{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T12:31:54Z","timestamp":1775305914785,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2015,3,13]],"date-time":"2015-03-13T00:00:00Z","timestamp":1426204800000},"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>Unlike landmark methods for estimating object asymmetry, continuous symmetry measures (CSM) can be used to measure the symmetry distance (ds) of inconsistent objects, such as plant leaves. Inconsistent objects have no homologous landmarks, no consistent topology, no quantitative consistency, and sometimes no matching points. When CSM is used in conjugation with LAMINA Leaf Shape Determination software, one can quickly and efficiently process a large number of scanned leaves. LAMINA automatically generates equally-spaced points around the perimeter of each leaf and the resulting x-y coordinates are normalized to average centroid size prior to estimating ds using a fold, average, unfold algorithm. We estimated shape asymmetry of leaves of three species of flowering plants: Ligustrum sinense (Chinese Privet), Rubus cuneifolius (blackberry), and Perilla frutescens (Perilla), as well as individual leaves from a few species of oaks (Quercus) and maples (Acer). We found that 100 to 200 equally-spaced points worked well for all three of the main species. Measurement error accounted for a small proportion of the asymmetry variation. Nevertheless, measurement error was great enough to generate some negative size scaling after normalization to average centroid size.<\/jats:p>","DOI":"10.3390\/sym7010255","type":"journal-article","created":{"date-parts":[[2015,3,13]],"date-time":"2015-03-13T11:51:52Z","timestamp":1426247512000},"page":"255-268","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Fluctuating Asymmetry of Plant Leaves: Batch Processing with LAMINA and Continuous Symmetry Measures"],"prefix":"10.3390","volume":"7","author":[{"given":"John","family":"Graham","sequence":"first","affiliation":[{"name":"Department of Biology, Berry College, Mount Berry, GA 30149, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mattie","family":"Whitesell","sequence":"additional","affiliation":[{"name":"Department of Biology, Berry College, Mount Berry, GA 30149, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark","family":"II","sequence":"additional","affiliation":[{"name":"School of Medicine, University of Connecticut, Farmington, CT 06032, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hagit","family":"Hel-Or","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Haifa, Haifa 31905, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eviatar","family":"Nevo","sequence":"additional","affiliation":[{"name":"Institute of Evolution, University of Haifa, Haifa 31905, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shmuel","family":"Raz","sequence":"additional","affiliation":[{"name":"Department of Information Systems, University of Haifa, Haifa 31905, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"466","DOI":"10.3390\/sym2020466","article-title":"Fluctuating asymmetry: Methods, theory, and applications","volume":"2","author":"Graham","year":"2010","journal-title":"Symmetry"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/BF02424508","article-title":"Developmental stability in plants: Symmetries, stress and epigenesis","volume":"89","author":"Freeman","year":"1993","journal-title":"Genetica"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Polak, M. (2003). Developmental instability: Causes and consequences, Oxford University Press.","DOI":"10.1093\/oso\/9780195143454.001.0001"},{"key":"ref_4","unstructured":"Arcelli, C., Cordella, L., and Sanniti di Baja, G. (1994). Aspects of visual form processing, World Scientific Publishing."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Liu, Y., Hel-Or, H., Kaplan, C.S., and Van Gool, L. (2009). Computational Symmetry in Computer Vision and Computer Graphics, Now Publishers Inc.","DOI":"10.1561\/9781601983657"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1154","DOI":"10.1109\/34.476508","article-title":"Symmetry as a continuous feature","volume":"17","author":"Zabrodsky","year":"1995","journal-title":"Pattern Anal. Mach. Intell. IEEE Trans."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2237","DOI":"10.1016\/j.patcog.2006.12.008","article-title":"A new measure of symmetry and its application to classification of bifurcating structures","volume":"40","author":"Milner","year":"2007","journal-title":"Pattern Recognit."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Milner, D., Hel-Or, H., Keren, D., Raz, S., and Nevo, E. (2005, January 1\u201314). Analyzing symmetry in biological systems. Genova, Italy.","DOI":"10.1109\/ICIP.2005.1529762"},{"key":"ref_9","unstructured":"Frid, A. (2008). Merging Local and Global Symmetry. [M.S. Thesis, University of Haifa]."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1111\/j.1469-8137.2007.02146.x","article-title":"A method for quantifying rotational symmetry","volume":"175","author":"Frey","year":"2007","journal-title":"New Phytol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Weyl, H. (1952). Symmetry, Princeton University Press.","DOI":"10.1515\/9781400874347"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bylesj\u00f6, M., Segura, V., Soolanayakanahally, R.Y., Rae, A.M., Trygg, J., Gustafsson, P., Jansson, S., and Street, N.R. (2008). Lamina: A tool for rapid quantification of leaf size and shape parameters. BMC Plant Biol., 8.","DOI":"10.1186\/1471-2229-8-82"},{"key":"ref_13","unstructured":"Zelditch, M.L., Swiderski, D.L., and Sheets, H.D. (2012). Geometric Morphometrics for Biologists: A Primer, Academic Press."},{"key":"ref_14","unstructured":"MATLAB Code for Continuous Symmetry Measures (CSM) of Leaves and Other Objects. Available online: http:\/\/facultyweb.berry.edu\/jgraham\/CSMCode.htm."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/S1361-8415(97)85012-8","article-title":"Landmark methods for forms without landmarks: Morphometrics of group differences in outline shape","volume":"1","author":"Bookstein","year":"1996\/7","journal-title":"Med. Image Anal."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Savriama, Y., and Klingenberg, C.P. (2011). Beyond bilateral symmetry: Geometric morphometric methods for any type of symmetry. BMC Evolut. Biol., 11.","DOI":"10.1186\/1471-2148-11-280"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.1095-8312.1998.tb01530.x","article-title":"Directional asymmetry and the measurement of developmental instability","volume":"64","author":"Graham","year":"1998","journal-title":"Biol. J. Linn. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1046\/j.1095-8312.2003.00220.x","article-title":"Growth models and the expected distribution of fluctuating asymmetry","volume":"80","author":"Graham","year":"2003","journal-title":"Biol. J. Linn. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.2307\/2411306","article-title":"Geometric morphometrics of developmental instability: Analyzing patterns of fluctuating asymmetry with procrustes methods","volume":"52","author":"Klingenberg","year":"1998","journal-title":"Evolution"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/7\/1\/255\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:43:30Z","timestamp":1760215410000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/7\/1\/255"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,13]]},"references-count":19,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,3]]}},"alternative-id":["sym7010255"],"URL":"https:\/\/doi.org\/10.3390\/sym7010255","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,13]]}}}