Abstract
In recent years, the analysis tasks of 3D point cloud models have also attracted wide attention from researchers. The most basic and important research work of 3D point cloud model analysis is the similarity measurement of 3D models. The similarity measurement of 3D point cloud models are generally calculated by shape descriptors, which can capture the most unique features for 3D point cloud models. However, the traditional feature extraction methods for 3D point cloud models are less robust, only focus on rigid deformation and less attention to non-rigid deformation. Recent publications introduce the Laplace-Beltrami operator to define shape descriptors and analysis the non-rigid deformation of models. In this paper, a concise 3D point cloud descriptor is defined to describe the internal structure of 3D point cloud models: scaling invariant harmonic wave kernel signature (SIHWKS). SIHWKS is a shape descriptor involving in the Laplace-Beltrami operator, which can effectively extract geometric and topological information from 3D point cloud models. Based on SIHWKS, the modified Hausdorff distance between SIHWKS values of 3D point cloud model is calculated as similarity measurement, which provides an effective method for 3D point cloud model analysis. Lastly, experiments conducted on public 3D shape datasets show the SIHWKS has the advantages of isometric invariance, scaling invariance and it is robust to topology, sampling and noise.
Supported by The Natural Science Foundation of Qinghai Province in China (NO. 2018−ZJ−777) and National Natural Science Foundation of China(No.62007019).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Deng, H., Wei, Z., Mortensen, E.N., et al.: Principal curvature-based region detector for object recognition. In: CVPR 2007, pp. 18–23 (2007)
Huangfu, Z., Yan, L., Zhang, S.: A new method for estimation of normal vector and curvature based on scattered point cloud. J. Comput. Inf. Syst. 8(19), 7937–7945 (2012)
Ke, Y.L., Li, A.: Rotational surface extraction based on principal direction Gaussian image from point cloud. J. Zhejiang Univ. (Eng. Sci.) 40(6), 942–946 (2006)
Sanchez, J., Denis, F., Coeurjolly, D., et al.: Robust normal vector estimation in 3D point clouds through iterative principal component analysis. ISPRS J. Photogrammetry Remote Sens. 163, 18–35 (2020)
Bao, L., Schnabel, R., Klein, R., et al.: Robust normal estimation for point clouds with sharp features. Comput. Graph. 34(2), 94–106 (2010)
Pei, L., Wu, Z., Xia, C., et al.: Robust normal estimation of point cloud with sharp features via subspace clustering. In: International Conference on Graphic & Image Processing (2014)
Srivastava, A., Kurtek, S., Klassen, E.: Statistical Shape Analysis. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston (2014). https://doi.org/10.1007/978-0-387-31439-6_778
Srivastava, A., Joshi, S.H., Mio, W., et al.: Statistical shape analysis: clustering, learning, and testing. IEEE Trans. Pattern Anal. Mach. Intell. 27(4), 590 (2005)
Bezerra, M.A., Bruns, R.E., Ferreira, S.: Statistical design-principal component analysis optimization of a multiple response procedure using cloud point extraction and simultaneous determination of metals by ICP OES. Analytica Chimica Acta 580(2), 251–257 (2006)
Rahmani, H., Mahmood, A., Q Huynh, D., Mian, A.: HOPC: histogram of oriented principal components of 3D pointclouds for action recognition. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014. LNCS, vol. 8690, pp. 742–757. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10605-2_48
Iqbal, M.Z., Bobkov, D., Steinbach, E.: Fuzzy logic and histogram of normal orientation-based 3D keypoint detection for point clouds. Pattern Recogn, Lett. 136, 40–47 (2020)
Fan, D., Liu, Y., Ying, H.: Recent progress in the Laplace-Beltrami operator and its applications to digital geometry processing. J. Comput. Aided Des. Comput. Graph. 27, 559–569 (2015)
Sun, J., Ovsjanikov, M., Guibas, L.: A concise and provably informative multi-scale signature based on heat diffusion. Comput. Graph. Forum 28(5), 1383–1392 (2010)
Bronstein, M.M., Kokkinos, I.: Scale-invariant heat kernel signatures for non-rigid shape recognition. In: 2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1704–1711. IEEE (2010)
Aubry, M., Schlickewei, U., Cremers, D.: The wave kernel signature: a quantum mechanical approach to shape analysis. In: IEEE International Conference on Computer 588 Vision Workshops, pp. 1626–1633 (2011)
Li, H., Li, S., Wu, X., et al.: Scale-invariant wave kernel signature for non-rigid 3D shape retrieval. In: 2018 IEEE International Conference on Big Data and Smart Computing. IEEE (2018)
Zhang, D., Wu, Z., Wang, X., et al.: 3D skull and face similarity measurements based on a harmonic wave kernel signature. Visual Comput. (7) (2020)
Rustamov, R.M.: Laplace-Beltrami eigenfunctions for deformation invariant shape representation. In: Proceedings of the 5th Eurographics Symposium on Geometry Processing, pp. 225–233 (2007)
Patané, G.: STAR Laplacian spectral kernels and distances for geometry processing and shape analysis. In: Proceedings of the Computer Graphics Forum, pp. 599–624 (2016)
Zhang, S., Zong, M., Sun, K., Liu, Y., Cheng, D.: Efficient kNN algorithm based on graph sparse reconstruction. In: Luo, X., Yu, J.X., Li, Z. (eds.) ADMA 2014. LNCS (LNAI), vol. 8933, pp. 356–369. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-14717-8_28
Dubuisson, M.P., Jain, A.K.: A modified Hausdorff distance for object matching. In: 600 International Conference on Pattern Recognition (2002)
Pickup, D., Sun, X., Rosin, P.L., et al.: SHREC 2015 track: canonical forms for non-rigid 3D shape retrieval. In: Eurographics Workshop on 3D Object Retrieval (2015)
Bronstein, A.M., Bronstein, M.M., Castellani, U., et al.: SHREC 2010: robust large-scale shape retrieval benchmark. In: Proceedings of the EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR) (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Zhang, D. et al. (2021). Scaling Invariant Harmonic Wave Kernel Signature for 3D Point Cloud Similarity. In: Peng, Y., Hu, SM., Gabbouj, M., Zhou, K., Elad, M., Xu, K. (eds) Image and Graphics. ICIG 2021. Lecture Notes in Computer Science(), vol 12890. Springer, Cham. https://doi.org/10.1007/978-3-030-87361-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-87361-5_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-87360-8
Online ISBN: 978-3-030-87361-5
eBook Packages: Computer ScienceComputer Science (R0)