An Invariant Approach to Statistical Analysis of Shapes

Lele, Subhash R.; Richtsmeier, Joan T.

doi:10.1201/9781420036176

Cited by 236 publications

(299 citation statements)

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“…We used Euclidean distance matrix analysis (EDMA, a three-dimensional morphometric method) (Richtsmeier and Lele, 1993;Lele and Richtsmeier, 1995;Lele and Cole, 1996;Richtsmeier et al, 1998;Lele and Richtsmeier, 2001) to test for differences in facial shape and growth patterns among the five species. EDMA is a coordinate-system invariant method (Lele and Richtsmeier, 2001) for comparing form, shape, or growth difference between two samples, which uses landmark coordinates as raw data and describes a three-dimensional object by the matrix of Euclidean distances between all possible unique landmark pairs.…”

Section: Morphometric Analysis Of Shape and Growth Similaritymentioning

confidence: 99%

“…EDMA is a coordinate-system invariant method (Lele and Richtsmeier, 2001) for comparing form, shape, or growth difference between two samples, which uses landmark coordinates as raw data and describes a three-dimensional object by the matrix of Euclidean distances between all possible unique landmark pairs. This matrix of distances is called the form matrix (FM).…”

Section: Morphometric Analysis Of Shape and Growth Similaritymentioning

confidence: 99%

“…This matrix of distances is called the form matrix (FM). The form matrix [or FM(A) for object A] is an equivalent representation of the landmark coordinate data that is invariant to the nuisance parameters of translation, rotation, and reflection (Lele and Richtsmeier, 2001).…”

Section: Morphometric Analysis Of Shape and Growth Similaritymentioning

confidence: 99%

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Common patterns of facial ontogeny in the hominid lineage

Ackermann

Krovitz²

2002

Anat. Rec.

102

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Recent evaluation of Neanderthal and modern human ontogeny suggests that taxon-specific features arose very early in development in both lineages, with early, possibly prenatal, morphological divergence followed by parallel postnatal developmental patterns. Here we use morphometric techniques to compare hominoid facial growth patterns, and show that this developmental phenomenon is, in fact, not unique to comparisons between Neanderthals and modern humans but extends to Australopithecus africanus and to the hominoid lineage more broadly. This finding suggests that a common pattern of juvenile facial development may be more widespread and that the roots of ontogenetically early developmental differentiation are deep-perhaps predating the ape/human split of 6؉ million years ago.

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Section: Morphometric Analysis Of Shape and Growth Similaritymentioning

confidence: 99%

Section: Morphometric Analysis Of Shape and Growth Similaritymentioning

confidence: 99%

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Common patterns of facial ontogeny in the hominid lineage

Ackermann

Krovitz²

2002

Anat. Rec.

102

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“…T he goal of Procrustes analysis is to superpose non-identical shapes in an optimal manner via scalings, translations, and rotations (1)(2)(3). Classical Procrustes analysis uses the unweighted least-squares (LS) criterion for finding the optimal transformations.…”

mentioning

confidence: 99%

Empirical Bayes hierarchical models for regularizing maximum likelihood estimation in the matrix Gaussian Procrustes problem

Theobald

Wuttke²

2006

Proc. Natl. Acad. Sci. U.S.A.

104

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Procrustes analysis involves finding the optimal superposition of two or more ''forms'' via rotations, translations, and scalings. Procrustes problems arise in a wide range of scientific disciplines, especially when the geometrical shapes of objects are compared, contrasted, and analyzed. Classically, the optimal transformations are found by minimizing the sum of the squared distances between corresponding points in the forms. Despite its widespread use, the ordinary unweighted least-squares (LS) criterion can give erroneous solutions when the errors have heterogeneous variances (heteroscedasticity) or the errors are correlated, both common occurrences with real data. In contrast, maximum likelihood (ML) estimation can provide accurate and consistent statistical estimates in the presence of both heteroscedasticity and correlation. Here we provide a complete solution to the nonisotropic ML Procrustes problem assuming a matrix Gaussian distribution with factored covariances. Our analysis generalizes, simplifies, and extends results from previous discussions of the ML Procrustes problem. An iterative algorithm is presented for the simultaneous, numerical determination of the ML solutions.heteroscedasticity ͉ morphometrics ͉ Procrustes analysis ͉ superpositions ͉ least-squares T he goal of Procrustes analysis is to superpose non-identical shapes in an optimal manner via scalings, translations, and rotations (1-3). Classical Procrustes analysis uses the unweighted least-squares (LS) criterion for finding the optimal transformations. LS implicitly assumes that the landmarks describing the forms' shapes are uncorrelated and that they have identical variances (i.e., that they are homoscedastic). However, in many practical applications these assumptions are known to be violated. For instance, when superpositioning macromolecular proteins, individual atoms (the landmarks) are connected via covalent chemical bonds, and thus the variance of a given atom can be correlated with the variance of atoms to which it is connected. Furthermore, certain atoms may have larger mobilities than others, or they may have spatial positions with relatively greater uncertainty due to experimental error. Similarly, when comparing the skulls from different members of a species, some homologous features may be highly variable relative to others. Hence, different landmarks can have widely different variances. Under these conditions, ordinary LS can give misleading results, even with large samples of data (4).The method of maximum likelihood (ML) is a common alternative to LS and is widely considered to be fundamental for statistical modeling and parameter estimation (5). Given the proper model, ML can provide accurate and robust estimates of parameters in the presence of both heteroscedasticity and correlation. Incorporating heterogeneous variances and non-zero correlations into the ML Procrustes problem involves weighting by two covariance matrices (a landmark and a dimensional covariance matrix). However, estimation of these covariance matrices...

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“…Procrustes superimposition, Euclidean Distance Matrix Analysis) exist for measuring and comparing morphological form (Richtsmeier et al, 2002). The use of landmarks in geometric morphometric research has become widespread because landmarks are repeatable and provide geometric information in terms of the relative location of structure (Bookstein, 1991;Lele & Richtsmeier, 2001). Using ImageJ software 24 landmarks (Table I, Fig. 2) were located and landmark coordinate values were recorded for analysis.…”

Section: Methodsmentioning

confidence: 99%

Quantitative Evaluation of the Facial Morphology of a Tolteca Figurine from Mexico using Geometric Morphometric Approaches

Starbuck¹

2014

Int. J. Morphol.

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SUMMARY:Morphometric approaches can be combined with 2D or 3D imaging to quantitatively evaluate craniofacial medical conditions depicted in material culture and to learn more about the culture being studied. A terra-cotta figurine (circa 500 A.D.) from the Tolteca culture of Mexico has previously been qualitatively "diagnosed" with Down syndrome (DS) based on the presence or absence of facial features typically associated with trisomy 21. The purpose of this research is to quantitatively test the hypothesis that the Tolteca figurine exhibits facial features consistent with DS. Landmarks (n = 24) were acquired from sex-and age-matched (5-20 yrs) facial images of DS individuals (n = 32), euploid individuals (n = 32), and the Tolteca figurine. Landmark coordinates were subjected to geometric morphometric analyses, and the results suggest that the Tolteca figurine displays facial morphology consistent with DS.

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An Invariant Approach to Statistical Analysis of Shapes

Cited by 236 publications

References 3 publications

Common patterns of facial ontogeny in the hominid lineage

Common patterns of facial ontogeny in the hominid lineage

Empirical Bayes hierarchical models for regularizing maximum likelihood estimation in the matrix Gaussian Procrustes problem

Quantitative Evaluation of the Facial Morphology of a Tolteca Figurine from Mexico using Geometric Morphometric Approaches

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