IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i3d10.1007_s00362-018-0986-0.html
   My bibliography  Save this article

Linear models for statistical shape analysis based on parametrized closed curves

Author

Listed:
  • Luis Gutiérrez

    (Pontificia Universidad Católica de Chile)

  • Ramsés H. Mena

    (Universidad Nacional Autónoma de México)

  • Carlos Díaz-Avalos

    (Universidad Nacional Autónoma de México)

Abstract

We develop a simple, yet powerful, technique based on linear regression models of parametrized closed curves which induces a probability distribution on the planar shape space. Such parametrization is driven by control points which can be estimated from the data. Our proposal is capable to infer about the mean shape, to predict the shape of an object at an unobserved location, and, while doing so, to consider the effect of predictors on the shape. In particular, the model is able to detect possible differences across the levels of the predictor, thus also applicable for two-sample tests. A simple MCMC algorithm for Bayesian inference is also presented and tested with simulated and real datasets. Supplementary material is available online.

Suggested Citation

  • Luis Gutiérrez & Ramsés H. Mena & Carlos Díaz-Avalos, 2020. "Linear models for statistical shape analysis based on parametrized closed curves," Statistical Papers, Springer, vol. 61(3), pages 1213-1229, June.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-018-0986-0
    DOI: 10.1007/s00362-018-0986-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-018-0986-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-018-0986-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. J. Gower, 1975. "Generalized procrustes analysis," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 33-51, March.
    2. Ellingson, Leif & Patrangenaru, Vic & Ruymgaart, Frits, 2013. "Nonparametric estimation of means on Hilbert manifolds and extrinsic analysis of mean shapes of contours," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 317-333.
    3. Vincenzo Viscosi & Andrea Cardini, 2011. "Leaf Morphology, Taxonomy and Geometric Morphometrics: A Simplified Protocol for Beginners," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-20, October.
    4. Kelvin Gu & Debdeep Pati & David B. Dunson, 2014. "Bayesian Multiscale Modeling of Closed Curves in Point Clouds," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1481-1494, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Meyners, Michael & Qannari, El Mostafa, 2001. "Relating principal component analysis on merged data sets to a regression approach," Technical Reports 2001,47, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Juliana Martins Ruzante & Valerie J. Davidson & Julie Caswell & Aamir Fazil & John A. L. Cranfield & Spencer J. Henson & Sven M. Anders & Claudia Schmidt & Jeffrey M. Farber, 2010. "A Multifactorial Risk Prioritization Framework for Foodborne Pathogens," Risk Analysis, John Wiley & Sons, vol. 30(5), pages 724-742, May.
    3. Barbara McGillivray & Gard B. Jenset & Khalid Salama & Donna Schut, 2022. "Investigating patterns of change, stability, and interaction among scientific disciplines using embeddings," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-15, December.
    4. Wei Wang & Stephen J Lycett & Noreen von Cramon-Taubadel & Jennie J H Jin & Christopher J Bae, 2012. "Comparison of Handaxes from Bose Basin (China) and the Western Acheulean Indicates Convergence of Form, Not Cognitive Differences," PLOS ONE, Public Library of Science, vol. 7(4), pages 1-7, April.
    5. Lisa Sakamoto & Hiromi Kajiya-Kanegae & Koji Noshita & Hideki Takanashi & Masaaki Kobayashi & Toru Kudo & Kentaro Yano & Tsuyoshi Tokunaga & Nobuhiro Tsutsumi & Hiroyoshi Iwata, 2019. "Comparison of shape quantification methods for genomic prediction, and genome-wide association study of sorghum seed morphology," PLOS ONE, Public Library of Science, vol. 14(11), pages 1-15, November.
    6. Mardia, Kanti V. & Wiechers, Henrik & Eltzner, Benjamin & Huckemann, Stephan F., 2022. "Principal component analysis and clustering on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Ibrahim, Muhammad Sohail & Dong, Wei & Yang, Qiang, 2020. "Machine learning driven smart electric power systems: Current trends and new perspectives," Applied Energy, Elsevier, vol. 272(C).
    8. John Gower & Garmt Dijksterhuis, 1994. "Multivariate analysis of coffee images: A study in the simultaneous display of multivariate quantitative and qualitative variables for several assessors," Quality & Quantity: International Journal of Methodology, Springer, vol. 28(2), pages 165-184, May.
    9. Modroño Herrán, Juan Ignacio & Fernández Aguirre, María Carmen & Landaluce Calvo, M. Isabel, 2003. "Una propuesta para el análisis de tablas múltiples," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    10. Peter Verboon & Willem Heiser, 1992. "Resistant orthogonal procrustes analysis," Journal of Classification, Springer;The Classification Society, vol. 9(2), pages 237-256, December.
    11. Dahl, Tobias & Naes, Tormod, 2006. "A bridge between Tucker-1 and Carroll's generalized canonical analysis," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3086-3098, July.
    12. Young-Jin Kwon & Do-Hyun Kim & Byung-Chang Son & Kyoung-Ho Choi & Sungbok Kwak & Taehong Kim, 2022. "A Work-Related Musculoskeletal Disorders (WMSDs) Risk-Assessment System Using a Single-View Pose Estimation Model," IJERPH, MDPI, vol. 19(16), pages 1-19, August.
    13. V Alex Sotola & Cody A Craig & Peter J Pfaff & Jeremy D Maikoetter & Noland H Martin & Timothy H Bonner, 2019. "Effect of preservation on fish morphology over time: Implications for morphological studies," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-16, March.
    14. Thomas W. Davies & Philipp Gunz & Fred Spoor & Zeresenay Alemseged & Agness Gidna & Jean-Jacques Hublin & William H. Kimbel & Ottmar Kullmer & William P. Plummer & Clément Zanolli & Matthew M. Skinner, 2024. "Dental morphology in Homo habilis and its implications for the evolution of early Homo," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    15. Huckemann, Stephan & Hotz, Thomas, 2009. "Principal component geodesics for planar shape spaces," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 699-714, April.
    16. Erdem, Seda & Rigby, Dan, 2011. "Using Best Worst Scaling To Investigate Perceptions Of Control & Concern Over Food And Non-Food Risks," 85th Annual Conference, April 18-20, 2011, Warwick University, Coventry, UK 108790, Agricultural Economics Society.
    17. Ian L. Dryden & Jonathan D. Hirst & James L. Melville, 2007. "Statistical Analysis of Unlabeled Point Sets: Comparing Molecules in Chemoinformatics," Biometrics, The International Biometric Society, vol. 63(1), pages 237-251, March.
    18. Edmund Peay, 1988. "Multidimensional rotation and scaling of configurations to optimal agreement," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 199-208, June.
    19. Aleix Alcacer & Irene Epifanio & M Victoria Ibáñez & Amelia Simó & Alfredo Ballester, 2020. "A data-driven classification of 3D foot types by archetypal shapes based on landmarks," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-19, January.
    20. Victor Patrangenaru & Robert Paige & K. David Yao & Mingfei Qiu & David Lester, 2016. "Projective shape analysis of contours and finite 3D configurations from digital camera images," Statistical Papers, Springer, vol. 57(4), pages 1017-1040, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-018-0986-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.