Landmark-free geometric methods in biological shape analysis

Large deformation diffeomorphic mapping of 3D shape variation reveals two distinct mandible and head capsule morphs in Atta vollenweideri leaf-cutter worker ants

Ants are crucial ecosystem engineers, and their ecological success is facilitated by a division of labour among sterile "workers". In some ant lineages, workers have undergone further morphological differentiation, resulting in differences in body size, shape, or both. Distinguishing between changes in size and shape is not trivial. Traditional approaches based on allometry reduce complex 3D shapes into simple linear, areal, or volume metrics; modern approaches using geometric morphometrics typically rely on landmarks, introducing observer bias and a trade-off between effort and accuracy. Here, we use a landmark-free method based on large deformation diffeomorphic metric mapping (LDDMM) to assess the co-variation of size and 3D shape in the mandibles and head capsules of Atta vollenweideri leaf-cutter ants, a species exhibiting extreme worker size-variation. Body mass varied by more than two orders of magnitude, but a shape atlas created via LDDMM on μ-CT-derived 3D mesh files revealed only two distinct head capsule and mandibles shapes-one for the minims (body mass < 1 mg) and one for all other workers. We discuss the functional significance of the identified 3D shape variation, and its implications for the evolution of extreme polymorphism in Atta.

A landmark-free analysis of the pelvic girdle in Sulawesi ricefishes (Adrianichthyidae): How 2D and 3D geometric morphometrics can complement each other in the analysis of a complex structure

Geometric morphometrics (GM) enable the quantification of morphological variation on various scales. Recent technical advances allow analyzing complex three-dimensional shapes also in cases where landmark-based approaches are not appropriate. Pelvic girdle bones (basipterygia) of Sulawesi ricefishes are 3D structures that challenge traditional morphometrics. We hypothesize that the pelvic girdle of ricefishes experienced sex-biased selection pressures in species where females provide brood care by carrying fertilized eggs supported by elongated pelvic fins ("pelvic brooding"). We test this by comparing pelvic bone shapes of both sexes in species exhibiting pelvic brooding and the more common reproductive strategy "transfer brooding," by using landmark-free 2D and 3D GM, as well as qualitative shape descriptions. Both landmark-free approaches revealed significant interspecific pelvic bone variation in the lateral process, medial facing side of the pelvic bone, and overall external and internal wing shape. Within pelvic brooders, the three analyzed species are clearly distinct, while pelvic bones of the genus Adrianichthys are more similar to transfer brooding Oryzias. Female pelvic brooding Oryzias exhibit prominent, medially pointing tips extending from the internal wing and basipterygial plate that are reduced or absent in conspecific males, Adrianichthys and transfer brooding Oryzias, supporting our hypothesis that selection pressures affecting pelvic girdle shape are sex-biased in Sulawesi ricefishes. Furthermore, both sexes of pelvic brooding Oryzias have overall larger pelvic bones than other investigated ricefishes. Based on these differences, we characterized two reproductive strategy- and sex-dependent pelvic girdle types for Sulawesi ricefishes. Morphological differences between the investigated pelvic brooding genera Adrianichthys and Oryzias provide additional evidence for two independent origins of pelvic brooding. Overall, our findings add to a better understanding on traits related to pelvic brooding in ricefishes and provide a basis for upcoming studies on pelvic girdle function and morphology.

Landmark-free Shape Analysis of the Human Duodenum. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2023;2023:1-4. [PMID: 38083606 DOI: 10.1109/embc40787.2023.10340464] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

The primary function of the duodenum is to undertake chemical digestion by ensuring that the partially digested food received from the stomach is well-mixed with the enzymes and chemicals secreted into it. However, little is known about the anatomical variations in the shape of the duodenum within humans, and thus the effect of duodenum shape on the flow and mixing occurring within the lumen has not been studied. In this work, a methodology for analyzing shape variations in the normal duodenal anatomy has been developed and applied to a publicly available dataset of abdominal CT images. This method does not require the placement of landmarks as it is based on the underlying tubular 'C' shape of the duodenum. The average duodenal length and radius of this dataset (consisting of 34 subjects) were 212.8 ± 38 mm and 10.8 ± 2.5 mm respectively. A Principal Component Analysis (PCA) was conducted on a sample of 34 duodenums after normalizing their lengths and the first five principal components were found to contribute to 82 % of the total variation. The first shape component (accounting for 42 % of overall variation) consisted of variations in the radius along the duodenum with no deformations normal to the central plane, and the subsequent shape modes consisted of twists in the centerline either in and out of the central plane, and radial variations at either the inlet or outlet. This is the first study to analyze shape variations in the human duodenum and the results can be combined with flow modeling to analyze the effect of shape on the flow and mixing occurring within the duodenum.Clinical relevance- The methods developed in this study can be used by clinicians to diagnose abnormalities in an individual's duodenum shape.

