{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T21:20:49Z","timestamp":1762464049348,"version":"build-2065373602"},"reference-count":50,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T00:00:00Z","timestamp":1605225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Computer-aided classification serves as the basis of virtual cultural relic management and display. The majority of the existing cultural relic classification methods require labelling of the samples of the dataset; however, in practical applications, there is often a lack of category labels of samples or an uneven distribution of samples of different categories. To solve this problem, we propose a 3D cultural relic classification method based on a low dimensional descriptor and unsupervised learning. First, the scale-invariant heat kernel signature (Si-HKS) was computed. The heat kernel signature denotes the heat flow of any two vertices across a 3D shape and the heat diffusion propagation is governed by the heat equation. Secondly, the Bag-of-Words (BoW) mechanism was utilized to transform the Si-HKS descriptor into a low-dimensional feature tensor, named a SiHKS-BoW descriptor that is related to entropy. Finally, we applied an unsupervised learning algorithm, called MKDSIF-FCM, to conduct the classification task. A dataset consisting of 3D models from 41 Tang tri-color Hu terracotta Eures was utilized to validate the effectiveness of the proposed method. A series of experiments demonstrated that the SiHKS-BoW descriptor along with the MKDSIF-FCM algorithm showed the best classification accuracy, up to 99.41%, which is a solution for an actual case with the absence of category labels and an uneven distribution of different categories of data. The present work promotes the application of virtual reality in digital projects and enriches the content of digital archaeology.<\/jats:p>","DOI":"10.3390\/e22111290","type":"journal-article","created":{"date-parts":[[2020,11,13]],"date-time":"2020-11-13T08:44:02Z","timestamp":1605257042000},"page":"1290","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Approach for 3D Cultural Relic Classification Based on a Low-Dimensional Descriptor and Unsupervised Learning"],"prefix":"10.3390","volume":"22","author":[{"given":"Hongjuan","family":"Gao","sequence":"first","affiliation":[{"name":"School of Information Science &amp; Technology, Northwest University, Xi\u2019an 710127, China"},{"name":"Xinhua College, Ningxia University, Yinchuan 750021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guohua","family":"Geng","sequence":"additional","affiliation":[{"name":"School of Information Science &amp; Technology, Northwest University, Xi\u2019an 710127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sheng","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Information Science &amp; Technology, Northwest University, Xi\u2019an 710127, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,13]]},"reference":[{"key":"ref_1","first-page":"74","article-title":"The dig of aesthetic uniqueness in the Tang dynasty by means of Tri-colored glazed pottery of the Tang dynasty","volume":"45","author":"Fan","year":"2009","journal-title":"China Ceram."},{"unstructured":"Kegang, W. (2017). Classification of Ancient Ceramic Relic Fragments Based on Learning Optimization and Information Fusion. [Ph.D. Thesis, Northwest University].","key":"ref_2"},{"doi-asserted-by":"crossref","unstructured":"Bronstein, M.M., and Kokkinos, I. (2010, January 13\u201318). Scale-invariant heat kernel signatures for non-rigid shape recognition. Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, CA, USA.","key":"ref_3","DOI":"10.1109\/CVPR.2010.5539838"},{"unstructured":"Godil, A., Dutagaci, H., Bustos, B., Choi, S., Dong, S., Furuya, T., Li, H., Link, N., Moriyama, A., and Meruane, R. (2015, January 2\u20133). SHREC\u201915: Ange Scans based 3D Shape Retrieval. Proceedings of the 2015 Eurographics Workshop on 3D Object Retrieval, Zurich, Switzerland.","key":"ref_4"},{"key":"ref_5","first-page":"22","article-title":"3D Object Classification Using Scale Invariant Heat Kernels with Collaborative Classification","volume":"Volume 7583","author":"Abdelrahman","year":"2012","journal-title":"Proceedings of the Public-Key Cryptography\u2013PKC 2018"},{"doi-asserted-by":"crossref","unstructured":"Li, C., and Hamza, A.B. (2014). Spatially Aggregating Spectral Descriptors for Nonrigid 3D Shape Retrieval: A Comparative Survey, Springer.","key":"ref_6","DOI":"10.1007\/s00530-013-0318-0"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1109\/34.765655","article-title":"Using spin images for efficient object recognition in cluttered 3D scenes","volume":"21","author":"Johnson","year":"1999","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"unstructured":"Toldo, R., Castellani, U., and Fusiello, A. (2009, January 29). Visual vocabulary signature for 3D object retrieval and partial matching. Proceedings of the Eurographics Workshop on 3D Object Retrieval, Munich, Germany.","key":"ref_8"},{"unstructured":"Ruiz-Correa, S., Shapiro, L.G., and Meli\u0103, M. (2001, January 8\u201314). A new signature-based method for efficient 3-D object recognition. Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR, Kauai, HI, USA.","key":"ref_9"},{"unstructured":"Gelfand, N., Mitra, N.J., Guibas, L.J., and Pottmann, H. (2005, January 4\u20136). Robust global registration. Proceedings of the Symposium on Geometry Processing, Vienna, Austria.","key":"ref_10"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1111\/j.1467-8659.2009.01515.x","article-title":"A Concise and Provably Informative Multi-Scale Signature Based on Heat Diffusion","volume":"28","author":"Sun","year":"2009","journal-title":"Comput. Graph. Forum"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1007\/s11263-009-0301-6","article-title":"A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching","volume":"89","author":"Bronstein","year":"2010","journal-title":"Int. J. Comput. Vis."},{"unstructured":"Rustamov, R.M. (2007, January 4\u20136). Laplace-beltrami eigenfunctions for deformation invariant shape representation. Proceedings of the Fifth Eurographics Symposium on Geometry Processing, Barcelona, Spain.","key":"ref_13"},{"doi-asserted-by":"crossref","unstructured":"Ovsjanikov, M., Bronstein, A.M., Bronstein, M.M., and Guibas, L.J. (October, January 27). Shape Google: A computer vision approach to isometry invariant shape retrieval. Proceedings of the 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops, Kyoto, Japan.","key":"ref_14","DOI":"10.1109\/ICCVW.2009.5457682"},{"doi-asserted-by":"crossref","unstructured":"Fang, Y., Sun, M., and Ramani, K. (2011, January 18). Temperature distribution descriptor for robust 3d shape retrieval. Proceedings of the Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment, CVPR, San Francisco, CA, USA.","key":"ref_15","DOI":"10.1109\/CVPRW.2011.5981684"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1109\/34.993558","article-title":"Shape matching and object recognition using shape contexts","volume":"24","author":"Belongie","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s00371-015-1146-3","article-title":"Retrieval and classification methods for textured 3D models: A comparative study","volume":"32","author":"Biasotti","year":"2015","journal-title":"Vis. Comput."},{"unstructured":"Tombari, F., Salti, S., and Di Stefano, L. (2010, January 8\u201310). Unique Signatures of Histograms for Local Surface Description. Proceedings of the Haptics: Generating and Perceiving Tangible Sensations, Amsterdam, the Netherlands.","key":"ref_18"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.neucom.2016.06.088","article-title":"3D shape recognition and retrieval based on multi-modality deep learning","volume":"259","author":"Bu","year":"2017","journal-title":"Neurocomputing"},{"unstructured":"Wang, F., Kang, L., and Li, Y. (2015, January 7\u201312). Sketch-based 3D shape retrieval using Convolutional Neural Networks. Proceedings of the 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA.","key":"ref_20"},{"unstructured":"Wu, Z., Song, S., Khosla, A., Yu, F., Zhang, L., Tang, X., and Xiao, J. (2015, January 7\u201312). 