A robust algorithm for fusing noisy depth estimates using stochastic approximation

The problem of structure from motion (SFM) is to extract the three-dimensional model of a moving scene from a sequence of images. Most of the algorithms which work by fusing the two-frame depth estimates (observations) assume an underlying statistical model for the observations and do not evaluate the quality of the individual observations. However, in real scenarios, it is often difficult to justify the statistical assumptions. Also, outliers are present in any observation sequence and need to be identified and removed from the fusion algorithm. We present a recursive fusion algorithm using the Robbins-Monro stochastic approximation (RMSA) which takes care of both these problems to provide an estimate of the real depth of the scene point. The estimate converges to the true value asymptotically. We also propose a method to evaluate the importance of the successive observations by computing the Fisher information (FI) recursively. Though we apply our algorithm in the SFM problem by modeling of a human face, it can be easily adopted to other data fusion applications.