Applications of Microct Imaging to Archaeobotanical Research

The potential applications of microCT scanning in the field of archaeobotany are only just beginning to be explored. The imaging technique can extract new archaeobotanical information from existing archaeobotanical collections as well as create new archaeobotanical assemblages within ancient ceramics and other artefact types. The technique could aid in answering archaeobotanical questions about the early histories of some of the world's most important food crops from geographical regions with amongst the poorest rates of archaeobotanical preservation and where ancient plant exploitation remains poorly understood. This paper reviews current uses of microCT imaging in the investigation of archaeobotanical questions, as well as in cognate fields of geosciences, geoarchaeology, botany and palaeobotany. The technique has to date been used in a small number of novel methodological studies to extract internal anatomical morphologies and three-dimensional quantitative data from a range of food crops, which includes sexually-propagated cereals and legumes, and asexually-propagated underground storage organs (USOs). The large three-dimensional, digital datasets produced by microCT scanning have been shown to aid in taxonomic identification of archaeobotanical specimens, as well as robustly assess domestication status. In the future, as scanning technology, computer processing power and data storage capacities continue to improve, the possible applications of microCT scanning to archaeobotanical studies will only increase with the development of machine and deep learning networks enabling the automation of analyses of large archaeobotanical assemblages.

A Comparison of Semilandmarking Approaches in the Analysis of Size and Shape

Often, few landmarks can be reliably identified in analyses of form variation and covariation. Thus, ‘semilandmarking’ algorithms have increasingly been applied to surfaces and curves. However, the locations of semilandmarks depend on the investigator’s choice of algorithm and their density. In consequence, to the extent that different semilandmarking approaches and densities result in different locations of semilandmarks, they can be expected to yield different results concerning patterns of variation and co-variation. The extent of such differences due to methodology is, as yet, unclear and often ignored. In this study, the performance of three landmark-driven semilandmarking approaches is assessed, using two different surface mesh datasets (ape crania and human heads) with different degrees of variation and complexity, by comparing the results of morphometric analyses. These approaches produce different semilandmark locations, which, in turn, lead to differences in statistical results, although the non-rigid semilandmarking approaches are consistent. Morphometric analyses using semilandmarks must be interpreted with due caution, recognising that error is inevitable and that results are approximations. Further work is needed to investigate the effects of using different landmark and semilandmark templates and to understand the limitations and advantages of different semilandmarking approaches.

A Comparison of Semilandmarking Approaches in the Visualisation of Shape Differences

In landmark-based analyses of size and shape variation and covariation among biological structures, regions lacking clearly identifiable homologous landmarks are commonly described by semilandmarks. Different algorithms may be used to apply semilandmarks, but little is known about the consequences of analytical results. Here, we assess how different approaches and semilandmarking densities affect the estimates and visualisations of mean and allometrically scaled surfaces. The performance of three landmark-driven semilandmarking approaches is assessed using two different surface mesh datasets with different degrees of variation and complexity: adult human head and ape cranial surfaces. Surfaces fitted to estimates of the mean and allometrically scaled landmark and semilandmark configurations arising from geometric morphometric analyses of these datasets are compared between semilandmarking approaches and different densities, as well as with those from warping to landmarks alone. We find that estimates of surface mesh shape (i.e., after re-semilandmarking and then re-warping) made with varying numbers of semilandmarks are generally consistent, while the warping of surfaces using landmarks alone yields surfaces that can be quite different to those based on semilandmarks, depending on landmark coverage and choice of template surface for warping. The extent to which these differences are important depends on the particular study context and aims.

Thirty years of geometric morphometrics: Achievements, challenges, and the ongoing quest for biological meaningfulness

The foundations of geometric morphometrics were worked out about 30 years ago and have continually been refined and extended. What has remained as a central thrust and source of debate in the morphometrics community is the shared goal of meaningful biological inference through a tight connection between biological theory, measurement, multivariate biostatistics, and geometry. Here we review the building blocks of modern geometric morphometrics: the representation of organismal geometry by landmarks and semilandmarks, the computation of shape or form variables via superimposition, the visualization of statistical results as actual shapes or forms, the decomposition of shape variation into symmetric and asymmetric components and into different spatial scales, the interpretation of various geometries in shape or form space, and models of the association between shape or form and other variables, such as environmental, genetic, or behavioral data. We focus on recent developments and current methodological challenges, especially those arising from the increasing number of landmarks and semilandmarks, and emphasize the importance of thorough exploratory multivariate analyses rather than single scalar summary statistics. We outline promising directions for further research and for the evaluation of new developments, such as "landmark-free" approaches. To illustrate these methods, we analyze three-dimensional human face shape based on data from the Avon Longitudinal Study of Parents and Children (ALSPAC).

