Applying Splat Regression Models to Particle Density Control in Radiance Fields

Adaptive density control decides where 3D Gaussian Splatting creates and removes primitives, but common rules still rely on proxy statistics such as position gradients, opacity, or image-space error. We study this decision under a fixed Gaussian budget, where each new primitive consumes capacity that could be used elsewhere. At each density-control step, we freeze the current Gaussian population, attach one auxiliary mass coordinate to each primitive, and differentiate the multiview reconstruction loss with respect to these coordinates. The resulting first-variation score gives a local density-control signal: high scores identify useful birth sites, while low scores inside a low-opacity pool identify slots that can be recycled with bounded immediate rendering change. Experiments on Mip-NeRF360, Tanks & Temples, and DeepBlending show that the score improves matched 3DGS-MCMC at fixed caps, with the largest gains under tight Gaussian budgets. The result is a density-control rule for budgeted 3DGS that queries the reconstruction objective rather than relying only on proxy statistics, preserving complex geometry and thin structures.