Huber Loss Reconstruction in Gradient-Domain Path Tracing

The focus of this thesis is to improve aspects related to the computational synthesis of photo-realistic images. Physically accurate images are generated by simulating the transportation of light between an observer and the light sources in a virtual environment. Path tracing is an algorithm that uses Monte Carlo methods to solve problems in the domain of light transport simulation, generating images by sampling light paths through the virtual scene. In this thesis we focus on the recently introduced gradient-domain path tracing algorithm. In addition to estimating the ordinary primal image, gradient-domain light transport algorithms also sample the horizontal and vertical gradients and solve a screened Poisson problem to reconstruct the final image. Using L2 loss for reconstruction produces an unbiased final image, but the results can often be visually unpleasing due to its sensitivity to extreme-value outliers in the sampled primal and gradient images. L1 loss can be used to suppress this sensitivity at the cost of introducing bias. We investigate the use of the Huber loss function in the reconstruction step of the gradient-domain path tracing algorithm. We show that using the Huber loss function for the gradient in the Poisson solver with a good choice of cut-off parameter can result in reduced sensitivity to outliers and consequently lower relative mean squared error than L1 or L2 when compared to ground-truth images. The main contribution of this thesis is a predictive multiplicative model for the cut-off parameter. The model takes as input pixel statistics, which can be computed on-line during sampling and predicts reconstruction parameters that on average outperforms reconstruction using L1 and L2