Biological Shape Analysis

The following sections are included:

• PREFACE
• REFERENCES
• CONTENTS
• LIST OF SYMPOSIUM PARTICIPANTS

Of the five senses, hearing, tasting, smelling, touching and seeing; vision is the predominant sense among primates, including humans. Humans rely almost exclusively on sight. It is via the visual system that we interact and make sense of the world around us. With the vision system as a starting point, the focus here will be primarily on three issues: (1) The role that visual perception plays in recognizing the biological form, (2) the function that form plays in biological processes, and (3) models as representations of form. The visual system can be considered as a part of the central nervous system (CNS) and acts as a major influence on other systems such as locomotion. However, more important, is the fact that it allows the brain to interact with the external environment. The human visual system is endowed with special qualities such as binocular vision allowing both eyes to look straight ahead facilitating 3D vision. Moreover, the vision system provides the ability to distinguish between different, often closely related forms, as well as allowing for the tracking of movement. All visual information entering the eyes is focused by the eye lens onto the retina. From the retina, it is transferred along the optic nerve to the visual cortex. The visual cortex lies at the posterior aspect of the brain. Sensory signals of objects are only recognized because similar experiences are stored in the brain as memories. Biological forms as perceived by the visual system are quite complex and attempts to characterize them can be accomplished by using models. Three such models are: (1) physical models, (2) heuristic models, and (3) mathematical models. For purposes here, the emphasis is on mathematical models; that is, to generate a mathematical representation of the biological form. More specifically, the focus here is on shape. Shape is defined as the outline of a biological form. It can be viewed in 2D or 3D terms. A mathematical model termed Computerized Shape Analysis is briefly presented here. It is composed of two aspects. Elliptical Fourier Descriptors (EFFs) to assess the boundary outline of a form and the Continuous wavelet transform (CWT) to extract localized features. This Fourier-wavelet model is intended as a model that generates substantially more of the visual information that is always present in the biological form.

A novel leaf identification system that incorporates shape, color, texture and vein features has been developed. The Polar Fourier Transform (PFT) was used to handle the shapes of leaves and lacunarity was used to describe texture on the leaves. Color was also added to improve the performance of the leaf identification system. To classify a leaf, a linear classifier called Linear Bayes Normal classifier was applied. Several experiments were conducted using the Flavia dataset, a common dataset that contains 32 kinds of green leaves. The Foliage dataset, a dataset that consists of 60 kinds of leaves with various colors and shapes was also utilized. The results show that the system yielded an accuracy rate of 95.94% when using the Flavia dataset and 93.25% when using the Foliage dataset.

Rapid, accurate identification of plant species is urgently needed for surveys of species diversity in the light of the global crisis in biodiversity driven by factors including climate change. Such identification systems are often most effective when they use vegetative parts alone, given the ephemeral nature of plant reproductive organs. This chapter describes a system that can be used as a practical method for identification of botanical herbarium specimens that have been digitized as images and has potential for creating large morphological datasets. The system is composed of an almost completely automated leaf shape extraction component and an artificial neural network, specifically a multilayer perceptron (MLP). First the leaves are found using deformable templates and evolutionary algorithms, and then a level set method is used to separate the leaf outline from the background. The length and width and other shape measurements are then extracted automatically, together with numerous measurements of the marginal teeth. The neural network is then able to identify plants from leaf shape alone. Furthermore, the system is also able to automatically refer specimens to a botanist for expert examination, in cases of uncertainty. Thus a methodology is presented here to provide a practical way for taxonomists to use a combination of neural networks and image processing as a tool for automated plant identification. A case study is provided using data extracted from specimens of four species of the tree genus Tilia in the herbarium of the Royal Botanic Gardens, Kew, UK. Over half the test specimens were identified correctly to species level using 41 automatically extracted leaf shape parameters. The remaining specimens were referred for further botanical study, together with suggestions as to their identity.

