. Finally, our methods also imply uniform Neumann heat kernel estimates for thin annular domains.

math.AP↗

arXiv2025

Random-phase Wave Splatting of Translucent Primitives for Computer-generated Holography

Holographic near-eye displays offer ultra-compact form factors for VR/AR systems but rely on advanced computer-generated holography (CGH) algorithms to convert 3D scenes into interference patterns on spatial light modulators (SLMs). Conventional CGH typically generates smooth-phase holograms, limiting view-dependent effects and realistic defocus blur, while severely under-utilizing the SLM space-bandwidth product. We propose Random-phase Wave Splatting (RPWS), a unified wave optics rendering framework that converts arbitrary 3D representations based on 2D translucent primitives into random-phase holograms. RPWS is fully compatible with modern 3D representations such as Gaussians and triangles, improves bandwidth utilization which effectively enlarges eyebox size, reconstructs accurate defocus blur and parallax, and leverages time-multiplexed rendering not as a heuristic for speckle suppression, but as a mathematically exact alpha-blending mechanism derived from first principles in statistics. At the core of RPWS are (1) a new wavefront compositing procedure and (2) an alpha-blending scheme for random-phase geometric primitives, ensuring correct color reconstruction and robust occlusion when compositing millions of primitives. RPWS departs substantially from the recent primitive-based CGH algorithm, Gaussian Wave Splatting (GWS). Because GWS uses smooth-phase primitives, it struggles to capture view-dependent effects and realistic defocus blur and under-utilizes the SLM space-bandwidth product; moreover, naively extending GWS to random-phase primitives fails to reconstruct accurate colors. In contrast, RPWS is designed from the ground up for arbitrary random-phase translucent primitives, and through simulations and experimental validations we demonstrate state-of-the-art image quality and perceptually faithful 3D holograms for next-generation near-eye displays.

cs.GR↗

arXiv2025

Gaussian Wave Splatting for Computer-Generated Holography

State-of-the-art neural rendering methods optimize Gaussian scene representations from a few photographs for novel-view synthesis. Building on these representations, we develop an efficient algorithm, dubbed Gaussian Wave Splatting, to turn these Gaussians into holograms. Unlike existing computer-generated holography (CGH) algorithms, Gaussian Wave Splatting supports accurate occlusions and view-dependent effects for photorealistic scenes by leveraging recent advances in neural rendering. Specifically, we derive a closed-form solution for a 2D Gaussian-to-hologram transform that supports occlusions and alpha blending. Inspired by classic computer graphics techniques, we also derive an efficient approximation of the aforementioned process in the Fourier domain that is easily parallelizable and implement it using custom CUDA kernels. By integrating emerging neural rendering pipelines with holographic display technology, our Gaussian-based CGH framework paves the way for next-generation holographic displays.

cs.GR↗

arXiv2025

Perturbing the principal Dirichlet eigenfunction

We study the principal Dirichlet eigenfunction $\varphi_U$ when the domain $U$ is a perturbation of a bounded inner uniform domain in a strictly local regular Dirichlet space. We prove that if $U$ is suitably contained in between two inner uniform domains, then $\varphi_U$ admits two-sided bounds in terms of the principal Dirichlet eigenfunctions of the two approximating domains. The main ingredients of our proof include domain monotonicity properties associated to Dirichlet boundary conditions, intrinsic ultracontractivity estimates, and parabolic Harnack inequality. As an application of our results, we give explicit expressions comparable to $\varphi_U$ for certain domains $U\subseteq \mathbb{R}^n$, as well as improved Dirichlet heat kernel estimates for such domains. We also prove that under a uniform exterior ball condition on $U$, a point achieving the maximum of $\varphi_U$ is separated away from the boundary, complementing a result of Rachh and Steinerberger arXiv:1608.06604. Our principal Dirichlet eigenfunction estimates are applicable to second-order uniformly elliptic operators in Euclidean space, Riemannian manifolds with nonnegative Ricci curvature, and Lie groups of polynomial volume growth.

math.PR↗

arXiv2024

Textured Gaussians for Enhanced 3D Scene Appearance Modeling

3D Gaussian Splatting (3DGS) has recently emerged as a state-of-the-art 3D reconstruction and rendering technique due to its high-quality results and fast training and rendering time. However, pixels covered by the same Gaussian are always shaded in the same color up to a Gaussian falloff scaling factor. Furthermore, the finest geometric detail any individual Gaussian can represent is a simple ellipsoid. These properties of 3DGS greatly limit the expressivity of individual Gaussian primitives. To address these issues, we draw inspiration from texture and alpha mapping in traditional graphics and integrate it with 3DGS. Specifically, we propose a new generalized Gaussian appearance representation that augments each Gaussian with alpha~(A), RGB, or RGBA texture maps to model spatially varying color and opacity across the extent of each Gaussian. As such, each Gaussian can represent a richer set of texture patterns and geometric structures, instead of just a single color and ellipsoid as in naive Gaussian Splatting. Surprisingly, we found that the expressivity of Gaussians can be greatly improved by using alpha-only texture maps, and further augmenting Gaussians with RGB texture maps achieves the highest expressivity. We validate our method on a wide variety of standard benchmark datasets and our own custom captures at both the object and scene levels. We demonstrate image quality improvements over existing methods while using a similar or lower number of Gaussians.

cs.CV↗

arXiv2024

Large \'Etendue 3D Holographic Display with Content-adaptive Dynamic Fourier Modulation

Emerging holographic display technology offers unique capabilities for next-generation virtual reality systems. Current holographic near-eye displays, however, only support a small \'etendue, which results in a direct tradeoff between achievable field of view and eyebox size. \'Etendue expansion has recently been explored, but existing approaches are either fundamentally limited in the image quality that can be achieved or they require extremely high-speed spatial light modulators. We describe a new \'etendue expansion approach that combines multiple coherent sources with content-adaptive amplitude modulation of the hologram spectrum in the Fourier plane. To generate time-multiplexed phase and amplitude patterns for our spatial light modulators, we devise a pupil-aware gradient-descent-based computer-generated holography algorithm that is supervised by a large-baseline target light field. Compared with relevant baseline approaches, our method demonstrates significant improvements in image quality and \'etendue in simulation and with an experimental holographic display prototype.

cs.GR↗

arXiv2021

A Spatial Mutation Model with Increasing Mutation Rates

We consider a spatial model of cancer in which cells are points on the $d$-dimensional torus $\mathcal{T}=[0,L]^d$, and each cell with $k-1$ mutations acquires a $k$th mutation at rate $μ_k$. We will assume that the mutation rates $μ_k$ are increasing, and we find the asymptotic waiting time for the first cell to acquire $k$ mutations as the torus volume tends to infinity. This paper generalizes results on waiting for $k\geq 3$ mutations by Foo, Leder, and Schweinsberg, who considered the case in which all of the mutation rates $μ_k$ were the same. In addition, we find the limiting distribution of the spatial distances between mutations for certain values of the mutation rates.

math.PR↗