{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T18:33:50Z","timestamp":1792866830447,"version":"4.5.0"},"reference-count":43,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2011,1,21]],"date-time":"2011-01-21T00:00:00Z","timestamp":1295568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In recent years, there is an emerging direction that leverages information theory to solve many challenging problems in scientific data analysis and visualization. In this article, we review the key concepts in information theory, discuss how the principles of information theory can be useful for visualization, and provide specific examples to draw connections between data communication and data visualization in terms of how information can be measured quantitatively. As the amount of digital data available to us increases at an astounding speed, the goal of this article is to introduce the interested readers to this new direction of data analysis research, and to inspire them to identify new applications and seek solutions using information theory.<\/jats:p>","DOI":"10.3390\/e13010254","type":"journal-article","created":{"date-parts":[[2011,1,24]],"date-time":"2011-01-24T03:22:54Z","timestamp":1295839374000},"page":"254-273","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":89,"title":["Information Theory in Scientific Visualization"],"prefix":"10.3390","volume":"13","author":[{"given":"Chaoli","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Computer Science, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Han-Wei","family":"Shen","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, The Ohio State University, 2015 Neil Avenue, Columbus, OH 43210, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2011,1,21]]},"reference":[{"key":"ref_1","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley-Interscience. [2nd ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kerren, A., Stasko, J.T., Fekete, J.D., and North, C. (2008). Information Visualization: Human-centered Issues and Perspectives, Springer-Verlag.","DOI":"10.1007\/978-3-540-70956-5"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1109\/TVCG.2010.132","article-title":"An Information-theoretic framework for visualization","volume":"16","author":"Chen","year":"2010","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1109\/TVCG.2008.140","article-title":"Importance-driven time-varying data visualization","volume":"14","author":"Wang","year":"2008","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1109\/TVCG.2007.70628","article-title":"A statistical approach to volume data quality assessment","volume":"14","author":"Wang","year":"2008","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1109\/18.61115","article-title":"Divergence measures based on the Shannon entropy","volume":"37","author":"Lin","year":"1991","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","unstructured":"Bordoloi, U.D., and Shen, H.W. (, January October). View selection for volume rendering. Proceedings of IEEE Visualization Conference, Minneapolis, MN, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1375","DOI":"10.1109\/TVCG.2009.197","article-title":"Visual exploration of climate variability changes using wavelet Analysis","volume":"15","author":"Mikolajewicz","year":"2009","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1111\/j.1467-8659.2009.01689.x","article-title":"Isosurface similarity maps","volume":"29","author":"Bruckner","year":"2010","journal-title":"Comput. Graph. Forum"},{"key":"ref_10","unstructured":"Takahashi, S., Fujishiro, I., Takeshima, Y., and Nishita, T. (, January October). A feature-driven approach to locating optimal viewpoints for volume visualization. Proceedings of IEEE Visualization Conference, Minneapolis, MN, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1109\/TVCG.2006.137","article-title":"Dynamic view selection for time-varying volumes","volume":"12","author":"Ji","year":"2006","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1216","DOI":"10.1109\/TVCG.2010.131","article-title":"An information-theoretic framework for flow visualization","volume":"16","author":"Xu","year":"2010","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_13","unstructured":"Furuya, S., and Itoh, T. (, January October). A streamline selection technique for integrated scalar and vector visualization. Proceedings of the IEEE Visualization Conference Poster Compendium, Columbus, OH, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1578","DOI":"10.1109\/TVCG.2010.212","article-title":"View-dependent streamlines for 3D vector fields","volume":"16","author":"Marchesin","year":"2010","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_15","unstructured":"Haidacher, M., Bruckner, S., Kanitsar, A., and Gr\u00f6ller, M.E. (, January October). Information-based transfer functions for multimodal visualization. Proceedings of Eurographics Workshop on Visual Computing for Biomedicine, Delft, The Netherlands."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1109\/TVCG.2006.159","article-title":"LOD map\u2014A visual interface for navigating multiresolution volume visualization","volume":"12","author":"Wang","year":"2006","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_17","first-page":"1384","article-title":"Multifield visualization using local statistical complexity","volume":"13","author":"Wiebel","year":"2007","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1109\/TVCG.2006.152","article-title":"Importance-driven focus of attention","volume":"12","author":"Viola","year":"2006","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_19","unstructured":"Sbert, M., Plemenos, D., Feixas, M., and Gonz\u00e1lez, F. (, January May). Viewpoint quality: Measures and applications. Proceedings of Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging, Girona, Spain."