Cereal grains are one of the major export agricultural commodities of Canada contributing sizable amounts to its annual GDP. Grain has to pass, a number of quality evaluation steps and grading before it comes to the global market. In the current Canadian grain grading system, grain visual appearance is the main component of a measure of quality. With significant research and advances in machine vision systems (MVS) and computer based grading and sorting the Canadian grain industry is on the verge of adopting an automated procedure for routine cereal grain grading. Most MVSs, however, rely on extracting visual appearance in terms of shape, size and colour features acquired from cereal grain digital images. These features are then used for automatic classification of the cereal grains into pre-determined categories. The challenge of automatic classification lies in the fact that grain kernels are not simple geometries that could be defined by simple mathematical equations and hence their visual features cannot easily be related to their shape features. Members of the Imaging and Spectroscopy Laboratory of the Department of Biosystems Engineering, have been developing various algorithms that extract morphological (shape and size), colour and textural features from grain kernels to characterize their visual appearance. This chapter discusses advances that have been made in computer-based classification algorithms and future prospects in this exciting and challenging research field. In this regard, mathematical techniques including morphological analysis, Fourier descriptors, colour quantification, and textural analysis (gray level run-length matrices and gray level co-occurrence matrices) coupled with non-linear data analysis techniques will be discussed. The chapter concludes with a look at future research that is believed to be essential in machine vision based classification before these systems are adopted across the grain industry worldwide.

The sweet potato weevil, Euscepes postfasciatus is one of a number of serious pests of sweet potato. The species is distributed throughout the Ryukyu Islands of Japan. Although a sterile insect technique (SIT) has been used to eradicate this species since 1994, it is still far from accomplishing the principal goal of eradication. One of the reasons for this delay is that the assumed mating systems including courtship behavior for this weevil is not well understood. In addition, there is also the problem of mass rearing as well. It was discovered that adult mature E. postfasciatus produce sounds when they are disturbed or under mating. Although it is thought that these sounds might play an important role during the weevil's communication, especially for recognizing enemies and for mating success. Thus, fundamental studies on the characteristics of these sounds would be desirable for an understanding of how mating recognition and avoidance of enemies via sound is carried out in this species. Several features were extracted from the distress sound readings of the weevil to determine differences between populations or sexes. Mass-reared lineages of varying rearing periods from six local populations in Ryukyu Islands were used as materials. It was determined that the characteristics of distress sounds were differentiated among different reared lineages. For timedomain features, females tended to produce longer period of echeme than males. In particular, although the slope of the regression between body size and the mean duration of the echeme varied significantly among lineages in males, the regression slopes were almost isotropic throughout localities in females. Such patterns of spatial and sexual variation may suggest the presence of a strong genetic basis that is responsible for the development of the stridulatory apparatus or sound emission system existing in E. postfasciatus.

In an eradication program using the sterile insect technique (SIT), a large number of individuals are mass-reared, sterilized and then released into the field. Since the ratio of sterile to normal males in the field is used to monitor the progress of the program, an extensive masstrapping survey is conducted in the whole target area. Although a definite marker for the released individuals is indispensable in this monitoring procedure, such a definite marker has not been developed for the sweet potato weevil Cylas formicarius. Consequently, the monitoring of the eradication program in this weevil has been hampered by the presence of less accuracy due to using an uncertain marker. Therefore, one needs to develop another marking system. Since the mass-rearing of the beneficial insect is conducted under highly artificial conditions compared to the field, such a condition prior to the emergence in the rearing facility, might lead to differences in morphological characters in the mass-reared individuals. In this study, the shape of the elytral contour between wild and mass-reared weevils was compared to assess the potential of an intraspecific differentiation pattern in C. formicarius. This comparison was conducted in spring and autumn for two successive years (four comparisons in total). The morphometric analysis using elliptic Fourier descriptors (EFDs) demonstrated that the elytral shape of the mass-reared weevil differed significantly to that of wild one in each comparison and the proportion of individuals that were correctly classified into original lineages was high (> 80%). Therefore, the EFDs are considered useful for identifying the source of the trapped weevils in an eradication program using the massreared individuals for the sweet potato weevil. Although the fine-scale intraspecific morphological variation is generally difficult to recognize, the present study suggests that the EFDs have potential to highlight these differences between closely related lineages within the same species.

