A New Twist on 3D PIV: Particle-Field Representation with Gaussian Splats Coupled with Photometric Warp–Based Velocity Estimation

Traditional volumetric PIV/PTV reconstructs 3D points from multiview intensities and then tracks them in time. Tracking is GPU-unfriendly—the particle count varies per frame and ambiguities arise when particles enter/exit the field of view—so it remains confined to shorter time sequences; moreover, point models ignore the finite support of seeded particles and their characteristic image footprints, limiting fidelity and scalability. We replace points with a time-varying particle density field represented as a compact mixture of small, isotropic 3D Gaussian radial basis functions whose centers and weights evolve over time, parameterized by a lightweight MLP with random Fourier features. Images are formed by analytic Gaussian splatting: each 3D Gaussian maps to a 2D elliptical Gaussian on each calibrated camera via the projection Jacobian. The forward model is fully differentiable and physically consistent—no ray tracing, no algebraic back-projection—enabling fast, memory-efficient training with many cameras. Beyond intensity, we jointly recover velocity by enforcing photometric warp consistency of the density across time, eliminating explicit Lagrangian matching/tracking and ad-hoc track-to-grid conversion. We validate on synthetic Poiseuille flow across noise levels and seeding densities and on time-resolved wall-bounded experiments, achieving accurate multiview reprojection, coherent 3D density reconstructions, and reliable velocity estimates, while avoiding backward mapping and scaling gracefully with camera count.