Hostname: page-component-7c8c6479df-fqc5m Total loading time: 0 Render date: 2024-03-19T05:41:19.029Z Has data issue: false hasContentIssue false

Online topological segmentation of visual sequences using the algebraic connectivity of graphs

Published online by Cambridge University Press:  24 February 2015

Jaime Boal*
Affiliation:
Institute for Research in Technology (IIT), ICAI School of Engineering, Comillas Pontifical University, Madrid, Spain
Álvaro Sánchez-Miralles
Affiliation:
Institute for Research in Technology (IIT), ICAI School of Engineering, Comillas Pontifical University, Madrid, Spain
*
*Corresponding author. E-mail: jaime.boal@iit.upcomillas.es

Summary

In the context of topological mapping, the automatic segmentation of an environment into meaningful and distinct locations is still regarded as an open problem. This paper presents an algorithm to extract places online from image sequences based on the algebraic connectivity of graphs or Fiedler value, which provides an insight into how well connected several consecutive observations are. The main contribution of the proposed method is that it is a theoretically supported alternative to tuning thresholds on similarities, which is a difficult task and environment dependent. It can accommodate any type of feature detector and matching procedure, as it only requires non-negative similarities as input, and is therefore able to deal with descriptors of variable length, to which statistical techniques are difficult to apply. The method has been validated in an office environment using exclusively visual information. Two different types of features, a bag-of-words model built from scale invariant feature transform (SIFT) keypoints, and a more complex fingerprint based on vertical lines, color histograms, and a few Star keypoints, are employed to demonstrate that the method can be applied to both fixed and variable length descriptors with similar results.

