{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T11:34:15Z","timestamp":1766748855789,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T00:00:00Z","timestamp":1581033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671258\uff1b61871247\uff1b61671412\uff1b61620106012"],"award-info":[{"award-number":["61671258\uff1b61871247\uff1b61671412\uff1b61620106012"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>With the wide applications of three-dimensional (3D) meshes in intelligent manufacturing, digital animation, virtual reality, digital cities and other fields, more and more processing techniques are being developed for 3D meshes, including watermarking, compression, and simplification, which will inevitably lead to various distortions. Therefore, how to evaluate the visual quality of 3D mesh is becoming an important problem and it is necessary to design effective tools for blind 3D mesh quality assessment. In this paper, we propose a new Blind Mesh Quality Assessment method based on Graph Spectral Entropy and Spatial features, called as BMQA-GSES. 3D mesh can be represented as graph signal, in the graph spectral domain, the Gaussian curvature signal of the 3D mesh is firstly converted with Graph Fourier transform (GFT), and then the smoothness and information entropy of amplitude features are extracted to evaluate the distortion. In the spatial domain, four well-performing spatial features are combined to describe the concave and convex information and structural information of 3D meshes. All the extracted features are fused by the random forest regression to predict the objective quality score of the 3D mesh. Experiments are performed successfully on the public databases and the obtained results show that the proposed BMQA-GSES method provides good correlation with human visual perception and competitive scores compared to state-of-art quality assessment methods.<\/jats:p>","DOI":"10.3390\/e22020190","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T11:50:28Z","timestamp":1581076228000},"page":"190","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Blind Mesh Assessment Based on Graph Spectral Entropy and Spatial Features"],"prefix":"10.3390","volume":"22","author":[{"given":"Yaoyao","family":"Lin","sequence":"first","affiliation":[{"name":"Faculty of Information Science and Engineering, Ningbo University, No. 818, Ningbo 315211, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2140-8756","authenticated-orcid":false,"given":"Mei","family":"Yu","sequence":"additional","affiliation":[{"name":"Faculty of Information Science and Engineering, Ningbo University, No. 818, Ningbo 315211, China"}]},{"given":"Ken","family":"Chen","sequence":"additional","affiliation":[{"name":"Faculty of Information Science and Engineering, Ningbo University, No. 818, Ningbo 315211, China"}]},{"given":"Gangyi","family":"Jiang","sequence":"additional","affiliation":[{"name":"Faculty of Information Science and Engineering, Ningbo University, No. 818, Ningbo 315211, China"}]},{"given":"Fen","family":"Chen","sequence":"additional","affiliation":[{"name":"Faculty of Information Science and Engineering, Ningbo University, No. 818, Ningbo 315211, China"}]},{"given":"Zongju","family":"Peng","sequence":"additional","affiliation":[{"name":"Faculty of Information Science and Engineering, Ningbo University, No. 818, Ningbo 315211, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15779","DOI":"10.1109\/ACCESS.2019.2894533","article-title":"Signal Processing on Static and Dynamic 3D Meshes: Sparse Representations and Applications","volume":"7","author":"Lalos","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s11760-008-0079-y","article-title":"Watermarking 3D models using spectral mesh compression","volume":"3","author":"Abdallah","year":"2009","journal-title":"Signal Image Video Process."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Abdallah, E.E., Ben Hamza, A., and Bhattacharya, P. (2007). Spectral graph-Theoretic approach to 3D mesh watermarking. Proc. Graph. Interface, 327\u2013334.","DOI":"10.1145\/1268517.1268570"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"24365","DOI":"10.1007\/s11042-018-5706-1","article-title":"Blind 3D mesh visual quality assessment using support vector regression","volume":"77","author":"Abouelaziz","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Guo, J., Vidal, V., Cheng, I., Basu, A., and Baskurt, A. (2017). Subjective and Objective Visual Quality Assessment of Textured 3D Meshes. ACM Trans. Appl. Percept., 14.","DOI":"10.1145\/2996296"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1109\/ICME.2002.1035879","article-title":"Mesh: Measuring errors between surfaces using the Hausdorff distance","volume":"1","author":"Aspert","year":"2002","journal-title":"IEEE Int. Conf. Multimed. Expo."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Karni, Z., and Gotsman, C. (2000, January 23\u201328). Spectral compression of mesh geometry. Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, New Orleans, LA, USA .","DOI":"10.1145\/344779.344924"},{"key":"ref_8","unstructured":"Sorkine, O., Cohenor, D., and Toledo, S. (2003, January 23\u201325). High-Pass quantization for mesh encoding. Proceedings of the Eurographics\/ACM SIGGRAPH Symposium on Geometry Processing, Aachen, Germany."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1109\/TMM.2006.886261","article-title":"Watermarked 3-D mesh quality assessment","volume":"9","author":"Corsini","year":"2007","journal-title":"IEEE Trans. Multimed."},{"key":"ref_10","unstructured":"Gelasca, E.D., Ebrahimi, T., Corsini, M., and Barni, M. (2015, January 27\u201330). Objective evaluation of the perceptual quality of 3D watermarking. Proceedings of the IEEE International Conference on Image Processing, Quebec City, QC, Canada."