Cultivars of a crop species sometimes show large infraspecific morphological variability in the organs or parts of a plant of interest to humans. The Genome-wide association study (GWAS) based on elliptic Fourier analysis is suited for the genetic dissection of infraspecific shape variation. In this chapter, a series of analyses are described for GWAS of biological shape based on elliptic Fourier analysis, using rice grain shape data as an example. Genotype data of 3,183 SNPs was used and grain shape data of 77 elliptic Fourier descriptors collected for 179 accessions from a world rice collection. Scores of the first three principal components of elliptic Fourier descriptors were used as grain shape phenotypes. In the rice accession, there was a subpopulation structure, among which the grain shape was differentiated. In GWAS, a Bayesian regression model was employed to estimate subpopulation structure effects and effects of all genome-wide SNPs simultaneously. In the first principal component, which accounted for the length-to-width ratio of the grain, two strong associations were detected on chromosome 3 and 5 at the locations that were close to known grain shape genes, GS3 and qSW5. In the second and third principal components, each of which explained minor (less than 2%) shape variation, relatively strong associations were found at several SNPs. These SNPs may be closely linked to genes controlling grain shape variation. The rice dataset and R scripts used in the analysis described in this chapter are available at .

As a complex trait underlying human health, body shape is believed to be under genetic control. While the traditional description of body shape based on length-width ratios and angles is criticized due to its simplicity, more sophisticated geometric morphometrics has been recently integrated with genetic mapping, leading to the birth of shape mapping, which can precisely capture subtle variation in body shape and its genetic underpinnings. In this chapter, it is argued that the incorporation of shape mapping into genome-wide association studies (GWAS) is an essential approach for elucidating the complete genetic architecture of global and local variation in body shape. Shape mapping allows GWAS researchers to test and estimate how specific genes pleiotropically affect co-variation of body shape with complex diseases and how such co-variation can be used to predict human health risk. Through this review, it is hoped that it will stimulate an in-depth exploration of body shape gene identification and highlight new directions for future work in this increasingly expanding genetic research area.

Various shapes of gastropod shells have evolved ever since the Cambrian. The fossil record suggests that ancestral snails had a coiled shell but during evolution some snail lineages like limpets have independently lost the coiled shell. Although a theoretical account of shell morphogenesis exists, the molecular basis of shell development remains unclear. In order to understand the development of shell shape in gastropods, focus was placed on the decapentaplegic (dpp) gene that is expressed around the shell gland. Expression patterns of dpp in the shell gland and the mantle tissues between coiled and non-coiled shelled gastropods were compared. In the limpets, Patella vulgata, dpp showed symmetric expression patterns throughout ontogeny. On the other hand, in the coiled shelled snail Lymnaea stagnalis, dpp showed an asymmetric expression and mirror image patterns between the dextral and sinistral lineages. Moreover when the embryos were treated with the Dpp regulator or signal inhibitor dorsomorphin at the veliger stage, juvenile shells grew showing a cone-like form rather than a normal coiled form. These results demonstrate that the shell coiling is controlled by using Dpp as a morphogen. The loss of coiling in Patellogastropoda was likely caused by loss of the asymmetric expression of dpp in the shell gland at the trochophore stage, a change which led to the symmetric expression of dpp at the veliger and adult stages.

