Continuous Procrustes Distance Between Two Surfaces

AbstractAn important topic in bioinformatics is the protein structure alignment. Some statistical methods have been proposed for this problem, but most of them align two protein structures based on the global geometric information without considering the effect of neighbourhood in the structures. In this paper, we provide a Bayesian model to align protein structures, by considering the effect of both local and global geometric information of protein structures. Local geometric information is incorporated to the model through the partial Procrustes distance of small substructures. These substructures are composed of

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Using Procrustes distance and shape space for automatic target recognition

10.1117/12.468018 ◽

2002 ◽

Cited By ~ 1

Author(s):

Gregory J. Meyer ◽

Steven C. Gustafson ◽

Gregory D. Arnold

Keyword(s):

Target Recognition ◽

Shape Space ◽

Automatic Target Recognition ◽

Procrustes Distance

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A Practical Introduction to Landmark-Based Geometric Morphometrics

The Paleontological Society Papers ◽

10.1017/s1089332600001868 ◽

2010 ◽

Vol 16 ◽

pp. 163-188 ◽

Cited By ~ 84

Author(s):

Mark Webster ◽

H. David Sheets

Keyword(s):

Geometric Morphometrics ◽

A Priori ◽

Comparative Morphology ◽

Statistical Testing ◽

Shape Variation ◽

Sample Mean ◽

Procrustes Distance ◽

Powerful Approach ◽

Canonical Variates ◽

Biological Shape

Landmark-based geometric morphometrics is a powerful approach to quantifying biological shape, shape variation, and covariation of shape with other biotic or abiotic variables or factors. The resulting graphical representations of shape differences are visually appealing and intuitive. This paper serves as an introduction to common exploratory and confirmatory techniques in landmark-based geometric morphometrics. The issues most frequently faced by (paleo)biologists conducting studies of comparative morphology are covered. Acquisition of landmark and semilandmark data is discussed. There are several methods for superimposing landmark configurations, differing in how and in the degree to which among-configuration differences in location, scale, and size are removed. Partial Procrustes superimposition is the most widely used superimposition method and forms the basis for many subsequent operations in geometric morphometrics. Shape variation among superimposed configurations can be visualized as a scatter plot of landmark coordinates, as vectors of landmark displacement, as a thin-plate spline deformation grid, or through a principal components analysis of landmark coordinates or warp scores. The amount of difference in shape between two configurations can be quantified as the partial Procrustes distance; and shape variation within a sample can be quantified as the average partial Procrustes distance from the sample mean. Statistical testing of difference in mean shape between samples using warp scores as variables can be achieved through a standard Hotelling's T2 test, MANOVA, or canonical variates analysis (CVA). A nonparametric equivalent to MANOVA or Goodall's F-test can be used in analysis of Procrustes coordinates or Procrustes distance, respectively. CVA can also be used to determine the confidence with which a priori specimen classification is supported by shape data, and to assign unclassified specimens to pre-defined groups (assuming that the specimen actually belongs in one of the pre-defined groups).Examples involving Cambrian olenelloid trilobites are used to illustrate how the various techniques work and their practical application to data. Mathematical details of the techniques are provided as supplemental online material. A guide to conducting the analyses in the free Integrated Morphometrics Package software is provided in the appendix.

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Evolutionary patterns of asymmetric genitalia in the beetle tribe Cyclocephalini (Coleoptera: Scarabaeidae: Dynastinae)

Contributions to Zoology ◽

10.1163/18759866-08202003 ◽

2013 ◽

Vol 82 (2) ◽

pp. 95-106 ◽

Cited By ~ 8

Author(s):

Thijmen Breeschoten ◽

Daniel R. Clark ◽

Menno Schilthuizen

Keyword(s):

Male Genitalia ◽

Ct Scans ◽

Micro Ct ◽

Strong Indication ◽

Terminal Part ◽

Evolutionary Patterns ◽

Procrustes Distance ◽

Asymmetry Analysis ◽

Reproductive Structures ◽

Left Right Asymmetry

The evolution of asymmetric genitalia is a common and recurrent phenomenon in a wide variety of insect taxa. However, little is understood about the evolution of left-right asymmetry in reproductive structures. Since a better knowledge of it could have an important impact on the study of genital evolution, in the present study we investigate the phylogenetic and evolutionary patterns of asymmetric male genitalia in Cyclocephalini. We use a Procrustes distance based method for quantifying asymmetry. Analysis of 119 species belonging to 14 genera revealed a diverse array of asymmetries with a strong indication that asymmetries are more strongly developed in the terminal part of the aedeagus. Further, we find that asymmetries have evolved repeatedly within this small taxon. Micro-CT scans, a technique not employed before in studies of genital asymmetry, are made of several symmetric and asymmetric species. This reveals unexpected asymmetric sclerotised structures inside the otherwise symmetric aedeagus of Cyclocephala amazona, which underlines that asymmetries are not restricted to the exterior of the male genitalia but are also found internally.

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