3D reconstruction quality analysis and its acceleration on GPU clusters

3D reconstruction has a wide variety of applications in computer graphics, robotics or digital cinema production, among others. With the rapid increase in computing power, it has become more feasible for the reconstruction algorithms to run online, even on mobile devices. Maximum likelihood estimation (MLE) is the adopted technique to deal with the sensor uncertainty. Most of the existing 3D reconstruction frameworks only recover the mean of the reconstructed geometry. Recovering also the variance is highly computationally intensive and is seldom performed. However, variance is the natural choice of estimate quality indicator. In this paper, the associated costs are analyzed and efficient but exact solutions to calculating partial matrix inverses are proposed, which apply to any general problem with many mutually independent variables. Speedups exceeding an order of magnitude are reported.