A data-driven classification of 3D foot types by archetypal shapes based on landmarks

The taxonomy of foot shapes or other parts of the body is important, especially for design purposes. We propose a methodology based on archetypoid analysis (ADA) that overcomes the weaknesses of previous methodologies used to establish typologies. ADA is an objective, data-driven methodology that seeks extreme patterns, the archetypal profiles in the data. ADA also explains the data as percentages of the archetypal patterns, which makes this technique understandable and accessible even for non-experts. Clustering techniques are usually considered for establishing taxonomies, but we will show that finding the purest or most extreme patterns is more appropriate than using the central points returned by clustering techniques. We apply the methodology to an anthropometric database of 775 3D right foot scans representing the Spanish adult female and male population for footwear design. Each foot is described by a 5626 × 3 configuration matrix of landmarks. No multivariate features are used for establishing the taxonomy, but all the information gathered from the 3D scanning is employed. We use ADA for shapes described by landmarks. Women’s and men’s feet are analyzed separately. We have analyzed 3 archetypal feet for both men and women. These archetypal feet could not have been recovered using multivariate techniques.

[1]  K. Boudolos,et al.  A footprint-based approach for the rational classification of foot types in young schoolchildren , 2006 .

[2]  Myung Hwan Yun,et al.  An anthropometric survey of Korean hand and hand shape types , 2016 .

[3]  Giancarlo Ragozini,et al.  Interval Archetypes: A New Tool for Interval Data Analysis , 2012, Stat. Anal. Data Min..

[4]  Hylton B. Menz,et al.  Foot shape of older people: implications for shoe design , 2010 .

[5]  Jeffrey A. Hudson,et al.  A Multivariate Anthropometric Method for Crew Station Design: Abridged , 1993 .

[6]  Elisabetta Marini,et al.  Somatotype in Alzheimer’s Disease , 2007, Gerontology.

[7]  T. Okura,et al.  Gender differences of foot characteristics in older Japanese adults using a 3D foot scanner , 2015, Journal of Foot and Ankle Research.

[8]  William F. Moroney,et al.  Empirical Reduction in Potential User Population as the Result of Imposed Multivariate Anthropometric Limits. , 1972 .

[9]  Enrica Fubini,et al.  INTERNATIONAL STANDARD ISO/TR 7250-2:“Basic human body measurements for technological design — Part 2: Statistical summaries of body measurements from national populations” , 2010 .

[10]  Sandra Alemany,et al.  Archetypoids: A new approach to define representative archetypal data , 2015, Comput. Stat. Data Anal..

[11]  Eric Horvitz,et al.  Clustering for set partitioning with a case study in ridesharing , 2016, 2016 IEEE 19th International Conference on Intelligent Transportation Systems (ITSC).

[12]  F. James Rohlf,et al.  Efficacy of diffeomorphic surface matching and 3D geometric morphometrics for taxonomic discrimination of Early Pleistocene hominin mandibular molars. , 2019, Journal of human evolution.

[13]  Amelia Simó,et al.  Archetypal shapes based on landmarks and extension to handle missing data , 2018, Adv. Data Anal. Classif..

[14]  Guillermo Vinué,et al.  Anthropometry: An R Package for Analysis of Anthropometric Data , 2017 .

[15]  Tyler Davis,et al.  Memory for Category Information Is Idealized Through Contrast With Competing Options , 2010, Psychological science.

[16]  Todd A. Hare,et al.  A Common Mechanism Underlying Food Choice and Social Decisions , 2015, PLoS Comput. Biol..

[17]  Gregory F. Zehner,et al.  The USAF Multivariate Accommodation Method , 1998 .

[18]  Ulf Brefeld,et al.  Frame-based Data Factorizations , 2017, ICML.

[19]  Sushma Jaswal,et al.  Anthropometric Assessment of Nutritional Status of Primary School Girls (6-8 years) from Punjab , 2001 .

[20]  Zoran Popovic,et al.  The space of human body shapes: reconstruction and parameterization from range scans , 2003, ACM Trans. Graph..

[21]  Simon Jobson,et al.  The influence of somatotype on anaerobic performance , 2018, PloS one.

[22]  Irene Epifanio,et al.  Detection of Anomalies in Water Networks by Functional Data Analysis , 2018, Mathematical Problems in Engineering.