Hadrosaurids were arguably the dominant megaherbivore dinosaurs during the last 15 million years of the Mesozoic Era. The morphological variation of a sample of ilia, pubes, and ischia corresponding to a taxonomically representative sample of hadrosaurid and basal hadrosauroid species is explored here. Patterns of inter-taxonomic variation that might unravel skeletal features useful for characterizing taxa were sought for. Each bone was decomposed into homologous structures represented by planar images and characterized by their anatomical boundaries. The morphological variation was quantified via a Riemannian Analysis of Elastic Curves (RAEC). In this technique, the boundaries of interest are represented by open continuous curves, parameterized by a square-root velocity function that maps each point of the curve to a vector in Rⁿ. Scale-invariance is imposed by dividing this function by its norm. The space of such translation and scale invariant functions becomes an infinite-dimensional Hilbert sphere equipped with a well-defined Riemannian metric. Distances between shapes were calculated using geodesics (shortest paths) analytically specified on the sphere. Rotation and re-parameterization invariance was further imposed enabling a true elastic matching. The results showed that these skeletal structures are primarily useful in distinguishing among higher taxonomic levels (i.e., main hadrosaurid subclades Saurolophinae and Lambeosaurinae) and between Hadrosauridae and the out-group Hadrosauroidea. Only the supra-acetabular crest of the ilium and the pre-pubic process of the pubis allowed characterization at lower taxonomic levels.

Contemporary shape analysis procedures are limited at present in their ability to represent, quantify, and summarize patterns of variation in any aspect of variation that cannot be represented by a set of landmarks or semilandmarks and/or features that are not present in every specimen across a population or sample. Yet, the problems presented to shape analysts for resolution fail to respect these rather stringent conceptual boundaries. An often-overlooked aspect of quantitative shape data inherent to all digital images is the pixel grid itself. For sets of images scaled to comparable pixel resolutions, this collection of quantitated brightness and colour values can be regarded as a set of semilandmarks that contain both spatial and feature-representational information. As such, the pixel grid can be considered to specify a ‘shape’ in the manner of a complex 3D (grayscale images) or as a 5D (colour images) surface and subjected to geometric morphometric analysis. Data analytic procedures necessary to implement the direct analysis of such digital image ‘shapes’ using standard geometric morphometric procedures are presented and discussed via reference to a hypothetical ladybird beetle dataset whose modes of variation are not well suited to traditional forms of shape analysis. Results indicate that all the formalisms associated with traditional shape analysis (e.g., summarisation of major patterns of form variation, visual portrayal of shape-based comparisons in an ordination space, empirical modelling of various locations within ordination spaces to inform either geometric and biological interpretation, a priori group discrimination, statistical testing of putative group differences) can be realised for the direct analysis of digital images. In addition, recent concerns that have been raised regarding the appropriateness of canonical variates analysis (CVA) as a useful procedure for shape data, and the proposal of between-groups principal components (BG-PCA) as an adequate alternative, are considered in light of the empirical results generated by the ladybird beetle dataset. So long as the ordination results of a CVA are tested statistically against expectations of reasonable null hypotheses (e.g., datasets drawn randomly from the same parent population), and so long as shape models are used to interpret the geometries of CVA ordination spaces, there seems no practical reason to prefer BG-PCA to CVA for the purpose of assessing group-structured shape variation hypotheses. When BG-PCA and CVA produce very different ordination patterns, the CVA result is likely to be the more useful especially insofar as it (1) utilises more information directly related to the group-discrimination problem (2) creates an ordination space more closely tied to the logic of the group-discrimination problem, (3) exhibits no insurmountable interpretive or statistical testing issues, and (4) usually achieves better group-discrimination results, than the former. Indeed, many of the same practical criticisms levelled at CVA are also true of BG-PCA, standard PCA, Procrustes PCA (= relative warps analysis), principal/partial warps analysis, and other geometric morphometric procedures when these are used to portray distinctions between a priori-defined groups. Precisely the same statistical procedures need to be implemented to assess and interpret the significance of the group-specific ordinations produced by these, alternative (and usually suboptimal), group-level data analysis procedures as are necessary for CVA.

