Topological descriptors for 3D surface analysis. (English) Zbl 1339.68284
Bac, Alexandra (ed.) et al., Computational topology in image context. 6th international workshop, CTIC 2016, Marseille, France, June 15–17, 2016. Proceedings. Cham: Springer (ISBN 978-3-319-39440-4/pbk; 978-3-319-39441-1/ebook). Lecture Notes in Computer Science 9667, 77-87 (2016).
Summary: We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for a 2D cubical filtration. In the next step we investigate different topological descriptors and measure their ability to discriminate structurally different 3D surface patches. We evaluate their sensitivity to different parameters and compare the performance of the resulting topological descriptors to alternative (non-topological) descriptors. We present a comprehensive evaluation that shows that topological descriptors are (i) robust, (ii) yield state-of-the-art performance for the task of 3D surface analysis and (iii) improve classification performance when combined with non-topological descriptors.
For the entire collection see [Zbl 1337.68003].
For the entire collection see [Zbl 1337.68003].
MSC:
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
| 68U10 | Computing methodologies for image processing |
Keywords:
3D surface classification; surface topology analysis; surface representation; persistence diagram; persistence imagesReferences:
| [1] | Adams, H., Chepushtanova, S., Emerson, T., Hanson, E., Kirby, M., Motta, F., Neville, R., Peterson, C., Shipman, P., Ziegelmeier, L.: Persistent images: A stable vector representation of persistent homology (2015). arXiv preprint arXiv:1507.06217 · Zbl 1431.68105 |
| [2] | Bauer, U., Kerber, M., Reininghaus, J.: Phat - persistent homology algorithms toolbox (2013). https://code.google.com/p/phat/ · Zbl 1402.65187 |
| [3] | Bauer, U., Kerber, M., Reininghaus, J., Wagner, H.: PHAT – Persistent homology algorithms toolbox. In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 137–143. Springer, Heidelberg (2014). http://dx.doi.org/10.1007/978-3-662-44199-2_24 · Zbl 1402.65187 · doi:10.1007/978-3-662-44199-2_24 |
| [4] | Belongie, S., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. Pattern Anal. Mach. Intell. 24(4), 509–522 (2002) · doi:10.1109/34.993558 |
| [5] | Crandall, D., Owens, A., Snavely, N., Huttenlocher, D.: Discrete-continuous optimization for large-scale structure from motion. In: 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3001–3008. IEEE (2011) · doi:10.1109/CVPR.2011.5995626 |
| [6] | Dalal, N., Triggs, B.: Histograms of oriented gradients for human detection. In: 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005, vol. 1, pp. 886–893. IEEE (2005) · doi:10.1109/CVPR.2005.177 |
| [7] | Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete Comput. Geom. 28, 511–533 (2002) · Zbl 1011.68152 · doi:10.1007/s00454-002-2885-2 |
| [8] | Freund, Y., Schapire, R.E.: A decision-theoretic generalization of on-line learning and an application to boosting. J. Comput. Syst. Sci. 55(1), 119–139 (1997) · Zbl 0880.68103 · doi:10.1006/jcss.1997.1504 |
| [9] | Guo, Z., Zhang, L., Zhang, D.: A completed modeling of local binary pattern operator for texture classification. IEEE Trans. Image Process. 19(6), 1657–1663 (2010) · Zbl 1371.94151 · doi:10.1109/TIP.2010.2044957 |
| [10] | Haralick, R.M., Shanmugam, K., Dinstein, I.H.: Textural features for image classification. IEEE Trans. Syst. Man Cybern. 6, 610–621 (1973) · doi:10.1109/TSMC.1973.4309314 |
| [11] | ISO-IEC: Information Technology - Multimedia Content Description Interface.15938, ISO/IEC, Moving Pictures Expert Group, 1st edn. (2002) |
| [12] | Johnson, A.E., Hebert, M.: Using spin images for efficient object recognition in cluttered 3D scenes. IEEE Trans. Pattern Anal. Mach. Intell. 21(5), 433–449 (1999) · doi:10.1109/34.765655 |
