## Treemap: An O(log n) Algorithm for Indoor. Simultaneous Localization and Mapping (2006)

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Venue: | Autonomous Robots |

Citations: | 33 - 4 self |

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@ARTICLE{Frese06treemap:an,

author = {Udo Frese},

title = {Treemap: An O(log n) Algorithm for Indoor. Simultaneous Localization and Mapping},

journal = {Autonomous Robots},

year = {2006},

volume = {20},

pages = {25--42}

}

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### Citations

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Matrix Analysis
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Citation Context ...R T , b M n = −RP −1 c + d (30) and passes it to the parent node. This is the well known marginalization formula for Gaussians (Thrun et al., 2005, Tab. 11.6) which is also known as Schur-complement (=-=Horn and Johnson, 1990-=-). Equation (29) is remarkable. It represents p(u|v) in terms of v as a single Gaussian in u with mean Hv + h. For general distributions no such simple relation will hold. Treemap stores p C n as (P −... |

1141 |
A Threshold Selection Method From Gray-Level Histogram
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Citation Context ...iew: ±45 ◦ ) at a height of 1.55m and controlled manually. We set circular fiducials throughout the floor (Fig. 10) that were visually detected by Hough-transform and a gray-level variance criterion (=-=Otsu, 1979-=-). Since the landmarks are identical, identification is based on their relative position employing two different strategies in parallel. Local 7 Processing time had 5ms resolution, so clock time has b... |

883 | Probabilistic Robotics - Thrun, Burgard, et al. - 2005 |

480 | Fastslam: A factored solution to simultaneous localization and mapping - Montemerlo, Thrun, et al. - 2002 |

464 | A multi-level algorithm for partitioning graphs - Hendrickson, Leland - 1995 |

460 | Globally consistent range scan alignment for environment mapping - Lu, Milios - 1997 |

449 |
Mattheyses, “A linear-time heuristic for improving network partitions
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Citation Context ...partitioned, i.e. x[n: ↓↑] contains few landmarks in all nodes n. Balancing is not difficult but hierarchical tree partitioning (HTP) is NP-complete. So we follow the tradition in graph partitioning (=-=Fiduccia and Mattheyses, 1982-=-) and optimize in greedy steps with each step being optimal. The goal was to make treemap O(k 3 log n) in a strict asymptotical sense given that the HTP subalgorithm succeeds in finding a suitable tre... |

414 | Estimating uncertain spatial relationships in robotics,” Autonomous Robot Vehicles - Smith, Self, et al. - 1990 |

206 | Simultaneous localization and mapping with sparse extended information filters,” Intl - Thrun, Liu, et al. - 2004 |

125 | Thin junction tree filters for simultaneous localization and mapping - Paskin - 2002 |

85 | Hierarchical slam: Real-time accurate mapping of large environments - Estrada, Neira, et al. - 2005 |

63 | Learning globally consistent maps by relaxation - Duckett, Marsland, et al. - 2000 |

55 | Decoupled stochastic mapping - Leonard, Feder - 1999 |

52 | Multi-robot slam with sparse extended information filers - Thrun, Liu - 2005 |

37 | Theoria combinationis observationum erroribus minimis obnoxiae: Pars posterior. Gottingische gelehrte Anzeigen - Gauss |

36 | Slam in large-scale cyclic environments using the atlas framework - Bosse, Newman, et al. - 2004 |

36 | Simultaneous localization and mapping - a discussion - Frese, Hirzinger - 2001 |

34 | Sparse extended information filters: Insights into sparsification - Eustice, Walter, et al. - 2005 |

31 | Closing a million-landmarks loop - Frese, Schroder - 2006 |

29 |
Numerical Recipes in C, second edition
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Citation Context ...ent (using so-called amortization). This can derogate map quality, since in the numerical literature, relaxation is reputed to need O(kn 2 ) time for reducing the equation error by a constant factor (=-=Press et al., 1992-=-). Imagine closing a loop of length n and going around that loop a second time. Still the estimate will not have reasonably converged because only O(k 2 n) time has been spent. If all landmarks are up... |

27 | Towards lazy data association in slam - Hähnel, Burgard, et al. - 2003 |

26 | Exploration with active loop-closing for FastSLAM - Stachniss, Haehnel, et al. - 2004 |

22 | A discussion of simultaneous localization and mapping - Frese - 2006 |

21 | A multigrid algorithm for simultaneous localization and mapping - Frese, Larsson, et al. - 2005 |

21 | Real time data association for fastslam - Nieto, Guivant, et al. - 2003 |

19 | A proof for the approximate sparsity of SLAM information matrices - Frese - 2005 |

18 | A provably consistent method for imposing exact sparsity in featurebased slam information filters - Walter, Eustice, et al. - 2005 |

14 | 2001. Optimization of the simultaneous localization and map building algorithm for real time implementation - Guivant, Nebot |

9 |
Generalization of Min-Cut Partitioning to Tree Structures and Its Applications
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(Show Context)
Citation Context ...problem is equivalent to the Hierarchical Tree Partitioning Problem known from graph theory and parallel computing and being NP-complete. However, successful heuristic algorithms have been developed (=-=Vijayan, 1991-=-) – the most popular of which is the Kernighan and Lin heuristic (Fiduccia and Mattheyses, 1982). It employs a greedy strategy in each step moving that node which minimizes the cost function. Hendrick... |

8 | An O(log n) Algorithm for Simulateneous Localization and Mapping of Mobile Robots in Indoor Environments - Frese |

7 | DP-SLAM: Fast, robust simulataneous localization and mapping without predetermined landmarks - Eliazar, Parr - 2003 |

1 | Nebot: 2003, ‘Solving computational and memory requirements of feature-based simultaneous localization and mapping algorithms - Guivant, E |