},{"key":"ref_20","unstructured":"V\u00e1zquez, P.P., Feixas, M., Sbert, M., and Heidrich, W. (, January November). Viewpoint selection using viewpoint entropy. Proceedings of Vision, Modeling, and Visualization Conference, Stuttgart, Germany."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.cag.2010.01.006","article-title":"Viewpoint information channel for illustrative volume rendering","volume":"34","author":"Ruiz","year":"2010","journal-title":"Comput. Graph."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/S0165-1684(98)00239-4","article-title":"A novel fuzzy entropy approach to image enhancement and thresholding","volume":"75","author":"Cheng","year":"1999","journal-title":"Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1023\/A:1007958904918","article-title":"Alignment by maximization of mutual information","volume":"24","author":"Viola","year":"1997","journal-title":"Int. J. Comput. Vision"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"986","DOI":"10.1109\/TMI.2003.815867","article-title":"Mutual-information-based registration of medical images","volume":"22","author":"Pluim","year":"2003","journal-title":"IEEE Trans. Med. Imag."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1109\/42.563664","article-title":"Multimodality image registration by maximization of mutual information","volume":"16","author":"Maes","year":"1997","journal-title":"IEEE Trans. Med. Imag."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1109\/83.887976","article-title":"Optimization of mutual information for multiresolution image registration","volume":"9","author":"Unser","year":"2000","journal-title":"IEEE Trans. Image Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1486","DOI":"10.1109\/TIP.2005.854442","article-title":"A nonparametric statistical method for image segmentation using information theory and curve evolution","volume":"14","author":"Kim","year":"2005","journal-title":"IEEE Trans. Image Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1109\/TMI.2005.854516","article-title":"DTI Segmentation using an information theoretic tensor dissimilarity measure","volume":"24","author":"Wang","year":"2005","journal-title":"IEEE Trans. Med. Imag."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Sbert, M., Feixas, M., Rigau, J., Chover, M., and Viola, I. (2009). Information Theory Tools for Computer Graphics, Morgan & Claypool Publishers.","DOI":"10.1007\/978-3-031-79546-6"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1111\/1467-8659.00331","article-title":"An information theory framework for the analysis of scene complexity","volume":"18","author":"Feixas","year":"1999","journal-title":"Comput. Graph. Forum"},{"key":"ref_31","unstructured":"Rigau, J., Feixas, M., and Sbert, M. (, January July). New contrast measures for pixel supersampling. Proceedings of Computer Graphics International, Bradford, UK."},{"key":"ref_32","unstructured":"Wong, L., Dumont, C., and Abidi, M. (, January November). Next best view system in a 3-D modeling task. Proceedings of International Symposium on Computational Intelligence in Robotics and Automation, Monterey, CA, USA."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1111\/1467-8659.00447","article-title":"Automatic camera placement for image-based modeling","volume":"19","author":"Fleishman","year":"2000","journal-title":"Comput. Graph. Forum"},{"key":"ref_34","unstructured":"Arbel, A., and Ferrie, F.P. (, January September). Viewpoint selection by navigation through entropy maps. Proceedings of International Conference on Computer Vision, Kerkyra, Corfu, Greece."},{"key":"ref_35","unstructured":"He, L.W., Cohen, M.F., and Salesin, D.H. (, January August). The virtual cinematographer: A paradigm for automatic real-time camera control and directing. Proceedings of ACM SIGGRAPH Conference, New Orleans, LA, USA."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1111\/j.1467-8659.2003.00717.x","article-title":"Automatic view selection using viewpoint entropy and its applications to image-based modelling","volume":"22","author":"Feixas","year":"2003","journal-title":"Comput. Graph. Forum"},{"key":"ref_37","unstructured":"Gumhold, S. (, January October). Maximum entropy light source placement. Proceedings of IEEE Visualization Conference, Boston, MA, USA."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/MCG.2008.41","article-title":"Viewpoint-based ambient occlusion","volume":"28","author":"Sbert","year":"2008","journal-title":"IEEE Comput. Graph. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/j.cag.2008.05.005","article-title":"Viewpoint-driven simplification using mutual information","volume":"32","author":"Sbert","year":"2008","journal-title":"Comput. Graph."},{"key":"ref_40","first-page":"1","article-title":"A unified information-theoretic framework for viewpoint selection and mesh saliency","volume":"6","author":"Feixas","year":"2009","journal-title":"ACM Trans. Graph."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/MCG.2008.34","article-title":"Informational aesthetics measures","volume":"28","author":"Rigau","year":"2008","journal-title":"IEEE Comput. Graph. Appl."},{"key":"ref_42","unstructured":"Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis, Chapman & Hall\/CRC."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Scott, D.W. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization, Wiley-Interscience.","DOI":"10.1002\/9780470316849"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/13\/1\/254\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:55:00Z","timestamp":1760219700000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/13\/1\/254"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,21]]},"references-count":43,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1]]}},"alternative-id":["e13010254"],"URL":"https:\/\/doi.org\/10.3390\/e13010254","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1,21]]}}}