Classifying organisms and artefacts by their outline shapes (original) (raw)
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The geometric methods for the statistical analysis of biological shape have traditionally been based on landmarks: points of reference in a biological struc-ture that presented a degree of correspondence (or homology) within and across samples. After the morphometric synthesis and the geometric "revolu-tion" in morphometrics, the contours of biological structures were considered unsatisfactory for bio-logical purposes, because the coordinates of points along the outline of an object lack the biological cor-respondence of landmarks. A recent development was the algorithm of spline relaxation or sliding semilandmarks (points of reference along a shape outline without known correspondence within and across samples) that allows one to incorporate out-line information by defining directions (tangents to the outline) along which the contour points can be slid in order to reduce the bending energy crite-rion of the thin plate spline. After filtering out the tangential differences...
Mapping morphological shape as a high-dimensional functional curve
Briefings in bioinformatics, 2017
Detecting how genes regulate biological shape has become a multidisciplinary research interest because of its wide application in many disciplines. Despite its fundamental importance, the challenges of accurately extracting information from an image, statistically modeling the high-dimensional shape and meticulously locating shape quantitative trait loci (QTL) affect the progress of this research. In this article, we propose a novel integrated framework that incorporates shape analysis, statistical curve modeling and genetic mapping to detect significant QTLs regulating variation of biological shape traits. After quantifying morphological shape via a radius centroid contour approach, each shape, as a phenotype, was characterized as a high-dimensional curve, varying as angle θ runs clockwise with the first point starting from angle zero. We then modeled the dynamic trajectories of three mean curves and variation patterns as functions of θ Our framework led to the detection of a few s...
Classifying Organisms and Artefacts By Their Shapes
2021
aDepartment of Mathematics, Brunel University London, Uxbridge, UB8 3PH, UK; bSchool of Humanities, University of Auckland, Auckland 1010, New Zealand; cSchool of Anthropology, University of Arizona, Tucson, AZ 85721-0030, USA; dClassical Art Research Centre, Ioannou Centre for Classical and Byzantine Studies, University of Oxford, Oxford, OX1 3LU, UK; eSchool of Science & Technology, Cape Breton University, Sydney, Nova Scotia, B1P 6L2, Canada; fDepartment of Biological Sciences University of Alberta, Edmonton, Alberta, T6G 2E9, Canada; gDepartment of Earth Sciences, Natural History Museum, London, SW7 5BD, UK; hDepartment of Life Sciences, Imperial College London, London, SW7 2AZ, UK; iSchool of Biological Sciences, University of Auckland, Auckland 1010, New Zealand; jTe Pūnaha Matatini, New Zealand; lSchool of Mathematics and Statistics, Victoria University of Wellington, Wellington 6012, New Zealand
On comparing biological shapes: Detection of influential landmarks
American Journal of Physical Anthropology, 1992
For problems of classification and comparison in biological research, the primary focus is on the similarity of forms. A biological form consists of size and shape. Several approaches for comparing biological forms using landmark data are available. If the two biological forms are demonstrated to be different, the next important issue is to localize the differences by identifying those areas which differ most between the two objects. In this paper we suggest a technique to detect influential landmarks, those which contribute most to the difference between forms. We study the effectiveness of the technique using three-dimensional simulated data sets and two examples. Results suggest that the technique is useful in the study of biological form and its variation.
Shape-changing chains for morphometric analysis of 2D and 3D, open or closed outlines
Scientific Reports, 2021
Morphometrics is a multivariate technique for shape analysis widely employed in biological, medical, and paleoanthropological applications. Commonly used morphometric methods require analyzing a huge amount of variables for problems involving a large number of specimens or complex shapes. Moreover, the analysis results are sometimes difficult to interpret and assess. This paper presents a methodology to synthesize a shape-changing chain for 2D or 3D curve fitting and to employ the chain parameters in stepwise discriminant analysis (DA). The shape-changing chain is comprised of three types of segments, including rigid segments that have fixed length and shape, scalable segments with a fixed shape, and extendible segments with constant curvature and torsion. Three examples are presented, including 2D mandible profiles of fossil hominin, 2D leaf outlines, and 3D suture curves on infant skulls. The results demonstrate that the shape-changing chain has several advantages over common morphometric methods. Specifically, it can be applied to a wide range of 2D or 3D profiles, including open or closed curves, and smooth or serrated curves. Additionally, the segmentation of profiles is a flexible and automatic protocol that can consider both biological and geometric features, the number of variables obtained from the fitting results for statistical analysis is modest, and the chain parameters that characterize the profiles can have physical meaning. Morphometry is the quantitative analysis of form including shape and size. Morphometric analysis is widely adopted in biology, medical imaging, anthropology, and even fundamental science and engineering applications 1,2. Based on the data being used, current morphometrics can be divided into traditional morphometrics and geometric morphometrics (GM). "Traditional" morphometric methods use multivariate statistical tools to analyze a small number of variables such as length measures and angles that characterize the overall form 3. There are several difficulties for traditional morphometrics, such as determining