Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
A stochastic map for uncertain spatial relationships
Proceedings of the 4th international symposium on Robotics Research
Matrix computations (3rd ed.)
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Probabilistic Networks and Expert Systems
Probabilistic Networks and Expert Systems
Globally Consistent Range Scan Alignment for Environment Mapping
Autonomous Robots
Fast, On-Line Learning of Globally Consistent Maps
Autonomous Robots
Distributed Multifrontal Factorization Using Clique Trees
Proceedings of the Fifth SIAM Conference on Parallel Processing for Scientific Computing
Practical parameterization of rotations using the exponential map
Journal of Graphics Tools
A column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing
International Journal of Robotics Research
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Fast incremental square root information smoothing
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Thin junction tree filters for simultaneous localization and mapping
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Covariance recovery from a square root information matrix for data association
Robotics and Autonomous Systems
Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning
A multilevel relaxation algorithm for simultaneous localization and mapping
IEEE Transactions on Robotics
Closing the Loop With Graphical SLAM
IEEE Transactions on Robotics
Large-Scale 6-DOF SLAM With Stereo-in-Hand
IEEE Transactions on Robotics
FrameSLAM: From Bundle Adjustment to Real-Time Visual Mapping
IEEE Transactions on Robotics
Efficient View-Based SLAM Using Visual Loop Closures
IEEE Transactions on Robotics
iSAM: Incremental Smoothing and Mapping
IEEE Transactions on Robotics
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Editors Choice Article: Visual SLAM: Why filter?
Image and Vision Computing
Reconstructing partially visible models using stereo vision, structured light, and the g2o framework
Proceedings of the 27th Conference on Image and Vision Computing New Zealand
Gaussian Process Gauss-Newton for non-parametric simultaneous localization and mapping
International Journal of Robotics Research
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We present a novel data structure, the Bayes tree, that provides an algorithmic foundation enabling a better understanding of existing graphical model inference algorithms and their connection to sparse matrix factorization methods. Similar to a clique tree, a Bayes tree encodes a factored probability density, but unlike the clique tree it is directed and maps more naturally to the square root information matrix of the simultaneous localization and mapping (SLAM) problem. In this paper, we highlight three insights provided by our new data structure. First, the Bayes tree provides a better understanding of the matrix factorization in terms of probability densities. Second, we show how the fairly abstract updates to a matrix factorization translate to a simple editing of the Bayes tree and its conditional densities. Third, we apply the Bayes tree to obtain a completely novel algorithm for sparse nonlinear incremental optimization, named iSAM2, which achieves improvements in efficiency through incremental variable re-ordering and fluid relinearization, eliminating the need for periodic batch steps. We analyze various properties of iSAM2 in detail, and show on a range of real and simulated datasets that our algorithm compares favorably with other recent mapping algorithms in both quality and efficiency.