Signed Pair Compositing for Gaussian Splatting

3D Gaussian Splatting (3DGS) renders a scene by projecting Gaussians to 2D elliptical footprints, sorting them by center depth, and alpha-compositing them front to back. Compositing these footprints in center order assumes that neighboring Gaussians do not overlap in depth, that their center order holds at every pixel, and that their coverages are uncorrelated. Most methods that address overlap relax the first two assumptions by re-sorting Gaussians per pixel or by evaluating them in 3D along each ray, but still treat coverages as independent. Instead, we keep the rasterization pipeline of 3DGS and restore the depth row of the projection Jacobian, which 3DGS sets to zero. This gives each Gaussian, at every pixel, a depth distribution derived from its existing 3D covariance, without changing its footprint. Building on these distributions, our signed pair compositing groups the sorted Gaussians at each pixel into disjoint adjacent pairs. Within a pair, the depth distributions give the probability that each Gaussian lies in front of the other, a soft per-pixel order. The shapes and positions of the two footprints relative to the pixel set the sign of a bounded correlation between their coverages. The compositing weights depend only on the existing geometry and opacities of the Gaussians, without learnable parameters. We prove that signed pair compositing leaves the coverage of every Gaussian unchanged and reduces to standard compositing in the correct depth order for pairs well separated in depth. It adds a constant cost per pair and can render models trained with standard compositing without retraining. We also replace the per-channel L1 loss with the nuclear norm of the per-view color residual matrix, whose gradient weights every principal direction of the color error equally.