ProbeGS: Closed-Form Scale for Error-Guided Gaussian Densification

A small Gaussian budget makes 3D Gaussian Splatting (3DGS) viable on low-capacity devices, but only if every new Gaussian has the right position and size. The standard photometric loss averages over pixels and can leave small, high-residual regions uncovered, yet the residual itself shows how large each correction should be: a broad residual calls for a wide Gaussian, a thin streak for a narrow, oriented one. ProbeGS therefore reads each new Gaussian's scale directly from the residual. It places corrective 2D Gaussians on the residual and lifts them to 3D. Around each pixel sampled in proportion to the residual, we measure how fast the residual decays on rings at several radii and set the standard deviation of the 2D Gaussian placed there in closed form, with no scale search. A short refinement moves only centers and colors, and a covariance lift inserts an ordinary 3DGS primitive that reproduces the fitted 2D Gaussian in its source view. We evaluate on Tanks & Temples, Deep Blending, and Mip-NeRF 360 at three requested Gaussian budgets. ProbeGS achieves state-of-the-art quality at 100K Gaussians, where it raises Deep Blending PSNR by 0.50 dB and lowers Tanks & Temples LPIPS by 14.5% over the next-best method. Its gain in fine detail concentrates where few training views see the surface.