3D ShapeNets: A deep representation for volumetric shapes. Proceedings of the 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA.","key":"ref_21"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4014","DOI":"10.1109\/TCYB.2016.2591583","article-title":"Deep Multimodal Distance Metric Learning Using Click Constraints for Image Ranking","volume":"47","author":"Yu","year":"2016","journal-title":"IEEE Trans. Cybern."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1049\/iet-cvi.2017.0005","article-title":"Fully convolutional networks for action recognition","volume":"11","author":"Yu","year":"2017","journal-title":"IET Comput. Vis."},{"unstructured":"Savva, M., Yu, F., Su, H., Aono, M., Chen, B., Cohen-Or, D., Deng, W., Su, H., Bai, S., and Bai, X. (2016, January 8). Shrec\u201916 track largescale 3d shape retrieval from shapenet core55. Proceedings of the EG workshop on 3D Object Recognition, Lisbon, Portugal.","key":"ref_24"},{"doi-asserted-by":"crossref","unstructured":"Maturana, D., and Scherer, S. (October, January 28). VoxNet: A 3D Convolutional Neural Network for real-time object recognition. Proceedings of the 2015 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany.","key":"ref_25","DOI":"10.1109\/IROS.2015.7353481"},{"doi-asserted-by":"crossref","unstructured":"Su, H., Maji, S., Kalogerakis, E., and Learned-Miller, E. (2015, January 7\u201313). Multi-view Convolutional Neural Networks for 3D Shape Recognition. Proceedings of the 2015 IEEE International Conference on Computer Vision (ICCV), Santiago, Chile.","key":"ref_26","DOI":"10.1109\/ICCV.2015.114"},{"doi-asserted-by":"crossref","unstructured":"Qi, C.R., Su, H., NieBner, M., Dai, A., Yan, M., and Guibas, L.J. (2016, January 27\u201330). Volumetric and Multi-view CNNs for Object Classification on 3D Data. Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA.","key":"ref_27","DOI":"10.1109\/CVPR.2016.609"},{"doi-asserted-by":"crossref","unstructured":"Fang, Y., Xie, J., Dai, G., Wang, M., Zhu, F., Xu, T., and Wong, E. (2015, January 7\u201312). 3D deep shape descriptor. Proceedings of the 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Boston, MA, USA.","key":"ref_28","DOI":"10.1109\/CVPR.2015.7298845"},{"doi-asserted-by":"crossref","unstructured":"Charles, R.Q., Su, H., Kaichun, M., and Guibas, L.J. (2017, January 26). PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation. Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA.","key":"ref_29","DOI":"10.1109\/CVPR.2017.16"},{"unstructured":"Qi, C.R., Yi, L., Su, H., and Guibas, L.J. (2017). PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space. arXiv.","key":"ref_30"},{"unstructured":"Li, Y., Bu, R., Sun, M., Wu, W., Di, X., and Chen, B. (2018). PointCNN: Convolution On X-Transformed Points. arXiv, Available online: https:\/\/arxiv.org\/abs\/1801.07791.","key":"ref_31"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.jvcir.2017.01.001","article-title":"Spectral shape classification: A deep learning approach","volume":"43","author":"Masoumi","year":"2017","journal-title":"J. Vis. Commun. Image Represent."},{"unstructured":"Menze, H.B., and Ur, J.A. (2007, January 12\u201314). Classification of multispectral ASTER imagery in archaeological settlement survey in the Near East. Proceedings of the 10th ISPMSRS (Intl. Symposium on Physical Measurements and Signatures in Remote Sensing), Davos, Switzerland.","key":"ref_33"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/s00339-008-4481-7","article-title":"Application of artificial neural networks for the rapid classification of archaeological ceramics by means of laser induced breakdown spectroscopy (LIBS)","volume":"92","author":"Ramil","year":"2008","journal-title":"Appl. Phys. A"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"588","DOI":"10.1016\/j.patcog.2010.09.016","article-title":"Artwork 3D model database indexing and classification","volume":"44","author":"Jordan","year":"2011","journal-title":"Pattern Recognit."},{"key":"ref_36","first-page":"82","article-title":"A Software System for Classification of Archaeological Artefacts Represented by 2D Plans","volume":"13","author":"Hristov","year":"2013","journal-title":"Cybern. Inf. Technol."