Elliptic Fourier Research Articles

Description of Gomphonella saldanensis sp. nov. (Bacillariophyceae) from hydromagnesite stromatolites in Salda Lake, Turkey

Lake Salda has a unique environment due to the presence of hydromagnesite stromatolites. Samples collected from the stromatolites contained a new diatom species, Gomphonella saldanensis sp. nov., which is described based on light and scanning electron microscopy. The main character of the taxon is its linear-lanceolate outline with a rostrate headpole and narrowly rounded footpole. The striae are strongly radiate mid-valve, becoming parallel to slightly radiate towards the poles. Elliptical Fourier and Linear Discriminant analyses indicate that there are different shape forms within the same taxon. Based on LM observations, G. saldanensis is similar to Gomphonema lagerheimii f. simplex, G. geisslerae, Gomphonella calcarea, G. olivacea, G. acsiae and G. coxiae. However, G. lagerheimii f. simplex differs with slightly radiate striae throughout the valve. Gomphonella geisslerae has a slightly undulate raphe and linear apices. Larger specimens of G. acsiae are lanceolate, clavate in smaller specimens. The remaining Gomphonella species, G. calcarea, G. coxiae and G. olivacea have broader outlines and lower stria densities.

A new Meckel's cartilage from the Devonian Hangenberg black shale in Morocco and its position in chondrichthyan jaw morphospace.

Fossil chondrichthyan remains are mostly known from their teeth, scales or fin spines only, whereas their cartilaginous endoskeletons require exceptional preservational conditions to become fossilized. While most cartilaginous remains of Famennian (Late Devonian) chondrichthyans were found in older layers of the eastern Anti-Atlas, such fossils were unknown from the Hangenberg black shale (HBS) and only a few chondrichthyan teeth had been found therein previously. Here, we describe a Meckel's cartilage from the Hangenberg black shale in Morocco, which is the first fossil cartilage from these strata. Since no teeth or other skeletal elements have been found in articulation, we used elliptical Fourier (EFA), principal component (PCA), and hierarchical cluster (HCA) analyses to morphologically compare it with 41 chondrichthyan taxa of different size and age and to evaluate its possible systematic affiliation. PCA and HCA position the new specimen closest to some acanthodian and elasmobranch jaws. Accordingly, a holocephalan origin was excluded. The jaw shape as well as the presence of a polygonal pattern, typical for tessellated calcified cartilage, suggest a ctenacanth origin and we assigned the new HBS Meckel's cartilage to the order Ctenacanthiformes with reservations.

Geometric morphometric analysis of spore shapes improves identification of fungi

Morphology of organisms is an essential source of evidence for taxonomic decisions and understanding of ecology and evolutionary history. The geometric structure (i.e., numeric description of shape) provides richer and mathematically different information about an organism's morphology than linear measurements. A little is known on how these two sources of morphological information (shape vs. size) contribute to the identification of organisms when implied simultaneously. This study hypothesized that combining geometric information on the outline with linear measurements results in better species identification than either evidence alone can provide. As a test system for our research, we used the microscopic spores of fungi from the genus Subulicystidium (Agaricomycetes, Basidiomycota). We analyzed 2D spore shape data via elliptic Fourier and principal component analyses. Using flexible discriminant analysis, we achieved the highest species identification success rate for a combination of shape and size descriptors (64.7%). The shape descriptors alone predicted species slightly better than size descriptors (61.5% vs. 59.1%). We conclude that adding geometric information on the outline to linear measurements improves the identification of the organisms. Despite the high relevance of spore traits for the taxonomy of fungi, they were previously rarely analyzed with the tools of geometric morphometrics. Therefore, we supplement our study with an open access protocol for digitizing and summarizing fungal spores' shape and size information. We propagate a broader use of geometric morphometric analysis for microscopic propagules of fungi and other organisms.

Discrimination of red porgy Pagrus pagrus (Sparidae) potential stocks in the south-western Atlantic by otolith shape analysis.

Otolith shape analysis is a powerful method for fish stock identification. We compared the otolith shape of Pagrus pagrus (Linnaeus 1758) along with its distribution in four south-western Atlantic regions where it is commercially fished: Rio de Janeiro, Rio Grande do Sul in southern Brazil, the Argentine-Uruguayan Common Fishing Zone (UA) and the Argentinian Exclusive Fishing Zone (AR). Otolith shapes were compared by Elliptical Fourier and Wavelet coefficients among specimens in a size range with similar otoliths, morphometric parameters and ages. Four potential stocks were identified: one in the AR, a second along the UA which included specimens from southern Brazil with well-marked opaque bands in its otoliths (MRS), the third in southern Brazil with faint or absent opaque bands in its otoliths (FRS) and the fourth along Rio de Janeiro. The difference in the otolith shape among regions followed differences reported using other stock identification techniques. The similarity between otoliths from UA and MRS (ANOVA-like, P > 0.01) can be explained by seasonal short-range migrations. Otoliths shape differences between MRS and FRS (ANOVA-like, P < 0.01) suggest that P. pagrus does not form a homogeneous group in southern Brazil.

