{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,26]],"date-time":"2026-04-26T00:49:54Z","timestamp":1777164594244,"version":"3.51.4"},"reference-count":25,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A comprehensive comparative study is presented of three approaches for color morphological processing: the proposed bitmixing transformation, lexicographic ordering, and conventional marginal processing. The novel bitmixing method converts RGB channels into a single 24-bit scalar representation through bit-interleaving, preserving both color information and spatial ordering relationships. This enables the direct application of grayscale morphological operators while generally preserving structural, chromatic, and visual relationships in processed objects. Under appropriate conditions\u2014such as when objects exhibit clear color-based boundaries and bilateral symmetry\u2014the method tends to maintain these symmetries more consistently than marginal or lexicographic alternatives. Experimental evaluation shows that the bitmixing approach achieves a competitive balance between color preservation and computational efficiency. In specific scenarios involving color-defined regions and symmetric structures, it demonstrates modest advantages over marginal and lexicographic methods. These findings suggest that the proposed method can serve as a viable alternative in applications where color fidelity, structural coherence, and symmetry preservation are desirable, though its benefits are context-dependent.<\/jats:p>","DOI":"10.3390\/sym17111858","type":"journal-article","created":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T11:11:16Z","timestamp":1762254676000},"page":"1858","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Comparative Study of Bitmixing, Marginal, and Lexicographic Methods for Color Image Morphological Processing"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7235-1614","authenticated-orcid":false,"given":"Carlos","family":"Paredes-Orta","sequence":"first","affiliation":[{"name":"Secihti-Centro de Investigaciones en \u00d3ptica, Aguascalientes 20200, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4950-4221","authenticated-orcid":false,"given":"Ang\u00e9lica Rosario","family":"Jim\u00e9nez-S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Aut\u00f3noma de Quer\u00e9taro, Santiago de Quer\u00e9taro 76010, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3519-6731","authenticated-orcid":false,"given":"Dami\u00e1n","family":"Vargas-V\u00e1zquez","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Aut\u00f3noma de Quer\u00e9taro, Santiago de Quer\u00e9taro 76010, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9719-829X","authenticated-orcid":false,"given":"Edgar Rafael","family":"Ponce de Le\u00f3n S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Facultad de Inform\u00e1tica, Universidad Aut\u00f3noma de Quer\u00e9taro, Quer\u00e9taro 76230, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0027-7176","authenticated-orcid":false,"given":"Israel","family":"Santillan","sequence":"additional","affiliation":[{"name":"Tecnol\u00f3gico Nacional de M\u00e9xico, Instituto Tecnol\u00f3gico de la Paz, La Paz 23080, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9173-0732","authenticated-orcid":false,"given":"Jorge Domingo","family":"Mendiola-Santiba\u00f1ez","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda, Universidad Aut\u00f3noma de Quer\u00e9taro, Santiago de Quer\u00e9taro 76010, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,4]]},"reference":[{"key":"ref_1","unstructured":"Serra, J. (1982). Image Analysis and Mathematical Morphology, Academic Press, Inc."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Soille, P. (2004). Morphological Image Analysis, Springer.","DOI":"10.1007\/978-3-662-05088-0"},{"key":"ref_3","unstructured":"Dougherty, E.R. (1993). Mathematical Morphology in Image Processing, Marcel Dekker. Optical Engineering."},{"key":"ref_4","unstructured":"Heijmans, H.J.A.M. (1994). Morphological Image Operators, Academic Press. Advances in Electronics and Electron Physics: Supplement."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gonzalez, R.C., and Woods, R.E. (2009). Digital Image Processing, Pearson Education. [3rd ed.].","DOI":"10.1117\/1.3115362"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Fairchild, M.D. (2013). Color Appearance Models, Wiley. [3rd ed.].","DOI":"10.1002\/9781118653128"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Plataniotis, K.N., and Venetsanopoulos, A.N. (2000). Color Image Processing and Applications, Springer.","DOI":"10.1007\/978-3-662-04186-4"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hanbury, A. (2003). Mathematical Morphology Applied to Circular Data, Elsevier. Advances in Imaging and Electron Physics.","DOI":"10.1016\/S1076-5670(03)80064-2"},{"key":"ref_9","unstructured":"Chanussot, J., and Lambert, P. (1999, January 20\u201323). Watershed approaches for color image segmentation. Proceedings of the IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-99, Antalya, Turkey."