μMatch: 3D Shape Correspondence for Biological Image Data

Modern microscopy technologies allow imaging biological objects in 3D over a wide range of spatial and temporal scales, opening the way for a quantitative assessment of morphology. However, establishing a correspondence between objects to be compared, a first necessary step of most shape analysis workflows, remains challenging for soft-tissue objects without striking features allowing them to be landmarked. To address this issue, we introduce the μMatch 3D shape correspondence pipeline. μMatch implements a state-of-the-art correspondence algorithm initially developed for computer graphics and packages it in a streamlined pipeline including tools to carry out all steps from input data pre-processing to classical shape analysis routines. Importantly, μMatch does not require any landmarks on the object surface and establishes correspondence in a fully automated manner. Our open-source method is implemented in Python and can be used to process collections of objects described as triangular meshes. We quantitatively assess the validity of μMatch relying on a well-known benchmark dataset and further demonstrate its reliability by reproducing published results previously obtained through manual landmarking.

Variation in Middle Stone Age mandibular molar enamel-dentine junction topography at Klasies River Main Site assessed by diffeomorphic surface matching

The morphology and variability of the Middle Stone Age (MSA) hominin fossils from Klasies River Main Site have been the focus of investigation for more than four decades. The mandibular remains have figured prominently in discussions relating to robusticity, size dimorphism, and symphyseal morphology. Variation in corpus size between the robust SAM-AP 6223 and the diminutive SAM-AP 6225 mandibles is particularly impressive, and the difference between the buccolingual diameters of their M₂s significantly exceeds recent human sample variation. SAM-AP 6223 and SAM-AP 6225 are the only Klasies specimens with homologous teeth (M₂ and M₃) that permit comparisons of crown morphology. While the differences in dental trait expression at the outer enamel surfaces of these molars are slight, diffeomorphic surface analyses of their underlying enamel-dentine junction (EDJ) topographies reveal differences that are well beyond the means of pairwise differences among comparative samples of Later Stone Age (LSA) Khoesan and recent African homologues. The EDJs of both SAM-AP 6225 molars and the SAM-AP 6223 M₃ fall outside the envelopes that define the morphospace of these two samples. Although the radiocarbon dated LSA individuals examined here differ by a maximum of some 7000 years, and the two Klasies jaws may differ by perhaps as much as 18,000 years, it is difficult to ascribe their differences to time alone. With reference to the morphoscopic traits by which the SAM-AP 6223 and SAM-AP 6225 EDJs differ, the most striking is the expression of the protoconid cingulum. This is very weakly developed on the SAM-AP 6223 molars and distinct in SAM-AP 6225. As such, this diminutive fossil exhibits a more pronounced manifestation of what is likely a plesiomorphic feature, thus adding to the morphological mosaicism that is evident in the Klasies hominin assemblage. Several possible explanations for the variation and mosaicism in this MSA sample are discussed.

Unveiling the third dimension in morphometry with automated quantitative volumetric computations

As computed tomography and related technologies have become mainstream tools across a broad range of scientific applications, each new generation of instrumentation produces larger volumes of more-complex 3D data. Lagging behind are step-wise improvements in computational methods to rapidly analyze these new large, complex datasets. Here we describe novel computational methods to capture and quantify volumetric information, and to efficiently characterize and compare shape volumes. It is based on innovative theoretical and computational reformulation of volumetric computing. It consists of two theoretical constructs and their numerical implementation: the spherical wave decomposition (SWD), that provides fast, accurate automated characterization of shapes embedded within complex 3D datasets; and symplectomorphic registration with phase space regularization by entropy spectrum pathways (SYMREG), that is a non-linear volumetric registration method that allows homologous structures to be correctly warped to each other or a common template for comparison. Together, these constitute the Shape Analysis for Phenomics from Imaging Data (SAPID) method. We demonstrate its ability to automatically provide rapid quantitative segmentation and characterization of single unique datasets, and both inter-and intra-specific comparative analyses. We go beyond pairwise comparisons and analyze collections of samples from 3D data repositories, highlighting the magnified potential our method has when applied to data collections. We discuss the potential of SAPID in the broader context of generating normative morphologies required for meaningfully quantifying and comparing variations in complex 3D anatomical structures and systems.