Type
Articles
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Choset, H. and Nagatani, K., “Topological simultaneous localization and mapping (SLAM): Toward exact localization without explicit localization,” IEEE Trans. Robot. Autom. 17 (2), 125137 (2001).CrossRefGoogle Scholar
2. Beeson, P., Jong, N. K. and Kuipers, B., “Towards Autonomous Topological Place Detection using the Extended Voronoi Graph,” Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 4373–4379.Google Scholar
3. Kortenkamp, D. and Weymouth, T., “Topological Mapping for Mobile Robots using a Combination of Sonar and Vision Sensing,” Proceedings of the AAAI 12th National Conference on Artificial Intelligence, Seattle, WA, USA (1994) pp. 979–984.Google Scholar
4. Kuipers, B., Modayil, J., Beeson, P., MacMahon, M. and Savelli, F., “Local Metrical and Global Topological Maps in the Hybrid Spatial Semantic Hierarchy,” Proceedings of the IEEE International Conferemce on Robotics and Automation, New Orleans, LA, USA, vol. 5 (2004) pp. 4845–4851.Google Scholar
5. Tapus, A. and Siegwart, R., “Incremental Robot Mapping with Fingerprints of Places,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Edmonton, AB, Canada (2005) pp. 2429–2434.Google Scholar
6. Romero, A. and Cazorla, M., “Topological visual mapping in robotics,” Cogn. Process. 13 (1 Suppl.), 305308 (2012).Google Scholar
7. Ranganathan, A. and Dellaert, F., “Bayesian Surprise and Landmark Detection,” Proceedings of the IEEE International Conference on Robotics and Automation, Kobe, Japan (2009) pp. 2017–2023.Google Scholar
8. Itti, L. and Baldi, P., “A Principled Approach to Detecting Surprising Events in Video,” Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, USA, vol. 1 (2005) pp. 631–637.Google Scholar
9. Sivic, J. and Zisserman, A., “Efficient visual search of videos cast as text retrieval,” IEEE Trans. Pattern Anal. Mach. Intell. 31 (4), 591606 (2009).Google Scholar
10. Ranganathan, A., “PLISS: Detecting and Labeling Places using Online Change-Point Detection,” Proceedings of the Robotics: Science and Systems, Zaragoza, Spain (2010).Google Scholar
11. Ranganathan, A., “PLISS: Labeling places using online changepoint detection,” Auton. Robots 32 (4), 351368 (2012).Google Scholar
12. Adams, R. P. and MacKay, D. J. C., “Bayesian online changepoint detection,” Technical Report. University of Cambridge, Cambridge, UK (2007). arXiv:0710.3742v1 [stat.ML].Google Scholar
13. Liu, M. and Siegwart, R., “DP-FACT: Towards Topological Mapping and Scene Recognition with Color for Omnidirectional Camera,” Proceedings of the IEEE International Conference on Robotics and Automation, Saint Paul, MN, USA (2012) pp. 3503–3508.Google Scholar
14. Liu, M. and Siegwart, R., “Topological mapping and scene recognition with lightweight color descriptors for an ominidirectional camera,” IEEE Trans. Robot. 30 (2), 310324 (2014).Google Scholar
15. Chapoulie, A., Rives, P. and Filliat, D., “Appearance-Based Segmentation of Indoors/Outdoors Sequences of Spherical Views,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan (2013) pp. 1946–1951.Google Scholar
16. Angeli, A., Doncieux, S., Meyer, J.-A. and Filliat, D., “Incremental Vision-Based Topological SLAM,” Proceedings of the IEEE/RSJ International Conference Intelligent Robots and Systems, Nice, France (2008) pp. 1031–1036.Google Scholar
17. Cha, S.-H., “Comprehensive survey on distance/similarity measures between probability density functions,” Int. J. Math. Models Methods Appl. Sci. 1 (4), 300307 (2007).Google Scholar
18. Liu, M., Colas, F. and Siegwart, R., “Regional Topological Segmentation based on Mutual Information Graphs,” Proceedings of the IEEE International Conference Robotics and Automation, Shanghai, China (2011) pp. 3269–3274.Google Scholar
19. Belkin, M. and Niyogi, P., “Laplacian eigenmaps for dimensionality reduction and data representation,” Neural Comput. 15, 13731396 (2003).Google Scholar
20. Ng, A. Y., Jordan, M. I. and Weiss, Y., “On spectral clustering: Analysis and an algorithm,” Adv. Neural Inform. Process. Syst. 14, 849856 (2002).Google Scholar
21. von Luxburg, U., “A tutorial on spectral clustering,” Stat. Comput. 17 (4), 395416 (2007).Google Scholar
22. Fiedler, M., “Algebraic connectivity of graphs,” Czech. Math. J. 23 (2), 298305 (1973).CrossRefGoogle Scholar
23. Chung, F. K., Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, vol. 92 (American Mathematical Society, Providence, RI, USA, 1997).Google Scholar
24. Spielman, D. A. and Teng, S.-H., “Spectral partitioning works: Planar graphs and finite element meshes,” Linear Algebra Appl. 421, 284305 (2006).Google Scholar
25. Chawla, S., “Sparsest Cut,” In: Encyclopedia of Algorithms (Kao, M.-Y., ed.) (Springer, New, York, NY, USA, 2008) pp. 868870.Google Scholar
26. Szymański, J., “Categorization of Wikipedia Articles with Spectral Clustering,” In: Proceedings of the International Conference on Intelligent Data Engineering and Automated Learning, Lecture Notes in Computer Science (Yin, H., Wang, W. and Rayward-Smith, V., eds.) vol. 6936 (Springer Berlin Heidelberg, Norwich, UK, 2011) pp. 108115.Google Scholar
27. Bach, F. R. and Jordan, M. I., “Learning spectral clustering, with application to speech separation,” J. Mach. Learn. Res. 7, 19632001 (2006).Google Scholar
28. Schultz, T. and Kindlmann, G. L., “Open-box spectral clustering: Applications to medical image analysis,” IEEE Trans. Vis. Comput. Graph. 19 (12), 21002108 (2013).Google Scholar
29. Billauer, E., “peakdet: Peak detection using MATLAB,” (2012). Available at: http://billauer.co.il/peakdet.html, accessed Apr. 27, 2014.Google Scholar
30. Stankiewicz, B. J. and Kalia, A. A., “Acquisition of structural versus object landmark knowledge,” J. Exp. Psychol.: Human Perception Perform. 33 (2), 378390 (2007).Google ScholarPubMed
31. Bradski, G., “The OpenCV library,” (2000). Available at: http://www.opencv.org, accessed Apr. 27, 2014.Google Scholar
32. Sanderson, C., “Armadillo: An open source C++ linear algebra library for fast prototyping and computationally intensive experiments,” Technical report, NICTA (2010). Available at: http://arma.sourceforge.net, accessed Apr. 27, 2014.Google Scholar
33. Luo, J., Pronobis, A., Caputo, B. and Jensfelt, P., “Incremental Learning for Place Recognition in Dynamic Environments,” Proceedings of the IEEE/RSJ International Conference Intelligent Robots and Systems, San Diego, CA, USA (2007) pp. 721–728.Google Scholar
34. Pronobis, A. and Caputo, B., “COLD: The cosy localization database,” Int. J. Robot. Res. 28, 588594 (2009).Google Scholar
35. Luo, J., Pronobis, A., Caputo, B. and Jensfelt, P., “The KTH-IDOL2 database,” Technical Report CVAP304, KTH Royal Institute of Technology, CVAP/CAS, Stockholm, Sweden (2006).Google Scholar
36. Lowe, D. G., “Distinctive image features from scale-invariant keypoints,” Int. J. Comput. Vis. 60 (2), 91110 (2004).Google Scholar
37. Boal, J., Sánchez-Miralles, Á. and Alvar, M., “Matching monocular lightweight features using n-gram techniques for topological location identification,” Robotica FirstView, 1–15 (2014).Google Scholar
38. Ranganathan, A. and Dellaert, F., “Online probabilistic topological mapping,” Int. J. Robot. Res. 30 (6), 755771 (2011).Google Scholar