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.cviu.2006.11.008","article-title":"Morphological colour operators in totally ordered lattices based on distances: Application to image filtering, enhancement and analysis","volume":"107","author":"Angulo","year":"2007","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2914","DOI":"10.1016\/j.patcog.2007.02.004","article-title":"A comparative study on multivariate mathematical morphology","volume":"40","author":"Aptoula","year":"2007","journal-title":"Pattern Recognit."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.jvcir.2015.02.010","article-title":"A novel set of image morphological operators using a modified vector distance measure with color pixel classification","volume":"30","year":"2015","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Sun, S., Huang, Y., Inoue, K., and Hara, K. (2023). Order space-based morphology for color image processing. J. Imaging, 9.","DOI":"10.3390\/jimaging9070139"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Sun, L., Sun, H., Wang, J., Wu, S., Zhao, Y., and Xu, Y. (2021). Breast Mass Detection in Mammography Based on Image Template Matching and CNN. Sensors, 21.","DOI":"10.3390\/s21082855"},{"key":"ref_15","first-page":"559","article-title":"Advanced processing techniques for remotely sensed imagery","volume":"13","author":"Zhang","year":"2009","journal-title":"J. Remote Sens."},{"key":"ref_16","unstructured":"Morton, G.M. (1966). A Computer Oriented Geodetic Data Base and a New Technique in File Sequencing, International Business Machines Company."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Lukac, R., and Plataniotis, K.N. (2006). Color Image Processing: Methods and Applications, CRC Press. [1st ed.].","DOI":"10.1201\/9781420009781"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Santillan, I., Terol-Villalobos, I.R., and Herrera-Ruiz, G. (2008, January 27\u201331). Color Morphological Image Segmentation on a New Opponent Color Space Based on the Notion of Critical Functions. Proceedings of the 2008 Seventh Mexican International Conference on Artificial Intelligence, Atizap\u00e1n de Zaragoza, Mexico.","DOI":"10.1109\/MICAI.2008.23"},{"key":"ref_19","first-page":"110410F","article-title":"Linear colour segmentation revisited","volume":"Volume 11041","author":"Smagina","year":"2019","journal-title":"Proceedings of the Eleventh International Conference on Machine Vision (ICMV 2018)"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"297","DOI":"10.2307\/1932409","article-title":"Measures of the amount of ecologic association between species","volume":"26","author":"Dice","year":"1945","journal-title":"Ecology"},{"key":"ref_21","first-page":"547","article-title":"\u00c9tude comparative de la distribution florale dans une portion des Alpes et des Jura","volume":"37","author":"Jaccard","year":"1901","journal-title":"Bull. Soci\u00e9t\u00e9 Vaudoise Sci. Nat."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Paredes-Orta, C., Mendiola-Santib\u00e1\u00f1ez, J.D., Ibrahimi, D., Rodr\u00edguez-Res\u00e9ndiz, J., D\u00edaz-Florez, G., and Olvera-Olvera, C.A. (2022). Hyperconnected Openings Codified in a Max Tree Structure: An Application for Skull-Stripping in Brain MRI T1. Sensors, 22.","DOI":"10.3390\/s22041378"},{"key":"ref_23","first-page":"3323","article-title":"Unsupervised Color Segmentation with Reconstructed Spatial Weighted Gaussian Mixture Model and Random Color Histogram","volume":"78","author":"Khan","year":"2024","journal-title":"Comput. Mater. Contin."},{"key":"ref_24","first-page":"27113","article-title":"p-value Adjustment for Monotonous, Unbiased, and Fast Clustering Comparison","volume":"36","author":"Klede","year":"2023","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1109\/TLA.2023.10015218","article-title":"A fuzzy approach to evaluate image segmentation based on image complexity","volume":"21","year":"2023","journal-title":"IEEE Lat. Am. Trans."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1858\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T11:38:18Z","timestamp":1762256298000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1858"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,4]]},"references-count":25,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111858"],"URL":"https:\/\/doi.org\/10.3390\/sym17111858","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,4]]}}}