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Lavou\u00e9, G., Gelasca, E.D., Dupont, F., Baskurt, A., and Ebrahimi, T. (2006). Perceptually driven 3D distance metrics with application to watermarking. Proc. SPIE-Int. Soc. Opt. Eng.","DOI":"10.1117\/12.686964"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1109\/TMM.2010.2060475","article-title":"A comparison of perceptually-Based metrics for objective evaluation of geometry processing","volume":"12","author":"Corsini","year":"2010","journal-title":"IEEE Trans. Multimed."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1111\/j.1467-8659.2012.03176.x","article-title":"Dihedral angle mesh error: A fast perception correlated distortion measure for fixed connectivity triangle meshes","volume":"31","author":"Jan","year":"2012","journal-title":"Comput. Graph. Forum"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1016\/j.cag.2012.06.004","article-title":"A fast roughness-Based approach to the assessment of 3D mesh visual quality","volume":"36","author":"Wang","year":"2012","journal-title":"Comput. Graph."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Abouelaziz, I., Omari, M., Hassouni, M.E., and Cherifi, H. (2015, January 23\u201327). Reduced Reference 3D Mesh Quality Assessment Based on Statistical Models. Proceedings of the 11th International Conference on Signal-Image Technology and Internet-Based Systems (SITIS), Bangkok, Thailand.","DOI":"10.1109\/SITIS.2015.129"},{"key":"ref_16","unstructured":"Abouelaziz, I., Hassouni, M.E., and Cherifi, H. (\u20131, January 30). No-Reference 3D mesh quality assessment based on dihedral angles model and support vector regression. Proceedings of the International Conference on Image and Signal Processing, Trois-Rivi\u00e8res, QC, Canada."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Abouelaziz, I., Hassouni, M.E., and Cherifi, H. (2017, January 17\u201320). A convolutional neural network framework for blind mesh visual quality assessment. Proceedings of the IEEE International Conference on Image Processing, Beijing, China.","DOI":"10.1109\/ICIP.2017.8296382"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Abouelaziz, I., Chetouani, A., Hassouni, M.E., and Cherifi, H. (2017, January 4\u20137). Mesh visual quality assessment Metrics: A Comparison Study. Proceedings of the 13th International Conference on Signal-Image Technology and Internet-Based Systems (SITIS), Jaipur, India.","DOI":"10.1109\/SITIS.2017.55"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/MSP.2012.2235192","article-title":"The emerging field of signal processing on graphs: Extending high-Dimensional data analysis to networks and other irregular domains","volume":"30","author":"Shuman","year":"2013","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5406","DOI":"10.1109\/TSP.2017.2731299","article-title":"Uncertainty Principles and Sparse Eigenvectors of graphs","volume":"65","author":"Teke","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","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."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.jvcir.2017.01.001","article-title":"A Spectral shape classification: A deep learning approach","volume":"43","author":"Masoumi","year":"2017","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Tseng, C.C., Lee, S.L., and Su, R.H. (2017, January 12\u201314). A missing temperature data estimation method using graph Fourier transform. Proceedings of the IEEE International Conference on Consumer Electronics-TW, Taipei, Taiwan.","DOI":"10.1109\/ICCE-China.2017.7991008"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1109\/JSTSP.2017.2726979","article-title":"On the Graph Fourier Transform for Directed Graphs","volume":"11","author":"Sardellitti","year":"2017","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1644","DOI":"10.1109\/TSP.2013.2238935","article-title":"Discrete Signal Processing on Graphs","volume":"61","author":"Sandryhaila","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2174","DOI":"10.1109\/TMM.2015.2484221","article-title":"Perceptual Quality Assessment for 3D Triangle Mesh Based on Curvature","volume":"17","author":"Dong","year":"2015","journal-title":"IEEE Trans. Multimed."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.cam.2017.05.007","article-title":"Mesh segmentation by combining mesh saliency with spectral clustering","volume":"329","author":"Jiao","year":"2017","journal-title":"J. Comput. Appl. Math."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Mart\u00ednez-Mart\u00ednez, C.T., and M\u00e9ndez-Berm\u00fadez, J.A. (2019). Information Entropy of Tight-Binding Random Networks with Losses and Gain: Scaling and Universality. Entropy, 21.","DOI":"10.3390\/e21010086"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Liu, J., Xu, M., Xu, X., and Haung, Y. (2019). Nonreference Image Quality Evaluation Algorithm Based on Wavelet Convolutional Neural Network and Information Entropy. Entropy, 21.","DOI":"10.3390\/e21111070"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Cohen-Steiner, D., and Morvan, J.M. (2003, January 8\u201310). Restricted Delaunay triangulations and normal cycle. Proceedings of the 19th annual symposium on Computational geometry (SCG \u201803), San Diego, CA, USA.","DOI":"10.1145\/777837.777839"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3282","DOI":"10.1109\/TIP.2015.2440172","article-title":"Image Quality Assessment Using Human Visual DOG Model Fused with Random Forest","volume":"24","author":"Peiand","year":"2015","journal-title":"IEEE Trans. Image Process."},{"key":"ref_32","unstructured":"ITU-T P.1401 (2012). Methods, Metrics and Procedures for Statistical Evaluation, Qualification and Comparison of Objective Quality Prediction Models, International Telecommunication Union."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/190\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:55:37Z","timestamp":1760172937000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/190"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,7]]},"references-count":32,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["e22020190"],"URL":"https:\/\/doi.org\/10.3390\/e22020190","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,2,7]]}}}