Transitory image sequences, asymptotic properties, and estimation of motion and structure

Abstract

Abstract-A transitory image sequence is one in which no scene element is visible through the entire sequence. When a camera system scans a scene which cannot be covered by a single view, the image sequence is transitory. This article deals with some major theoretical and algorithmic issues associated with the task of estimating structure and motion from transitory image sequences. It is shown that integration with a transitory sequence has properties that are very different from those with a nontransitory one. Two representations, world-centered (WC) and camera-centered (CC), behave very differently with a transitory sequence. The asymptotic error rates derived in this article indicate that one representation is significantly superior to the other, depending on whether one needs camera-centered or world-centered estimates. To establish the tightness of these error rates, it has been shown that these reachable error rates are in fact the lowest possible given by a theoretical lower error bound, the Cramér-Rao error bound. Based on these results, we introduce an efficient "cross-frame" estimation technique for the CC representation. For the WC representation, our analysis indicates that a good technique should be based on camera global pose instead of interframe motions. In addition to testing with synthetic data, rigorous experiments were conducted with real-image sequences taken by a fully calibrated camera system. The comparison of the experimental results with the ground truth has demonstrated that a good accuracy can be obtained from transitory image sequences.

Symbolic Models and Emergent Models: A Review

“…Weng et al [70] studied transitory sequences which are those image sequences whose first view does not share any scene element with the last, as shown in Fig. 6.…”

“…6. Their incremental optimization algorithm [70] generated an image-intensity mapped 3-D world map associated with estimated viewer locations and poses along the trajectory. This was done by optimally integrating a transitory image sequence using auto- [74]).…”

“…6. This problem was later called simultaneous localization and mapping (SLAM) [71]- [73], where range sensors are often used for environment sensing instead of the stereo cameras used in [70]. An example of the FastSLAM algorithm [74] is shown in Fig.…”

“…The theoretical analysis in Weng et al [70] showed that the error of the reconstructed world map through a transitory sequence intrinsically suffers from at least a linearly increasing accumulation of error determined by the Cramér-Rao lower error bound. The farther the robot goes, the larger the expected error is in the estimated location of the world map.…”

Motion Estimation from Image and Inertial Measurements

“…Weng, et al [60] investigated 2 by deriving an analytical result describing the accuracy of optimal shape and motion estimates from image measurements as the percentage of missing observations varies. They show that for a scenario including some reasonable simplifying assumptions, the error variance in both the estimated shape and motion increases as O(n/(f 2 )), where the n is the number of images and f is the average number of images that each point was visible in.…”