[23]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[24]  P. Cavanagh,et al.  Gender differences in adult foot shape: implications for shoe design. , 2001, Medicine and science in sports and exercise.

[25]  Peter Ahnert,et al.  Novel Anthropometry Based on 3D-Bodyscans Applied to a Large Population Based Cohort , 2016, PloS one.

[26]  M Mochimaru,et al.  Analysis of 3-D human foot forms using the Free Form Deformation method and its application in grading shoe lasts , 2000, Ergonomics.

[27]  Lefteris Angelis,et al.  A novel single-trial methodology for studying brain response variability based on archetypal analysis , 2015, Expert Syst. Appl..

[28]  Valery Naranjo,et al.  Automatic classification of human facial features based on their appearance , 2019, PloS one.

[29]  Zaïd Harchaoui,et al.  Fast and Robust Archetypal Analysis for Representation Learning , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[30]  C. Ji An Archetypal Analysis on , 2005 .

[31]  Youlian Hong,et al.  Gender differences in foot shape: a study of Chinese young adults , 2011, Sports biomechanics.

[32]  T. Horstmann,et al.  Sex-related differences in foot shape of adult Caucasians – a follow-up study focusing on long and short feet , 2011, Ergonomics.

[33]  Giancarlo Ragozini,et al.  On the use of archetypes as benchmarks , 2008 .

[34]  F. Palumbo,et al.  Archetypal analysis for data‐driven prototype identification , 2017, Stat. Anal. Data Min..

[35]  I. Epifanio,et al.  Forecasting basketball players' performance using sparse functional data , 2019, Stat. Anal. Data Min..

[36]  CurlessBrian,et al.  The space of human body shapes , 2003 .

[37]  Norman MacLeod The Direct Analysis of Digital Images (Eigenimage) with a Comment on the Use of Discriminant Analysis in Morphometrics , 2015 .

[38]  Robert A. Walker,et al.  Anthropometric Survey of U.S. Army Personnel: Summary Statistics, Interim Report for 1988 , 1989 .

[39]  C. Maiwald,et al.  Sex-related differences in foot shape , 2008, Ergonomics.

[40]  Pasquale Poppa,et al.  A new atlas for the evaluation of facial features: advantages, limits, and applicability , 2011, International Journal of Legal Medicine.

[41]  Yu-Chi Lee,et al.  Taiwanese adult foot shape classification using 3D scanning data , 2015, Ergonomics.

[42]  Ameersing Luximon Handbook of footwear design and manufacture , 2013 .

[43]  Irene Epifanio,et al.  Robust multivariate and functional archetypal analysis with application to financial time series analysis , 2018, Physica A: Statistical Mechanics and its Applications.

[44]  Morten Mørup,et al.  Archetypal analysis of diverse Pseudomonas aeruginosa transcriptomes reveals adaptation in cystic fibrosis airways , 2013, BMC Bioinformatics.

[45]  Arzu Vuruskan,et al.  Identification of female body shapes based on numerical evaluations , 2011 .

[46]  Ya-Lih Lin,et al.  Investigation of anthropometry basis grouping technique for subject classification , 1999 .

[47]  Ravindra S. Goonetilleke,et al.  Model based foot shape classification using 2D foot outlines , 2012, Comput. Aided Des..

[48]  Anuj Srivastava,et al.  Statistical Shape Analysis , 2014, Computer Vision, A Reference Guide.

[49]  Francesco Amenta,et al.  Gender and age related differences in foot morphology. , 2014, Maturitas.

[50]  Lars Kai Hansen,et al.  Archetypal analysis for machine learning , 2010, 2010 IEEE International Workshop on Machine Learning for Signal Processing.

[51]  Manuel J. A. Eugster,et al.  Performance Profiles based on Archetypal Athletes , 2012 .

[52]  Kathleen M. Robinette,et al.  User's Guide to the Anthropometric Database at the Computerized Anthropometric Research and Design (CARD) Laboratory. Second Edition , 1992 .

[53]  M Koleva,et al.  Somatotype and Disease Prevalence in Adults , 2002, Reviews on environmental health.

[54]  Toralf Kirsten,et al.  Body typing of children and adolescents using 3D-body scanning , 2017, PloS one.

[55]  Gang Yang,et al.  A Probabilistic Weighted Archetypal Analysis Method with Earth Mover's Distance for Endmember Extraction from Hyperspectral Imagery , 2017, Remote. Sens..