Superimposition is a popular technique to separate scaling, position and orientation differences from true differences in shape represented as landmark configurations. The wellknown generalized Procrustes superimposition (GPS), however, is affected by outliers (Pinocchio-effect) and assumes variation of the landmarks to be homoscedastic and uncorrelated, which influences the correctness of the superimposition. This chapter proposes and investigates two robust superimposition methods, which are generalizations (superimposing more than two landmark configurations) of two ordinary (superimposing two landmark configurations) superimposition methods from recent literature: Outlier Process (from the framework of dysmorphometrics) and Scaled Mixture. In their generalization and in contrast to the GPS approach, the landmarks are not assumed to be homoscedastic. Furthermore, both methods are robust against the Pinocchio-effect. While the Outlier Process Generalization (OPG) explicitly introduces the concept of outliers and assumes the inliers to follow a normal distribution, the Scaled Mixture Generalization (SMG) assumes the displacements of the landmarks to follow a student-t distribution, which is outlier-tolerant. In a first test set-up the methods are tested in their ability to recover a known covariance structure (containing 6 to 20 landmarks), based on perturbed configurations. Additionally, a database of 469 facial images is used, on which 7,150 3D quasi-landmarks are established using an Anthropometric Mask. After generalized superimposition, different quasi-landmarks appear to have a difference in variance, confirming the importance of a separate displacement distribution per landmark. Both OPG and SMG are able to detect these differences. In a last test set-up, an artificially created Pinocchio aspect, containing large outliers at the nose, is added to the database. This allows the investigation of the outlier detection capability of the two methods. The OPG performs better than the SMG in estimating a known covariance structure and is able to correctly and explicitly delineate the region of atypical facial variation in the face of Pinocchio.

Shape-regression is an important technique in geometric morphometrics for investigating the effects of various independent variables on biological morphology represented using landmark configurations (dependent variables). Spatially-dense (in contrast to the traditional sparse) landmark configurations, typically cover the complete shape with thousands of landmarks such that salient features of the shape are not overlooked. Furthermore, as proposed in this chapter, spatially-dense configurations allow for the computation and representation of shape variation in terms of local shape characteristics such as curvature, area, and normal displacement. One challenge in using spatially-dense data is the large number of correlated dependent variables in comparison to the number of observations, leading to model instability when using an ordinary least squares regression. This problem has been addressed by using the more advanced technique of partial least squares regression (PLSR), which uses the correlation between the dependent variables for model stabilization, and have investigated genomic ancestry and sex in relation to 3D facial morphology. Briefly, the effect on facial morphology with respect to a particular landmark is measured as the magnitude or Euclidean distance of its displacement in 3D space. The effect-size or strength of the relationship is reported as the variance explained by the PLSR model. Statistical significance is tested under permutation for multivariate regressions. While the effect and effect-size provide insight into which parts of the face are being affected it fails to summarize and convey how facial characteristics are changing. Therefore, the PLS regression framework has been expanded to analyze local effects on normal displacement, curvature, and area. The results are in agreement with general expectations for differences in facial shape due to sex and genomic ancestry. The incorporation of normal displacement, curvature, and area provide additional and valuable biological insight and feedback of the effects on facial morphology due to sex and genomic ancestry.