Shape Changing Robots: Bioinspiration, Simulation, and Physical Realization

One of the key differentiators between biological and artificial systems is the dynamic plasticity of living tissues, enabling adaptation to different environmental conditions, tasks, or damage by reconfiguring physical structure and behavioral control policies. Lack of dynamic plasticity is a significant limitation for artificial systems that must robustly operate in the natural world. Recently, researchers have begun to leverage insights from regenerating and metamorphosing organisms, designing robots capable of editing their own structure to more efficiently perform tasks under changing demands and creating new algorithms to control these changing anatomies. Here, an overview of the literature related to robots that change shape to enhance and expand their functionality is presented. Related grand challenges, including shape sensing, finding, and changing, which rely on innovations in multifunctional materials, distributed actuation and sensing, and somatic control to enable next-generation shape changing robots are also discussed.

Estimating Phylogenies from Shape and Similar Multidimensional Data: Why It Is Not Reliable

In recent years, there has been controversy whether multidimensional data such as geometric morphometric data or information on gene expression can be used for estimating phylogenies. This study uses simulations of evolution in multidimensional phenotype spaces to address this question and to identify specific factors that are important for answering it. Most of the simulations use phylogenies with four taxa, so that there are just three possible unrooted trees and the effect of different combinations of branch lengths can be studied systematically. In a comparison of methods, squared-change parsimony performed similarly well as maximum likelihood, and both methods outperformed Wagner and Euclidean parsimony, neighbor-joining and UPGMA. Under an evolutionary model of isotropic Brownian motion, phylogeny can be estimated reliably if dimensionality is high, even with relatively unfavorable combinations of branch lengths. By contrast, if there is phenotypic integration such that most variation is concentrated in one or a few dimensions, the reliability of phylogenetic estimates is severely reduced. Evolutionary models with stabilizing selection also produce highly unreliable estimates, which are little better than picking a phylogenetic tree at random. To examine how these results apply to phylogenies with more than four taxa, we conducted further simulations with up to eight taxa, which indicated that the effects of dimensionality and phenotypic integration extend to more than four taxa, and that convergence among internal nodes may produce additional complications specifically for greater numbers of taxa. Overall, the simulations suggest that multidimensional data, under evolutionary models that are plausible for biological data, do not produce reliable estimates of phylogeny. [Brownian motion; gene expression data; geometric morphometrics; morphological integration; squared-change parsimony; phylogeny; shape; stabilizing selection.].

Computational geometric tools for quantitative comparison of locomotory behavior

A fundamental challenge for behavioral neuroscientists is to accurately quantify (dis)similarities in animal behavior without excluding inherent variability present between individuals. We explored two new applications of curve and shape alignment techniques to address this issue. As a proof-of-concept we applied these methods to compare normal or alarmed behavior in pairs of medaka (Oryzias latipes). The curve alignment method we call Behavioral Distortion Distance (BDD) revealed that alarmed fish display less predictable swimming over time, even if individuals incorporate the same action patterns like immobility, sudden changes in swimming trajectory, or changing their position in the water column. The Conformal Spatiotemporal Distance (CSD) technique on the other hand revealed that, in spite of the unpredictability, alarmed individuals exhibit lower variability in overall swim patterns, possibly accounting for the widely held notion of “stereotypy” in alarm responses. More generally, we propose that these new applications of established computational geometric techniques are useful in combination to represent, compare, and quantify complex behaviors consisting of common action patterns that differ in duration, sequence, or frequency.

Efficacy of diffeomorphic surface matching and 3D geometric morphometrics for taxonomic discrimination of Early Pleistocene hominin mandibular molars

Morphometric assessments of the dentition have played significant roles in hypotheses relating to taxonomic diversity among extinct hominins. In this regard, emphasis has been placed on the statistical appraisal of intraspecific variation to identify morphological criteria that convey maximum discriminatory power. Three-dimensional geometric morphometric (3D GM) approaches that utilize landmarks and semi-landmarks to quantify shape variation have enjoyed increasingly popular use over the past twenty-five years in assessments of the outer enamel surface (OES) and enamel-dentine junction (EDJ) of fossil molars. Recently developed diffeomorphic surface matching (DSM) methods that model the deformation between shapes have drastically reduced if not altogether eliminated potential methodological inconsistencies associated with the a priori identification of landmarks and delineation of semi-landmarks. As such, DSM has the potential to better capture the geometric details that describe tooth shape by accounting for both homologous and non-homologous (i.e., discrete) features, and permitting the statistical determination of geometric correspondence. We compare the discriminatory power of 3D GM and DSM in the evaluation of the OES and EDJ of mandibular permanent molars attributed to Australopithecus africanus, Paranthropus robustus and early Homo sp. from the sites of Sterkfontein and Swartkrans. For all three molars, classification and clustering scores demonstrate that DSM performs better at separating the A. africanus and P. robustus samples than does 3D GM. The EDJ provided the best results. P. robustus evinces greater morphological variability than A. africanus. The DSM assessment of the early Homo molar from Swartkrans reveals its distinctiveness from either australopith sample, and the "unknown" specimen from Sterkfontein (Stw 151) is notably more similar to Homo than to A. africanus.

