Adaptive bracketing for median-depth binary search

Develop adaptive bracketing strategies to initialize and tighten the depth interval used by the binary search that locates the median depth (the transmittance T=0.5 crossing) along camera rays in Gaussian Splatting, in order to reduce search steps and accelerate training.

Background

The method computes median depth by exploiting the monotonicity of transmittance and performing a binary search within a preset interval around an initial estimate. A wide fixed interval increases search steps and slows optimization, and for large-scale scenes the true median depth can lie outside the preset interval.

The authors explicitly state that tightening the initial depth interval is left for future work to achieve additional speedups; elsewhere in the limitations they further suggest adaptive bracketing strategies to reliably locate the median and reduce the interval.