Elliptic Fourier Transformation Research Articles

Application of Harmonized Elliptic Fourier Transform Coefficients for Comparing the Shapes of Biological Structures (Example of the Attachment Organs of Monogenea)

Application of Harmonized Elliptic Fourier Transform Coefficients for Comparing the Shapes of Biological Structures (Example of the Attachment Organs of Monogenea)

Curvature Analysis of Seed Silhouettes in Silene L.

The application of seed morphology to descriptive systematics requires methods for shape analysis and quantification. The complexity of lateral and dorsal views of seeds of Silene species is investigated here by the application of the Elliptic Fourier Transform (EFT) to representative seeds of four morphological types: smooth, rugose, echinate and papillose. The silhouettes of seed images in the lateral and dorsal views are converted to trigonometric functions, whose graphical representations reproduce them with different levels of accuracy depending on the number of harmonics. A general definition of seed shape in Silene species is obtained by equations based on 40 points and 20 harmonics, while the detailed representation of individual tubercles in each seed image requires between 100 and 200 points and 60–80 harmonics depending on their number and complexity. Smooth-type seeds are accurately represented with a low number of harmonics, while rugose, echinate and papillose seeds require a higher number. Fourier equations provide information about tubercle number and distribution and allow the analysis of curvature. Further estimation of curvature values in individual tubercles reveals differences between seeds, with higher values of curvature in S. latifolia, representative of echinate seeds, and lower in S. chlorifolia with rugose seeds.

Automated Identification of Morphological Characteristics of Three Thunnus Species Based on Different Machine Learning Algorithms

Tuna are economically important fish species. The automated identification of tuna species is of importance in fishery production and resource assessment in that it would facilitate the informed monitoring of tuna fishing vessels and the establishment of electronic observer systems. As morphological characteristics are important for tuna identification, this study aims to verify the performance of the automated identification of three Thunnus species through morphological characteristics based on different machine learning algorithms. Firstly, morphological outlines were visually analyzed using EFT (elliptic Fourier transform) and CNN (convolutional neural network). Then, the EFT feature data and deep feature data of the tuna outline images were extracted, and principal component analysis of the two different morphological characteristics was performed. Finally, different machine learning algorithms were used to analyze the identification performance of tuna of the same genus and different species. The experimental results showed that EFT features had the highest identification accuracy in KNN (K-nearest neighbor), with 90% for T. obesus, 90% for T. albacores, and 85% for T. alalunga. Deep features had the best identification performance in SVM (support vector machine), with 80% for T. obesus, 90% for T. albacores, and 100% for T. alalunga. Deep features were better than EFT features in identification performance. The biodiversity and intergeneric differences among tuna species can be well analyzed using these two different morphological characteristics. Machine learning algorithms open up the way for rapid near-real-time electronic observer systems in these important international fisheries.

Seed Silhouettes as Geometric Objects: New Applications of Elliptic Fourier Transform to Seed Morphology

Historically, little attention has been paid to the resemblance between seed silhouettes to geometric figures. Cardioid and derivatives, ellipses, heart curves, lemniscates, lenses, lunes, ovals, superellipses, waterdrops, and other figures can be used to describe seed shape, as well as models for quantification. Algebraic expressions representing the average silhouettes for a group of seeds are available, and their shape can be described and quantified by comparison with geometric models. Bidimensional closed-plane figures resulting from the representation of Fourier equations can be used as models for shape analysis. Elliptic Fourier Transform equations reproduce the seed silhouettes for any closed-plane curve corresponding to the contour of the image of a seed. We review the geometric properties of the silhouettes from seed images and discuss them in the context of seed development, plant taxonomy, and environmental adaptation. Silene is proposed as a model for the study of seed morphology. Three groups have been recently defined among Silene species based on the structure of their seed silhouettes, and their geometric properties are discussed. Using models based on Fourier Transform equations is useful in Silene species where the seeds are homogenous in shape but don’t adjust to described figures.

The earliest record of fossil solid-wood-borer larvae—immature beetles in 99 million-year-old Myanmar amber

Interactions between animals and plants represent an important driver of evolution. Especially the group Insecta has an enormous impact on plants, e.g., by consuming them. Among beetles, the larvae of different groups (Buprestidae, Cerambycidae, partly Eucnemidae) bore into wood and are therefore called wood-borer larvae or borers. While adults of these beetle groups are well known in the fossil record, there are barely any fossils of the corresponding larvae. We report here four new wood-borer larvae from Cretaceous Kachin amber (Myanmar, ca. 99 Ma). To compare these fossils with extant wood-borer larvae, we reconstructed the body outline and performed shape analysis via elliptic Fourier transformation and a subsequent principal component analysis. Two of the new larvae plot closely together and clearly in the same area as modern representatives of Buprestidae. As they furthermore lack legs, they are interpreted as representatives of Buprestidae. The other two new larvae possess legs and plot far apart from each other. They are more difficult to interpret; they may represent larvae of early offshoots of either Cerambycidae or Buprestidae, which still retain longer legs. These findings represent the earliest fossil record of larvae of Buprestidae and possibly of Cerambycidae known to date.

Split-footed lacewings declined over time: indications from the morphological diversity of their antlion-like larvae

Nymphidae, the group of split-footed lacewings, is a rather species-poor group. Split-footed lacewings nowadays are restricted to Australasia, while fossil forms are also known from other areas of the world, indicating that the group was more species-rich and therefore likely diverse in the past. Split-footed lacewings have rather distinct larvae, roughly resembling antlion larvae, but differing from the latter especially with regard to the mandibles. Antlion larvae usually have three prominent teeth on each mandible, while at least extant larvae of split-footed lacewings only have a single prominent tooth per mandible. Fossils interpreted as larvae of split-footed lacewings are well known from amber from Myanmar (ca. 100 myr; Burmese amber) and by a single specimen from Baltic amber (about 40 myr). We here report additional fossil specimens from Myanmar amber, expanding the known record of fossil forms from six depicted specimens to 15. For the extant fauna, we could compile 25 larvae. We compare the diversity of shape of extant and fossil larvae through time using an outline analysis (based on elliptic Fourier transformation) of the head. The results of this analysis indicate that the morphological diversity, or disparity, of split-footed lacewing larvae was higher in the past than it is today. With this type of analysis, we can show a loss of diversity over time, without the necessity to identify the fossil larvae down to a narrow taxonomical range. A similar pattern has already been recognised in silky lacewings, Psychopsidae. This might indicate a general loss of diversity of lacewing larvae.

Diversity of hippoidean crabs - considering ontogeny, quantifiable morphology, and phenotypic plasticity

Representatives of Hippoidea, often called sand crabs or mole crabs, are an ingroup of Anomala. These marine crustaceans inhabit the tropical and subtropical coasts of the world, yet some also appear in temperate climates. Their adults are specialized for digging and living in sandy substrates. Hippoidean zoea-type larvae are planktic and reach large sizes up to a few centimetres. These larvae transform into megalopa larvae, strongly resembling the adult, mediating the transition to the benthic lifestyle of the adult. We reconstructed outlines in dorsal view of over 80 shields of hippoideans, including representatives of Blepharipodidae (sister group to all others), Albuneidae, and Hippidae and including adults, megalopa-type, and zoea-type larvae from all three ingroups. We conducted a morphological analysis on this data using an elliptic Fourier transformation and principal component analysis. We used the results of the analysis to discuss the life history of hippoideans and the special function of megalopae, which often lack emphasis in current research. Early stage zoea larvae, megalopae, and adults show a linear gradient in their morphological development according to our analysis. However, late stage zoea larvae deviate from this pattern, possibly due to their specialization to a long-lasting planktic life. Lastly, we discuss the influence of phenotypic plasticity in hippoidean zoea larvae.

Comparison of otolith shape descriptors and morphometrics for stock discrimination of yellow croaker along the Chinese coast

This study compared and evaluated the efficiency of two otolith shape descriptors (i.e., the elliptic Fourier transform (EFT) and discrete wavelet transform (DWT)) and morphometrics for stock discrimination. To accomplish this, sample fish from three stocks of yellow croaker Larimichthys polyactis along the Chinese coast (LDB stock from the Liaodong Bay of the Bohai Sea, JZB stock from the Jiaozhou Bay of the Yellow Sea and CJE stock from the Changjiang River estuary of the East China Sea) were used for otolith morphology analyses. The results showed that morphometrics produced an overall classification success rate of 70.8% in contrast with success rates of 80.0% or 82.0% obtained using EFT or DWT, respectively. This suggests that the two shape descriptors comparably discriminated among the stocks and performed more efficiently than morphometrics. During data adjustment and acquisition, some size variables were excluded from the subsequent discriminant analysis for stock discrimination because they were statistically “ineffective,” which could reduce the efficiency of morphometrics and lead to relatively low overall classification success. Both EFT and DWT retain the contour coefficients and thus provide a detailed description of otolith shape, which could improve discriminatory efficiency compared with morphometrics.