Landmark Typology in Applied Morphometrics Studies: What's the Point?

Landmarks are the hallmark of biological shape analysis as discrete anatomical points of correspondence. Various systems have been developed for their classification. In the most widely used system, developed by Bookstein in the 1990s, landmarks are divided into three distinct types based on their anatomical locations and biological significance. As Bookstein and others have argued that different landmark types possess different qualities, e.g., that Type 3 landmarks contain deficient information about shape variation and are less reliably measured, researchers began using landmark types as justification for selecting or avoiding particular landmarks for measurement or analysis. Here, we demonstrate considerable variation in landmark classifications among 17 studies using geometric morphometrics (GM), due to disagreement in the application of both Bookstein's landmark typology and individual landmark definitions. A review of the literature furthermore shows little correlation between landmark type and measurement reproducibility, especially when factors such as differences in measurement tools (calipers, digitizer, or computer software) and data sources (dry crania, 3D models, or 2D images) are considered. Although landmark typology is valuable when teaching biological shape analysis, we find that employing it in research design introduces confusion without providing useful information. Instead, researchers should choose landmark configurations based on their ability to test specific research hypotheses, and research papers should include justifications of landmark choices along with landmark definitions, details on landmark collection methods, and appropriate interobserver and intraobserver analyses. Hence, while the landmarks themselves are crucial for GM, we argue that their typology is of little use in applied studies. Anat Rec, 302:1144-1153, 2019. © 2018 Wiley Periodicals, Inc.

Development and Assessment of Fully Automated and Globally Transitive Geometric Morphometric Methods, With Application to a Biological Comparative Dataset With High Interspecific Variation

Automated geometric morphometric methods are promising tools for shape analysis in comparative biology, improving researchers' abilities to quantify variation extensively (by permitting more specimens to be analyzed) and intensively (by characterizing shapes with greater fidelity). Although use of these methods has increased, published automated methods have some notable limitations: pairwise correspondences are frequently inaccurate and pairwise mappings are not globally consistent (i.e., they lack transitivity across the full sample). Here, we reassess the accuracy of published automated methods-cPDist (Boyer et al. Proc Nat Acad Sci 108 () 18221-18226) and auto3Dgm (Boyer et al.: Anat Rec 298 () 249-276)-and evaluate several modifications to these methods. We show that a substantial percentage of alignments and pairwise maps between specimens of dissimilar geometries were inaccurate in the study of Boyer et al. (Proc Nat Acad Sci 108 () 18221-18226), despite a taxonomically partitioned variance structure of continuous Procrustes distances. We show these inaccuracies are remedied using a globally informed methodology within a collection of shapes, rather than relying on pairwise comparisons (c.f. Boyer et al.: Anat Rec 298 () 249-276). Unfortunately, while global information generally enhances maps between dissimilar objects, it can degrade the quality of correspondences between similar objects due to the accumulation of numerical error. We explore a number of approaches to mitigate this degradation, quantify their performance, and compare the generated pairwise maps (and the shape space characterized by these maps) to a "ground truth" obtained from landmarks manually collected by geometric morphometricians. Novel methods both improve the quality of the pairwise correspondences relative to cPDist and achieve a taxonomic distinctiveness comparable to auto3Dgm. Anat Rec, 301:636-658, 2018. © 2017 Wiley Periodicals, Inc.

Minimum action principle and shape dynamics

In this paper, we propose a new method for computing a distance between two shapes embedded in three-dimensional space. Instead of comparing directly the geometric properties of the two shapes, we measure the cost of deforming one of the two shapes into the other. The deformation is computed as the geodesic between the two shapes in the space of shapes. The geodesic is found as a minimizer of the Onsager-Machlup action, based on an elastic energy for shapes that we define. Its length is set to be the integral of the action along that path; it defines an intrinsic quasi-metric on the space of shapes. We illustrate applications of our method to geometric morphometrics using three datasets representing bones and teeth of primates. Experiments on these datasets show that the variational quasi-metric we have introduced performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers.