Validation of Lepidopteran Classification by Morphological Fractal Dimension Analysis

Authors

  • Anna Rose P. Nillama
  • Mark S. Borres University of San Jose-Recoletos
  • Ricky B. Villeta University of San Jose-Recoletos
  • Roramie V. Arco University of San Jose-Recoletos
  • Joyce C. Unabia University of San Jose-Recoletos

DOI:

https://doi.org/10.32871/rmrj1402.01.19

Keywords:

lepidoptera species, fractal geometry, fractal dimension, morphological dimensions and tresholding effect

Abstract

The paper uses fractal geometry through the fractal dimension of photos of the
Lepidopteran species, the commonly named butterflies, collected from the regions of Central Visayas, Philippines to determine if the morphological dimensions can discriminate one species over the other for classification purposes. The images of species were converted into a binary image using the simplest form of image processing known as thresholding effect. The binary images provide a simple view and ease for computing its fractal dimension. The fractal dimension explains the space – filling property of the image. The species available for use were the Cethosia, Idea, Pachliopta, Catopsilia, Troides where 10 subspecies of each were chosen. Also, the male species were isolated and tallied separately from the females. Empirical results revealed that the fractal dimensions can differentiate the species from one another with a general p – value of 0.000 and F – value of 6.483. All sample pairwise comparisons were tested for the significant differences and still differentiates one over the other as evidenced by the corresponding p - values of all equal to 0.000, respectively. Moreover, the fractal dimensions, in relation to the species gender, were tested for possible significant differences, and findings showed that it could differentiate across butterfly’s gender with a p – value of 0.000 and F- value of 8.037. The empirical probability of wrong classification using the fractal dimension is less than 1%.

Author Biographies

Mark S. Borres, University of San Jose-Recoletos

graduated Bachelor of Science in Mathematics–major in Pure Mathematics at the University of the Philippines, Cebu College. Since 2009, he worked for the University of San Jose- Recoletos as a faculty member of the College of Arts and Sciences and handled Mathematics subjects such as College Algebra, Advanced Algebra, Abstract Algebra, Analytical Geometry, Euclidean geometry, Trigonometry, Business Mathematics, Linear Programming, Mathematics of Investment, Discrete Structure, and Statistics across colleges.

Ricky B. Villeta, University of San Jose-Recoletos

graduated from Mindanao State University – Iligan Institute of Technology (MSU-IIT) with a degree of Bachelor of Science in Mathematics (Pure Mathematics) in 2003 as a fulltime scholar, City Mayor’s scholar (Iligan City) granted from having graduated in high school as class valedictorian and a COE (Center of Excellence in Mathematics) scholar awarded by MSU-IIT Mathematics department. He also obtained his Master of Science in Mathematics degree in 2007, with a specialization in Abstract Algebra (group theory) at MSU-IIT. He had served as Mathematics Lecturer from 2003 to 2005 and as graduate teaching assistant from 2005 to 2006 at the Mathematics Department of the College of Science and Mathematics of MSU-IIT. At the same time, he worked as Mathematics Instructor at Systems Technology Institute – Iligan from 2005 to 2006. Since 2006 to present, he is a faculty member of the Department of Mathematics and Sciences of the College of Arts and Sciences at University of San Jose – Recoletos, Cebu City. He handles classes on quantitative analysis in business, calculus for business, differential equations for engineering, probability theory, abstract algebra, linear algebra, number theory, problem solving, differential calculus, integral calculus, applied statistics in business, biostatistics, behavioral statistics, computer aided statistical analysis, mathematics of investment and the like. His research works and interests are in abstract algebra (group theory), graph theory, differential equation, mathematical modeling and simulation, fractal statistics, data mining and theory development. He also serves as a research statistician in graduate and undergraduate theses of the university and a member of the Mathematical Society of the Philippines.

Roramie V. Arco, University of San Jose-Recoletos

is a science instructor at the Department of Mathematics and Sciences of the University of San Jose- Recoletos. She obtained her Bachelor of Science in Biology from the University of the Philippines Tacloban College. She earned academic units in Master of Science in Wildlife Studies at the University of the Philippines at Los Banos. She finished her Master of Arts in Education major in Science and Technology from the University of the Visayas through the Expanded Tertiary Education Equivalency and Accreditation Program. Her research interest focuses on microbiology and wildlife conservation. She has attended several training seminars and workshops on science education, instructional materials development and research trends. She is a member of several scientific organizations and has participated in training courses and conferences.

Joyce C. Unabia, University of San Jose-Recoletos

obtained her Bachelor of Science in Chemistry and Bachelor of Science in Secondary Education major in Chemistry at the Ateneo de Davao University as CHED scholar. She completed her Master of Arts in Education major in Chemistry from the University of San Jose-Recoletos (USJ-R), Cebu City. Currently she is a full-time science teacher of the Department of Mathematics and Sciences at USJ-R. Ms. Unabia’s research interests are in Biochemistry and Chemistry education. She also has attended several trainings, seminars and forums on science education.

References

Books

Baltazar, C. R. (1991). An inventory of Philippine Insects II. Order Lepidoptera (Rhopalocera). -399 pp., Los Banos, Philippines (College of Agriculture, University of the Philippines.)

Briggs, J. & Peat, D. F. (1989). Turbulent Mirror. New York: Harper & Row, Publishers, Inc.

Corbet, A. S. & Pendlebury, H.M. (1992). The Butterflies of the Malay Peninsula. Kuala Lumpur. United Selangor Press Sdn. Bhd.

Smart, P. (1976). Encyclopedia of the Butterfly World. Hamlyn Publishing Group Ltd.

Tsukada, E., (1980). Butterflies of the South East Asian Islands, I, Papilionidae.-51, 91, 230-231 pp., 277 incl. 27, 63 pls., Plapac, Japan.

Tsukada, E., (1981). Butterflies of the South East Asian Islands, II, Pieridae. Danaidae.-47-49, 153-157, 262-264, 518-520 pp., incl. 15-17, 113-117 pls., Plapac, Japan.

Tsukada, E., (1985). Butterflies of the South East Asian Islands, IV. Nymphalidae (I).-75, 292 pp., incl. 43 pls., Plapac, Japan.

Journal

Borres, M. (2013). From Fractal Geometry to Statistical Fractal.

Lapinig, V. T., Almirol, C. C., Sabandal, M. O., Gov. Alfonso D. Tan College, Mindanao University of Science and Technology, Northwestern Mindanao State College, Tangub City (2013), Classification of Mangrove
Species Based on Leaf Fractal Dimensions.

Padua, R.; Palompon, D.; Onton, D. (2012). Data Roughness and Fractal Statistics (CNU Journal of Higher Education Research, CHED-JAS Category A, Vol. 7, no. 2.

Literature Cited

Benson, T. (2013, November). Digital Trends: What is DSLR? It’s the camera that raises you from amateur to advanced hobbyist. Retrieved from http://www.digitaltrends.com/photography/what-is-a-dslr/

Cain, A.J. (2014). A classification of living organisms. Encyclopedia Britannica. Retrieved from http://www.britannica.com/EBchecked/topic/584695/taxonomy/48704/A-classification-of-livingorganisms

Chang, A. (1993, February). Fractals in Biological Systems. Retrieved from http://poignance.coiraweb.com/math/Fractals/FractBio/FractBio.html

Dean, C. R., et al. (2013, May). Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature International weekly journal of Science. Retrieved from http://www.eurekalert.org/pub_releases/2013-05/cu-fdp051313.php

Jeanson, N. T. (2010). New Frontiers in Animal Classification. Retrieved from http://www.icr.org/article/new-frontiers-animal-classification/

Knowlton, N., and J. B. C. Jackson. (1994). New taxonomy and niche partitioning on coral reeds – jack of all trades or master of some. (Trends Ecol. Evol. 9: 7-9)

Kumar, S. (February 2013). Role of Butterflies in the Ecosystem. Retrieved from http://justbefirsttoknow.blogspot.com/2013/02/role-ofbutterflies-in-ecosystem.html

Okubo, P. (2012). Fractal Geometry in the San Andres Fault System. Journal of Geophysical Research: Solid Earth. 92, 345-355. DOI: 10.1029/JB092iB01p00345

Peng, F., Yu, X., Xu, G., and Xia, Q. (2005, NOvember). Fuzzy Classification Based on Fractal Features for Undersea Image. International Journal of Information Technology, Vol. 11. Retrieved from
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.97.6264&rep=rep1&type=pdf

Perfect, E. & Kay, B. D. (1995, November). Applications of fractals in soil and tillage research: a review. Soil and Tillage Research, 36 (1-2), 1-20. Retrieved from http://www.sciencedirect.com/science/article/pii/0167198796813973#

Shashikumar, L. ( 2013, March). Butterflies reflect health of ecosystem. Retrieved from http://www.deccanherald.com/content/316469/butterfliesreflect-health-ecosystem.html

Spatz, J. (2013, December). The geometry of cancer cells. Max-Planck-Gesellschaft. Retrieved from http://www.mpg.de/7647926/cancer_cell_fractal

Williams, A. (2009). How to tell the gender of the butterfly. Retrieved from http://animals.pawnation.com/tell-gender-butterfly-6608.html

Downloads

Published

2014-06-30

How to Cite

Nillama, A. R. P., Borres, M. S., Villeta, R. B., Arco, R. V., & Unabia, J. C. (2014). Validation of Lepidopteran Classification by Morphological Fractal Dimension Analysis. Recoletos Multidisciplinary Research Journal, 2(1). https://doi.org/10.32871/rmrj1402.01.19

Issue

Vol. 2 No. 1 (2014)

Section

Articles

License

Copyright of the Journal belongs to the University of San Jose-Recoletos

Most read articles by the same author(s)

1 2 3 > >>