Work

Dirichlet Splatting: Differentiable Rendering for Wave-Based Inverse Problems

Year: 2026

Type: article

Abstract: We present Dirichlet Splatting , a physically grounded differentiable rendering method for inverse problems with wave-based coherent sensors. Unlike optical cameras, these sensors observe a scene in a band-limited Fourier space whose continuous point response is complex-valued and oscillatory. Our key observation is that the point spread function of a reflector in this Fourier space is the Dirichlet kernel , not a Gaussian. We instantiate each splat as a Dirichlet kernel in closed form, model each primitive as a planar surfel rendered through a surfel-aware Dirichlet splat whose complex amplitude is set by wave propagation physics, and introduce a sliding Frank-Wolfe adaptation tailored to the rugged, non-convex landscape that the Dirichlet oscillation induces. On terahertz tomography, Dirichlet Splatting recovers reflector geometry with an order of magnitude fewer parameters, faster convergence, and higher accuracy than 3D Gaussian Splatting.

Source: ACM Transactions on Graphics

DOI: 10.1145/3842559

Authors: Xingyu Chen, Wuqiong Zhao, Xinyu Zhang, Tzu-Mao Li

Institution: University of California San Diego

Language: English

Topic: Computer Graphics and Visualization Techniques

Subfield: Computer Graphics and Computer-Aided Design

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Awards: NeTS: Medium: Generative Channel Cartography for Giga MIMO Networks on the 6G Upper Mid-band, MRI: Track 1 Development of an Integrated Instrument for 6G Sub-THz Joint Communication and Sensing, HCC: Small: Beyond Pixels: Resolution-Independent and Discontinuity-Preserving Neural Image Representations for Computer Graphics, CAREER: Differentiable Programming for Visual Computing