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Dellaert,
Frank
Dellaert,
Frank
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ItemIncremental Light Bundle Adjustment for Structure From Motion and Robotics(Georgia Institute of Technology, 2015) Indelman, Vadim ; Roberts, Richard ; Dellaert, FrankBundle adjustment (BA) is essential in many robotics and structure-from-motion applications. In robotics, often a bundle adjustment solution is desired to be available incrementally as new poses and 3D points are observed. Similarly in batch structure from motion, cameras are typically added incrementally to allow good initializations. Current incremental BA methods quickly become computationally expensive as more camera poses and 3D points are added into the optimization. In this paper we introduce incremental light bundle adjustment (iLBA), an efficient optimization framework that substantially reduces computational complexity compared to incremental bundle adjustment. First, the number of variables in the optimization is reduced by algebraic elimination of observed 3D points, leading to a structureless BA. The resulting cost function is formulated in terms of three-view constraints instead of re-projection errors and only the camera poses are optimized. Second, the optimization problem is represented using graphical models and incremental inference is applied, updating the solution using adaptive partial calculations each time a new camera is incorporated into the optimization. Typically, only a small fraction of the camera poses are recalculated in each optimization step. The 3D points, although not explicitly optimized, can be reconstructed based on the optimized camera poses at any time. We study probabilistic and computational aspects of iLBA and compare its accuracy against incremental BA and another recent structureless method using real-imagery and synthetic datasets. Results indicate iLBA is 2-10 times faster than incremental BA, depending on number of image observations per frame.
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ItemConcurrent Filtering and Smoothing: A Parallel Architecture for Real-Time Navigation and Full Smoothing(Georgia Institute of Technology, 2014) Williams, Stephen ; Indelman, Vadim ; Kaess, Michael ; Roberts, Richard ; Leonard, John J. ; Dellaert, FrankWe present a parallelized navigation architecture that is capable of running in real-time and incorporating long-term loop closure constraints while producing the optimal Bayesian solution. This architecture splits the inference problem into a low-latency update that incorporates new measurements using just the most recent states (filter), and a high-latency update that is capable of closing long loops and smooths using all past states (smoother). This architecture employs the probabilistic graphical models of Factor Graphs, which allows the low-latency inference and high-latency inference to be viewed as sub-operations of a single optimization performed within a single graphical model. A specific factorization of the full joint density is employed that allows the different inference operations to be performed asynchronously while still recovering the optimal solution produced by a full batch optimization. Due to the real-time, asynchronous nature of this algorithm, updates to the state estimates from the high-latency smoother will naturally be delayed until the smoother calculations have completed. This architecture has been tested within a simulated aerial environment and on real data collected from an autonomous ground vehicle. In all cases, the concurrent architecture is shown to recover the full batch solution, even while updated state estimates are produced in real-time.
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ItemProbabilistic Analysis of Incremental Light Bundle Adjustment(Georgia Institute of Technology, 2013-01) Indelman, Vadim ; Roberts, Richard ; Dellaert, FrankThis 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.
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ItemIncremental Light Bundle Adjustment(Georgia Institute of Technology, 2012-09) Indelman, Vadim ; Roberts, Richard ; Beall, Chris ; Dellaert, FrankFast and reliable bundle adjustment is essential in many applications such as mobile vision, augmented reality, and robotics. Two recent ideas to reduce the associated computational cost are structure-less SFM (structure from motion) and incremental smoothing. The former formulates the cost function in terms of multi-view constraints instead of re-projection errors, thereby eliminating the 3D structure from the optimization. The latter was developed in the SLAM (simultaneous localization and mapping) community and allows one to perform efficient incremental optimization, adaptively identifying the variables that need to be recomputed at each step. In this paper we combine these two key ideas into a computationally efficient bundle adjustment method, and additionally introduce the use of three-view constraints to remedy commonly encountered degenerate camera motions. We formulate the problem in terms of a factor graph, and incrementally update a directed junction tree which keeps track of the current best solution. Typically, only a small fraction of the camera poses are recalculated in each optimization step, leading to a significant computational gain. If desired, all or some of the observed 3D points can be reconstructed based on the optimized camera poses. To deal with degenerate motions, we use both two and three-view constraints between camera poses, which allows us to maintain a consistent scale during straight-line trajectories. We validate our approach using synthetic and real-imagery datasets and compare it to standard bundle adjustment, in terms of performance, robustness and computational cost.
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ItemConcurrent Filtering and Smoothing(Georgia Institute of Technology, 2012-07) Kaess, Michael ; Williams, Stephen ; Indelman, Vadim ; Roberts, Richard ; Leonard, John J. ; Dellaert, FrankThis paper presents a novel algorithm for integrating real-time filtering of navigation data with full map/trajectory smoothing. Unlike conventional mapping strategies, the result of loop closures within the smoother serve to correct the real-time navigation solution in addition to the map. This solution views filtering and smoothing as different operations applied within a single graphical model known as a Bayes tree. By maintaining all information within a single graph, the optimal linear estimate is guaranteed, while still allowing the filter and smoother to operate asynchronously. This approach has been applied to simulated aerial vehicle sensors consisting of a high-speed IMU and stereo camera. Loop closures are extracted from the vision system in an external process and incorporated into the smoother when discovered. The performance of the proposed method is shown to approach that of full batch optimization while maintaining real-time operation.