the most appropriate size normalization method, identifying small changes that cannot be reflected by overall variables, and obtaining a graphical representation of the differences between shapes from the variables. "Geometric morphometrics", including landmark-based methods and outline-based methods, has been the mainstream morphometric approach to study biological shape differences 4-7. Geometric morphometrics can capture the complete geometric information of a morphological structure and retain the information intact throughout the analysis. Landmark-based methods compare the locations of landmarks or semilandmarks, the former of which are a set of anatomically homologous points, while the latter are interpolated points on smooth regions (curves or surfaces) that lack precise landmarks. For landmark-based methods, the biological homology of landmarks is always arguable, not to mention semilandmarks which are merely mathematically homologous. In addition, semilandmarks often requires comparing hundreds and thousands of points to achieve acceptable accuracy, thus data redundancy is also a problem for landmark-based methods 8. Outline-based methods compare coefficients of mathematical functions used to fit points along the contours. Elliptic Fourier analysis (EFA) is one of the most popular approaches in outline-based methods 7,9,10. EFA has several limitations too. First, EFA was not designed to match open curves. Second, it is susceptible to slight interference in the contour 11. For shapes with complex boundaries, EFA requires a large number of harmonics to achieve satisfying fitting accuracy, and thus needs a comparison of numerous coefficients. These coefficients are mathematical variables and don't have
Shape-Based Classification of Partially Observed Curves, With Applications to Anthropology
Frontiers in Applied Mathematics and Statistics, 2021
We consider the problem of classifying curves when they are observed only partially on their parameter domains. We propose computational methods for (i) completion of partially observed curves; (ii) assessment of completion variability through a nonparametric multiple imputation procedure; (iii) development of nearest neighbor classifiers compatible with the completion techniques. Our contributions are founded on exploiting the geometric notion of shape of a curve, defined as those aspects of a curve that remain unchanged under translations, rotations and reparameterizations. Explicit incorporation of shape information into the computational methods plays the dual role of limiting the set of all possible completions of a curve to those with similar shape while simultaneously enabling more efficient use of training data in the classifier through shape-informed neighborhoods. Our methods are then used for taxonomic classification of partially observed curves arising from images of fos...
Paleobiology, 2010
Biometric analyses are useful tools for the study of organisms, their phylogenetic affiliation, and the pattern and rate of their evolution. Various morphometric techniques have been developed to analyze morphological variation, but methodological choices are often made arbitrarily because quantitative comparisons are lacking or inconclusive. Here we address morphometric quantification of taxa with few unambiguously identifiable landmarks (,15), utilizing ornamented and unornamented gastropod shells. Support vector machines were applied to evaluate classification performances of landmark (LMA), elliptic Fourier (EFA), and semi-landmark analysis (SLM). This evaluation is based on the discrimination of between-group differences relative to within-group variation, and thus allows comparing how the techniques treat different types of biological information. The results suggest that EFA performs slightly better than SLM (and certainly LMA) in discerning a priori identified taxa with unornamented shells, but that SLM is significantly superior to other techniques for ornamented shells. Alignment and homology problems may cause the subtle variations in ornamentation to become blurred as noise in EFA, even though EFA is often cited to be able to deal with complex shapes. Performance of LMA depends entirely on how accurately the structure can be covered with landmarks. Guidelines in choosing a morphometric technique in diverse cases are provided.
Statistical Shape Analysis: Clustering, Learning, and Testing
Using a differential-geometric treatment of planar shapes, we present tools for: (i) hierarchical clustering of imaged objects according to the shapes of their boundaries, (ii) learning of probability models from clustered shapes, and (iii) testing of newly observed shapes under competing probability models. Clustering at any level of hierarchy is performed using a mimimum dispersion criterion and a Markov search process. Statistical means of clusters provide shapes to be clustered at the next higher level, thus building a hierarchy of shapes. Using finite-dimensional approximations of spaces tangent to the shape space at sample means, we (implicitly) impose probability models on the shape space; results are illustrated via random sampling and classification (hypothesis testing). Together, hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval. Examples are presented using shapes and images from ETH, Surrey, and AMCOM databases.
Patterns and processes in morphospace: Geometric morphometrics of three dimensional objects
Focusing on geometric morphometrics (GMM), we review methods for acquiring morphometric data from 3D objects (including fossils), algorithms for producing shape variables and morphospaces, the mathematical properties of shape space, especially how they relate to morphogenetic and evolutionary factors, and issues posed by working with fossil objects. We use Raup's shell coiling equations to illustrate the complexity of the relationship between such factors and GMM morphospaces. The complexity of these issues re-emphasize what are arguably the two most important recommendations for GMM studies: (1) always use multivariate methods and all of the morphospace axes in an analysis; and (2) always anticipate the possibility that the factors of interest may have a complex, non-linear relationships with shape.