[56]  Irene Epifanio,et al.  Archetypoid analysis for sports analytics , 2017, Data Mining and Knowledge Discovery.

[57]  Camila Aguirre,et al.  Correction: The ArcAB two-component regulatory system promotes resistance to reactive oxygen species and systemic infection by Salmonella Typhimurium , 2019, PloS one.

[58]  Mariusz Ozimek,et al.  Somatotype, body composition, and physical fitness in artistic gymnasts depending on age and preferred event , 2019, PloS one.

[59]  Kathleen M. Robinette,et al.  An Alternative to Percentile Models , 1981 .

[60]  Ravindra S. Goonetilleke,et al.  The science of footwear , 2012 .

[61]  George P Nassis,et al.  Somatotype, size and body composition of competitive female volleyball players. , 2008, Journal of science and medicine in sport.

[62]  S. P. Singh,et al.  Somatotype and Disease – A Review , 2007 .

[63]  Amelia Simó,et al.  Archetypal Analysis With Missing Data: See All Samples by Looking at a Few Based on Extreme Profiles , 2020, The American Statistician.

[64]  Sandra Alemany,et al.  Archetypal analysis: Contributions for estimating boundary cases in multivariate accommodation problem , 2013, Comput. Ind. Eng..

[65]  Jorgen A Wullems,et al.  Reliability and validity of the international physical activity questionnaire compared to calibrated accelerometer cut-off points in the quantification of sedentary behaviour and physical activity in older adults , 2018, PloS one.

[66]  Beatriz Nacher,et al.  Anthropometric Survey of the Spanish Female Population Aimed at the Apparel Industry , 2010 .

[67]  L. Alegre,et al.  Foot morphology in Spanish school children according to sex and age , 2014, Ergonomics.

[68]  Irene Epifanio,et al.  ARCHETYPAL ANALYSIS: AN ALTERNATIVE TO CLUSTERING FOR UNSUPERVISED TEXTURE SEGMENTATION , 2019, Image Analysis & Stereology.

[69]  Bruce Bradtmiller,et al.  3D Head Models for Protective Helmet Development , 2003 .

[70]  Silvestar Sesnic,et al.  Stochastic Collocation Applications in Computational Electromagnetics , 2018 .

[71]  C McCollin Applied stochastic models in business and industry , 2011 .

[72]  Yuval Hart,et al.  Geometry of the Gene Expression Space of Individual Cells , 2015, PLoS Comput. Biol..

[73]  Andrea Cardini,et al.  Leaf Morphology, Taxonomy and Geometric Morphometrics: A Simplified Protocol for Beginners , 2011, PloS one.

[74]  Masaaki Mochimaru,et al.  Errors in landmarking and the evaluation of the accuracy of traditional and 3D anthropometry. , 2011, Applied ergonomics.

[75]  Igor Kononenko,et al.  Weighted archetypal analysis of the multi-element graph for query-focused multi-document summarization , 2014, Expert Syst. Appl..

[76]  Irene Epifanio,et al.  Functional archetype and archetypoid analysis , 2016, Comput. Stat. Data Anal..

[77]  Christian Burkhardt,et al.  Quality Control of Motor Unit Number Index (MUNIX) Measurements in 6 Muscles in a Single-Subject “Round-Robin” Setup , 2016, PloS one.

[78]  Elizabeth K Bye,et al.  An analysis of apparel industry fit sessions , 2005 .

[79]  Wol-Hee Do,et al.  Classification of Elderly Women's Foot Type , 2014 .

[80]  Theekapun Charoenpong,et al.  Face shape classification from 3D human data by using SVM , 2014, The 7th 2014 Biomedical Engineering International Conference.

[81]  Weiwei Sun,et al.  Pure endmember extraction using robust kernel archetypoid analysis for hyperspectral imagery , 2017 .

[82]  Morten Mørup,et al.  Archetypal Analysis for Modeling Multisubject fMRI Data , 2016, IEEE Journal of Selected Topics in Signal Processing.

[83]  Georgina Charlesworth,et al.  Core outcome measures for interventions to prevent or slow the progress of dementia for people living with mild to moderate dementia: Systematic review and consensus recommendations , 2017, PloS one.

[84]  Martin Friess Multivariate Accommodation Models using Traditional and 3D Anthropometry , 2005 .