The traditional approach for characterizing the biological form consists of linear distances, angles, and ratios; known as the conventional metrical approach (CMA). Distances presumably measure size while angles are a measure of shape. In spite of the widespread use of CMA, this approach suffers from limitations that include, the fact that the measurements as commonly used are too sparse to actually measure the precise form of complex and irregular morphologies encountered in the biological sciences, and that it suffers from the limitation that these measurements form a disconnected dataset and cannot adequately describe the boundary or shape of biological forms. This arises because linear measurements precisely apply only to regular objects and were never intended for the measurement of irregular structures like the human skull. Alternative methods such as Fourier Descriptors (FDs) have been successfully applied to describe the boundary of biological forms in 2-space (ℝ²). Although, such measurements in R² are highly useful and have produced useful data, there remain limitations with such studies. Namely, that the overwhelming majority of biological information resides in ℝ³. The quantitative representation of the biological form in 3D continues to present challenges. This study is a continuation of our research to quantify the mandibular morphology in 3-space. A sample of 10 normal cases was utilized for comparison with two cases exhibiting hemifacial microsomia (HM). Five steps were required: (1) 3D CT scans of the mandible were obtained, and the boundary outline digitized utilizing Dolphin software from Dolphin Imaging and Management Solutions; (2) once the 104 points had been digitized, the x, y, and z coordinates were exported from the Dolphin software into a format acceptable to EFFA, a routine that generates FDs; that is, curves in 3D, (3) since superimposition is necessary for clinical comparisons; this required the calculation of a centroid and the bounded surface area. A special routine, Surface Evolver, was required for this procedure; (4) once the centroid and surface area are available it is a comparatively straightforward procedure to superimpose the mean of the control mandibles (n=10) onto the mean of the HM clinical cases (n=2); (5) finally, the EFFA-generated 3D curves were superimposed using both area-standardization and Procrustes superimpositions and displayed graphically, allowing for a visual assessment of the differences between controls and abnormals in a clinical setting.

Current analyses of 3-D CBCT images used in orthodontic and orthognathic surgery diagnosis/treatment planning still rely upon 2-D linear and angular measures, along with subjective visual evaluation, to assess complex facial disharmony and other dentofacial characteristics. The overall objective of this investigation is to overcome these limitations by developing and testing protocol for mapping and averaging human skull surfaces in three dimensions. A selection of 10 female patient files ranging in age from 19 to 35 was selected as an initial sample for development of the technical protocol. Existing CBCT files in DICOM format were segmented using a triangular mesh approach. The topology of each skull was then corrected using a principal axis star map and smoothing of the extrapolated regions. Shapes were mapped onto a sphere using conformal and area preserving maps, which were then registered using a spherical patch mapping approach. Finally, an average was created using a 7-parameter Procrustes alignment. Size-standardized and non-size standardized average skull models were generated for the sample population. A single patient was then superimposed on the average and color-coded displacement maps were generated to demonstrate the clinical applicability of this protocol. The results of this investigation suggest that it is possible to average multiple shapes of highly variable topology such as the human skull. The most immediate application of this research will be rapid and detailed diagnostic imaging analysis for orthodontic and surgical treatment planning, particularly in complex cases. There is also great potential for application to areas outside orthodontics such as anthropometrics and genomics.

Studies of the human body form based on standardized photos, were initiated by W. H. Sheldon in the 1940's. These led to the familiar anthropometric archetypes of ectomorph, endomorph, and mesomorph to describe body physique. Recent studies of body form are either largely descriptive or based on indirect measures like the BMI. Quantitative assessments of total body images have been rarely attempted because of the lack of available methods. In contrast, Fourier Descriptors (FDs) provide for: (1) a precise quantitative as well as visual depiction of body outlines and (2) an analysis of shape thereby controlling for the effect of size. Elliptical Fourier functions (EFFs), a particular FD, was used to fit the body shape of Japanese female college students in the frontal and lateral views (n = 144). The mean age was 19.63±1.15 years. The goodness-of-fit or residual of the EFF with the actual observed frontal outline was 0.96±0.04 pixel units (roughly 0.17± 0.01 mm). Similar results were found with the lateral view. Using the BMI as a criterion, comparison of the body shape of the 10^th percentile with the 90^th percentile produced statistically significant results utilizing a MANOVA and displayed clear body outline differences in both the frontal and side views. Superimposition approaches were implemented to provide a visual assessment. These include size-standardized data and Procrustes superimposition. Assessment of these superimposed images was judged with a shape difference index (SDI) specifically designed for this purpose. It is proposed that whole body images analyzed with EFFs can provide useful information for: (1) the effects of nutrition and disease on body shape, (2) body perception studies, (3) body shape in health compromised situations such as Anorexia Nervosa, etc., (4) the quantification of developmental obesity, and (5) provide for the building of reference standards for studies of body shape.

The following section is included:

• INDEX