LeafletAnalyzer, an Automated Software for Quantifying, Comparing and Classifying Blade and Serration Features of Compound Leaves during Development, and among Induced Mutants and Natural Variants in the Legume Medicago truncatula.

Diverse leaf forms ranging from simple to compound leaves are found in plants. It is known that the final leaf size and shape vary greatly in response to developmental and environmental changes. However, changes in leaf size and shape have been quantitatively characterized only in a limited number of species. Here, we report development of LeafletAnalyzer, an automated image analysis and classification software to analyze and classify blade and serration characteristics of trifoliate leaves in Medicago truncatula. The software processes high quality leaf images in an automated or manual fashion to generate size and shape parameters for both blades and serrations. In addition, it generates spectral components for each leaflets using elliptic Fourier transformation. Reconstruction studies show that the spectral components can be reliably used to rebuild the original leaflet images, with low, and middle and high frequency spectral components corresponding to the outline and serration of leaflets, respectively. The software uses artificial neutral network or k-means classification method to classify leaflet groups that are developed either on successive nodes of stems within a genotype or among genotypes such as natural variants and developmental mutants. The automated feature of the software allows analysis of thousands of leaf samples within a short period of time, thus facilitating identification, comparison and classification of leaf groups based on leaflet size, shape and tooth features during leaf development, and among induced mutants and natural variants.

The Domestication Syndrome in Phoenix dactylifera Seeds: Toward the Identification of Wild Date Palm Populations.

Investigating crop origins is a priority to understand the evolution of plants under domestication, develop strategies for conservation and valorization of agrobiodiversity and acquire fundamental knowledge for cultivar improvement. The date palm (Phoenix dactylifera L.) belongs to the genus Phoenix, which comprises 14 species morphologically very close, sometimes hardly distinguishable. It has been cultivated for millennia in the Middle East and in North Africa and constitutes the keystone of oasis agriculture. Yet, its origins remain poorly understood as no wild populations are identified. Uncultivated populations have been described but they might represent feral, i.e. formerly cultivated, abandoned forms rather than truly wild populations. In this context, this study based on morphometrics applied to 1625 Phoenix seeds aims to (1) differentiate Phoenix species and (2) depict the domestication syndrome observed in cultivated date palm seeds using other Phoenix species as a “wild” reference. This will help discriminate truly wild from feral forms, thus providing new insights into the evolutionary history of this species. Seed size was evaluated using four parameters: length, width, thickness and dorsal view surface. Seed shape was quantified using outline analyses based on the Elliptic Fourier Transform method. The size and shape of seeds allowed an accurate differentiation of Phoenix species. The cultivated date palm shows distinctive size and shape features, compared to other Phoenix species: seeds are longer and elongated. This morphological shift may be interpreted as a domestication syndrome, resulting from the long-term history of cultivation, selection and human-mediated dispersion. Based on seed attributes, some uncultivated date palms from Oman may be identified as wild. This opens new prospects regarding the possible existence and characterization of relict wild populations and consequently for the understanding of the date palm origins. Finally, we here describe a pipeline for the identification of the domestication syndrome in seeds that could be used in other crops.

A tool for developing an automatic insect identification system based on wing outlines.

For some insect groups, wing outline is an important character for species identification. We have constructed a program as the integral part of an automated system to identify insects based on wing outlines (DAIIS). This program includes two main functions: (1) outline digitization and Elliptic Fourier transformation and (2) classifier model training by pattern recognition of support vector machines and model validation. To demonstrate the utility of this program, a sample of 120 owlflies (Neuroptera: Ascalaphidae) was split into training and validation sets. After training, the sample was sorted into seven species using this tool. In five repeated experiments, the mean accuracy for identification of each species ranged from 90% to 98%. The accuracy increased to 99% when the samples were first divided into two groups based on features of their compound eyes. DAIIS can therefore be a useful tool for developing a system of automated insect identification.

