Probabilistic analysis of incremental light bundle adjustment

This paper presents a probabilistic analysis of the recently introduced incremental light bundle adjustment method (iLBA) [6]. In iLBA, the observed 3D points are algebraically eliminated, resulting in a cost function with only the camera poses as variables, and an incremental smoothing technique is applied for efficiently processing incoming images. While we have already showed that compared to conventional bundle adjustment (BA), iLBA yields a significant improvement in computational complexity with similar levels of accuracy, the probabilistic properties of iLBA have not been analyzed thus far. In this paper we consider the probability distribution that corresponds to the iLBA cost function, and analyze how well it represents the true density of the camera poses given the image measurements. The latter can be exactly calculated in bundle adjustment (BA) by marginalizing out the 3D points from the joint distribution of camera poses and 3D points. We present a theoretical analysis of the differences in the way that LBA and BA use measurement information. Using indoor and outdoor datasets we show that the first two moments of the iLBA and the true probability distributions are very similar in practice.