},{"key":"ref_37","first-page":"465","article-title":"An experimental design for the classification of archaeological ceramic data from Cyprus, and the tracing of inter-class relationships","volume":"7","author":"Charalambous","year":"2016","journal-title":"J. Archaeol. Sci. Rep."},{"unstructured":"Manferdini, A.M., Remondino, F., Baldissini, S., and Gaiani, M. (2008, January 20\u201325). 3D modeling and semantic classification of archaeological finds for management and visualization in 3D archaeological databases. Proceedings of the 14th International Conference on Virtual Systems and Multimedia, Limassol, Cyprus.","key":"ref_38"},{"doi-asserted-by":"crossref","unstructured":"Desai, P., Pujari, J., Ayachit, N.H., and Prasad, V.K. (2013, January 22\u201325). Classification of archaeological monuments for different art forms with an application to CBIR. Proceedings of the 2013 International Conference on Advances in Computing, Communications and Informatics (ICACCI), Mysore, India.","key":"ref_39","DOI":"10.1109\/ICACCI.2013.6637332"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.microc.2008.11.006","article-title":"Investigations by various analytical techniques to the correct classification of archaeological finds and delineation of technological features","volume":"91","author":"Mangone","year":"2009","journal-title":"Microchem. J."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"4567267","DOI":"10.1155\/2018\/4567267","article-title":"Sex Determination of 3D Skull Based on a Novel Unsupervised Learning Method","volume":"2018","author":"Gao","year":"2018","journal-title":"Comput. Math. Methods Med."},{"unstructured":"Ohbuchi, R., and Furuya, T. (2008, January 3\u20135). Accelerating bag-of-features sift algorithm for 3d model retrieval. Proceedings of the SAMT Workshop on Semantic 3D Media (S-3D), Koblenz, Germany.","key":"ref_42"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1023\/B:VISI.0000027790.02288.f2","article-title":"Scale & Affine Invariant Interest Point Detectors","volume":"60","author":"Mikolajczyk","year":"2004","journal-title":"Int. J. Comput. Vis."},{"doi-asserted-by":"crossref","unstructured":"Chum, O., Philbin, J., Sivic, J., Isard, M., and Zisserman, A. (2007, January 14\u201320). Total Recall: Automatic Query Expansion with a Generative Feature Model for Object Retrieval. Proceedings of the 2007 IEEE 11th International Conference on Computer Vision, Rio de Janeiro, Brazil.","key":"ref_44","DOI":"10.1109\/ICCV.2007.4408891"},{"unstructured":"Liu, Y., Zha, H., and Qin, H. (2006, January 17\u201322). Shape Topics: A Compact Representation and New Algorithms for 3D Partial Shape Retrieval. Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition\u2013Volume 1 (CVPR\u201906), Washington, DC, USA.","key":"ref_45"},{"unstructured":"Mitra, N.J., Guibas, L., Giesen, J., and Pauly, M. (2006, January 26\u201328). Probabilistic fingerprints for shapes. Proceedings of the Eurographics symposium on Geometry processing, Cagliari, Sardinia.","key":"ref_46"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.patrec.2016.04.009","article-title":"A spectral graph wavelet approach for nonrigid 3D shape retrieval","volume":"83","author":"Masoumi","year":"2016","journal-title":"Pattern Recognit. Lett."},{"doi-asserted-by":"crossref","unstructured":"Jalal, A., Khalid, N., and Kim, K. (2020). Automatic Recognition of Human Interaction via Hybrid Descriptors and Maximum Entropy Markov Model Using Depth Sensors. Entropy, 22.","key":"ref_48","DOI":"10.3390\/e22080817"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0098-3004(84)90020-7","article-title":"FCM: The fuzzy c-means clustering algorithm","volume":"10","author":"Bezdek","year":"1984","journal-title":"Comput. Geosci."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1109\/TNNLS.2015.2424995","article-title":"Extreme Learning Machine for Multilayer Perceptron","volume":"27","author":"Tang","year":"2015","journal-title":"IEEE Trans. Neural Netw. Learn. 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