Finite-dimensional representations of the elliptic modular double

We investigate the kernel space of an integral operator M(g) depending on the “spin” g and describing an elliptic Fourier transformation. The operator M(g) is an intertwiner for the elliptic modular double formed from a pair of Sklyanin algebras with the parameters η and τ, Imτ > 0, Imη > 0. For two-dimensional lattices g = nη + mτ/2 and g = 1/2 + nη + mτ/2 with incommensurate 1, 2η, τand integers n,m > 0, the operator M(g) has a finite-dimensional kernel that consists of the products of theta functions with two different modular parameters and is invariant under the action of generators of the elliptic modular double.

Inferring the agrobiodiversity of Vitis vinifera L. (grapevine) in ancient Greece by comparative shape analysis of archaeological and modern seeds

The origins and biogeographical history of Vitis vinifera L. (domesticated grapevine) remain largely unknown. Shape and size have long been used as criteria to distinguish between wild and domesticated grape pips. Here we have analyzed variations of seed morphology in order to provide accurate criteria for the discrimination of different groups of varieties. Diversity in present-day cultivars and wild grapevines of Greek and east Mediterranean origin in relation to other Asiatic and European varieties and wild grapevines provides the basis for our analysis, which aims to allow the characterization of the ancient diversity of cultivated grapes in relation to present-day cultivars. Geometric morphometric analyses (Elliptic Fourier Transform method) have been used to characterize the seed shape and size of modern and archaeological material using 40 variables per seed. 197 archaeological grape pips from the 7th century bc sanctuary of Hera in Samos, Greece were compared with an extended reference collection of 269 modern cultivars and 83 wild populations, 10,518 seeds in total. Our study confirms the relationships between seed shape and domestication. Modern diversity is partly structured by the geographical origin of cultivars, but influence of other factors may play a significant role in clustering. The wide diversity of varieties offered at the Heraion of Samos during the Archaic Period, including cultivars growing on the island, imported grapes and wild morphotypes, is related to the history and geographical location of the island as well as to the diversity in the geographical range of pilgrims making offerings to the sanctuary.

Evaluation of shape variability of stallion sperm heads by means of image analysis and Fourier descriptors

This study quantified and evaluated the variability of sperm head shape for 10 different stallions. Sperm head shape characteristics including sperm head length to width ratio, position of the center of gravity, curvature, and degree of roundness were assessed and analysed from images using elliptic Fourier descriptors and inverse Fourier transformation. The first four principal components accounted for 88.46–92.33% of the total variance and provided a good summary of the overall data. In the case of the ejaculate with defective sperm heads the components accounted for 97.35–98.21% of variation. The study was able to quantitatively confirm that head length to width ratio, which contributed 48.63–53.48% and 71.30–73.34% to the total variance for normal and defective sperm, respectively, was the predominant determining parameter of sperm head shape. There were no statistical significant relationships between Fourier descriptors and values of sperm concentration and/or motility.

Mandible shape and dwarfism in squirrels (Mammalia, Rodentia): interaction of allometry and adaptation

Squirrels include several independent lineages of dwarf forms distributed into two ecological groups: the dwarf tree and flying squirrels. The mandible of dwarf tree squirrels share a highly reduced coronoid process and a condylar process drawn backwards. Dwarf flying squirrels on the other hand, have an elongated coronoid process and a well-differentiated condylar process. To interpret such a difference, Elliptic Fourier Transform was used to evaluate how mandible shape varies with dwarfism in sciurids. The results obtained show that this clear-cut difference cannot be explained by a simple allometric relationship in relation with size decrease. We concluded that the retention of anteriorly positioned eye sockets, in relation with distance estimation, allowed the conservation of a well-differentiated coronoid process in all flying species, despite the trend towards its reduction observed among sciurids as their size decreases.

