Adaptively weighted discrete Laplacian for Inverse Rendering

Abstract

The Laplacian-based precondition method, especially in the inverse rendering of geometry, effectively reduces variances in Stochastic Gradient Descent. This technique improves the stability of the optimization process and produces a more reliable result than adding other Laplacian regularizers to the objective function, reducing the geometrical errors. However, the problem of biases caused by the diffusion coefficient and the discretization of Laplacian slows down the convergence rate of the optimization process and hinders the convergence to final results, which appears as an over-smoothness effect.

We propose a new adaptively weighted discrete Laplacian applied to gradient preconditioning for geometric optimization in differentiable rendering. Inspired by the adaptive method from the rendering field, we find the locally optimal bandwidth on kernel-weighted discrete Laplacian.

Our adaptive method is applied to all the Laplacian smoothing, including the gradient smoothing in the inverse rendering of geometry—our method improves numerical convergence and reconstructs high-frequency details. We demonstrate the performance of our method on the two possible geometric inverse rendering frameworks applying Laplacian gradient smoothing.