| [13] | Juda, M., Mrozek, M., Brendel, P., Wagner, H., et al.: CAPD::RedHom (2010–2015). http://redhom.ii.uj.edu.pl |
| [14] | Juda, M., Mrozek, M.: CAPD:RedHom v2 - homology software based on reduction algorithms. In: Hong, H., Yap, C. (eds.) ICMS 2014. LNCS, vol. 8592, pp. 160–166. Springer, Heidelberg (2014) · Zbl 1402.57021 · doi:10.1007/978-3-662-44199-2_27 |
| [15] | Li, C., Ovsjanikov, M., Chazal, F.: Persistence-based structural recognition. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 2003–2010. IEEE (2014) · doi:10.1109/CVPR.2014.257 |
| [16] | López, V., Fernández, A., García, S., Palade, V., Herrera, F.: An insight into classification with imbalanced data: Empirical results and current trends on using data intrinsic characteristics. Inf. Sci. 250, 113–141 (2013) · doi:10.1016/j.ins.2013.07.007 |
| [17] | Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004) · doi:10.1023/B:VISI.0000029664.99615.94 |
| [18] | Ojala, T., Pietikäinen, M., Harwood, D.: A comparative study of texture measures with classification based on featured distributions. Pattern Recogn. 29(1), 51–59 (1996) · doi:10.1016/0031-3203(95)00067-4 |
| [19] | Othmani, A., Lew Yan Voon, L., Stolz, C., Piboule, A.: Single tree species classification from terrestrial laser scanning data for forest inventory. Pattern Recogn. Lett. 34(16), 2144–2150 (2013) · doi:10.1016/j.patrec.2013.08.004 |
| [20] | Poincaré, H.J.: Sur le probleme des trois corps et les équations de la dynamique. Acta Math. 13, 1–270 (1890) · JFM 22.0907.01 · doi:10.1007/BF02392514 |
| [21] | Poincaré, H.J.: Les méthodes nouvelles de la mécanique céleste. Gauthiers-Villars, Paris (1892, 1893, 1899) |
| [22] | Poincaré, H.J.: Analysis situs. J. Éc. Polytech., ser. 2 1, 1–123 (1895) |
| [23] | Reininghaus, J., Huber, S., Bauer, U., Kwitt, R.: A stable multi-scale kernel for topological machine learning (2014). arXiv preprint arXiv:1412.6821 |
| [24] | Rusu, R.B., Marton, Z.C., Blodow, N., Beetz, M.: Persistent point feature histograms for 3D point clouds. In: Proceedings of the 10th International Conference on Intel Autonomous System (IAS-10), Baden-Baden, Germany, pp. 119–128 (2008) |
| [25] | Seiffert, C., Khoshgoftaar, T.M., Van Hulse, J., Napolitano, A.: Rusboost: A hybrid approach to alleviating class imbalance. IEEE Trans. Syst. Man Cybern. Part A: Syst. Hum. 40(1), 185–197 (2010) · doi:10.1109/TSMCA.2009.2029559 |
| [26] | Vedaldi, A., Fulkerson, B.: Vlfeat: An open and portable library of computer vision algorithms. In: Proceedings of the International Conference on Multimedia, pp. 1469–1472. ACM (2010) · doi:10.1145/1873951.1874249 |
| [27] | Wohlfeil, J., Strackenbrock, B., Kossyk, I.: Automated high resolution 3D reconstruction of cultural heritage using multi-scale sensor systems and semi-global matching. Int. Arch. Photogrammetry Remote Sens. Spat. Inf. Sci. XL-4 W 4, 37–43 (2013) · doi:10.5194/isprsarchives-XL-4-W4-37-2013 |
| [28] | Wu, C.: Towards linear-time incremental structure from motion. In: 2013 International Conference on 3DTV, pp. 127–134. IEEE (2013) · doi:10.1109/3DV.2013.25 |
| [29] | Zeppelzauer, M., Poier, G., Seidl, M., Reinbacher, C., Breiteneder, C., Bischof, H., Schulter, S.: Interactive segmentation of rock-art in high-resolution 3D reconstructions. In: 2015 Digital Heritage, vol. 2, pp. 37–44, September 2015. doi: 10.1109/DigitalHeritage.2015.7419450 |
| [30] | Zeppelzauer, M., Seidl, M.: Efficient image-space extraction and representation of 3D surface topography. In: Proceedings of the IEEE International Conference on Image Processing (ICIP). IEEE, Quebec, Canada (2015). http://arXiv.org/pdf/1504.08308v3.pdf · doi:10.1109/ICIP.2015.7351322 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