Uluburun shipwreck stowaway house mouse: molar shape analysis and indirect clues about the vessel's last journey

Human translocation by stowaway transport is the widely accepted vector of the current worldwide distribution of commensal rodents but its historical process has never been directly evidenced. The anecdotal find of the small murine (mice and rats) mandible among the wealthy cargo of the Uluburun shipwreck provide us with an unexpected opportunity to directly evidence the species associated with this stowaway and provide indirect clues regarding the ship's route. Taxonomic identification and geographic sourcing has been performed using outline molar shape analysis by Elliptic Fourier Transform comparing the Uluburun mouse molar phenotype with extant populations from eastern Mediterranean sibling species. Results showed that the mandible belonged to the house mouse ( Mus musculus domesticus) with significant phenotypic similarities with extant Syrian house mouse populations. These results provide the earliest direct evidence for stowaway transports highlighting the historical process of the house mouse invasion of the Mediterranean. Using modern behavioural comparisons, combined with archaeological and historical sources, it has been argued that the servicing port of Ugarit (Minet el Beida) was a likely step on the vessel's last journey.

The Bornean Lithocarpus Bl. section Synaedrys (Lindl.) Barnett (Fagaceae): its circumscription and description of a new species

The Bornean species of Lithocarpus Bl. section Synaedrys (Lindl.) Barnett (Fagaceae) are discussed in terms of their unifying characteristics, and keys to the species are provided. A novel morphological feature present in the genus, where the seed in the mature fruit is enclosed by a lignified and thickened receptacle, is illustrated. A new species, L. palungensis Cannon & Manos, is described. It can be distinguished from L. pulcher (King) Markgr. by its submontane distribution, prominent reflexed cupular spines, present at all stages, and broadly oblong leaves with scattered open fasciculate trichomes on the abaxial surface. Foliar trichome types present within the section are also described. Distinctiveness of fruit wall and receptacle shape, as described by two-dimensional elliptic Fourier transformation, is demonstrated by principal components analysis.

The Bornean Lithocarpus B1. section Synaedrys (Lindl.) Barnett (Fagaceae): its circumscription and description of a new species

The Bornean species of Lithocarpus B1. section Synaedrys (Lindl.) Barnett (Fagaceae) are discussed in terms of their unifying characteristics, and keys to the species are provided. A novel morphological feature present in the genus, where the seed in the mature fruit is enclosed by a lignified and thickened receptacle, is illustrated. A new species, L palungensis Cannon & Manos, is described. It can be distinguished from L. pulcher (King) Markgr. by its submontane distribution, prominent reflexed cupular spines, present at all stages, and broadly oblong leaves with scattered open fasciculate trichomes on the abaxial surface. Foliar trichome types present within the section are also described. Distinctiveness of fruit wall and receptacle shape, as described by two-dimensional elliptic Fourier transformation, is demonstrated by principal components analysis.

Treatment field shape verification using elliptic Fourier transform.

An automated field shape correlation technique based on elliptic Fourier transform (EFT) is developed to verify the radiation treatment field in digital portal images. In this method, the edge of the treatment field is initially extracted from the portal image and is then approximated by a polygon. The polygon is further represented with elliptic Fourier coefficients. The invariants to shift, rotation, and scale are computed from the elliptic Fourier coefficients to characterize the genuine shape feature and are used to match the reference treatment field. Invariants calculated from both test and reference field shapes are compared to determine the similarity between two treatment fields. The proposed procedure uses the first approved field shape as the reference for automated comparison with subsequent portal images. This technique not only verifies the shape of each portal field but also provides information about relative shift, rotation, and scale. A set of generic shapes is simulated to test the robustness of the algorithm and to determine the parameters used in the decision procedure. Experimental results on the simulated shapes show that this method can detect shape distortions of 2% in area and the standard deviations are 0 for shifting, 0.24 degrees for rotation, and 0.0031 for scaling. Preliminary tests on clinical portal images indicated that this technique is potentially useful for automated real-time portal verification.

Wing Shape of Gelechiid Moths and Its Functions: Analysis by Elliptic Fourier Transformation

Most micromoths have distinct hairs around their wings. Difficulty in setting homologous reference points on the wing-hairs has prevented the development of morphometric study on the wing shape. To establish a method for analyzing wing shape including the hairs, we applied image analysis and elliptic Fourier transformation to 16 species of the Gelechiidae. Image analysis indicated that smaller moths had more slender wing membranes and longer wing-hairs. This tendency is interpreted as an adaptation of small moths to relatively high viscosity of the air. Fourier transformation showed that the shape of wing membranes varied greatly between the species, but that the shape of wings including the hairs remained relatively uniform. We present adaptive and nonadaptive hypotheses to explain this uniformity.