The utility of three-dimensional models of paranasal sinuses to establish age, sex, and ancestry across three modern populations: A preliminary study

ABSTRACT Technological advances have furthered the development and understanding of trace materials such that DNA and fingerprints have become the foundation of human identification. However, when a body undergoes damage such as in cases of arson, these methods of identification may not be possible, and alternative methods of identification become critical. Previous studies have quantified the variability of the paranasal sinuses between individuals and have begun to explore their ability to provide biological information. However, the published literature investigating these structures in a forensic anthropology context offers variable findings. This study presents a new approach for establishing a biological profile using three-dimensional (3D) reconstructions of the paranasal sinuses. 3D models were produced from a database of modern CT scans provided by University College London Hospital (UCLH), London, UK. Elliptic Fourier and linear analysis produced from the 3D models demonstrated notable variations and patterns for discriminating age, sex, and ancestry across three distinct ethnic groups. The most promising classification rates ranged from 82.8% (p =.027) to 76.9% (p =.003) for age and sex prediction. The findings offer insights into the potential for using the paranasal sinuses as an attribute for discriminating between individuals and the identification of unknown human remains in crime reconstruction investigations.

Ontogenetic Trends in Frontal Sinus Shape

Adult frontal sinus morphology has been studied in biological anthropology, both in terms of its function and variation. Overall, this structure is known to be highly variable among individuals, to such an extent that it is used to make positive identifications in the medicolegal setting. However, very little is known about the growth and developmental processes leading to the wide ranges of frontal sinus size and shape. Although several studies investigate frontal sinus ontogeny in terms of size and linear dimensions, much less is known regarding the ontogeny of its shape. This study partially addresses this gap by examining frontal sinus outlines using longitudinal radiographic data to evaluate when the frontal sinus attains its adult shape.Longitudinal radiographs for 107 individuals (57M/50F) spanning 5–29 years of age (yoa) were obtained from the AAOF Craniofacial Growth Legacy Collection ( www.aaoflegacycollection.org). Superior borders of frontal sinus outlines were digitally traced in ImageJ; the superior orbital border demarcated inferior sinus boundaries. Age of first appearance was also recorded. A total of 749 outlines were imported into SHAPE‐software, where elliptical Fourier (20 harmonics) and principal components (PC) analyses were conducted. PC1 (49.18% variation explained) reflects height‐to‐breadth relationships, while PC2 (11.74%) reflects asymmetry in right versus left lobe dominance.To assess when the frontal sinus attains its adult shape, Euclidean distances of PCs 1–9 (91.58% cumulative variance) between each age point and the 18‐year point were calculated within individuals; this process was repeated for the 20‐year point. Scatterplots with Loess curves for each distance plotted against age suggest adult shape is attained around 20yoa. Sexual dimorphic trends are evident in the Loess curves, whereby males exhibit greater distances from 20yoa at early ages. An analysis of variance confirms these sex‐based differences (F=7.063, P&lt;0.0001); Tukey post‐hocs further suggest that while adult females are not significantly different in shape from adult males or younger females/males (13–19yoa), adult males are significantly different from males 15yoa and younger. T‐tests failed to find significant sex‐based differences for age‐of‐first‐appearance (t=1.482, P=0.142) and adult‐shape (PC1: t=−0.670, P=0.505; PC2: t=1.827, P=0.058). Thus, it appears that while both sexes display similar start times in sinus development and reach similar adult‐shapes, females attain their adult shape sooner. This suggests a slower developmental process in males. Additional studies are needed to determine how these ontogenetic patterns in 2D sinus‐shape relate to the overall size and 3D dimensions of the sinus.

楕円フーリエ－主成分分析法を用いた前浜堆積物の粒子形状評価と波浪・地形との関係性

楕円フーリエ－主成分分析法を用いた前浜堆積物の粒子形状評価と波浪・地形との関係性

Evaluation of the grain shapes by elliptic Fourier and principal component analyses (EF-PCA) to determine depositional environments.

Evaluation of the grain shapes by elliptic Fourier and principal component analyses (EF-PCA) to determine depositional environments.

Subspecific taxonomy of the desert locust, Schistocerca gregaria (Orthoptera: Acrididae), based on molecular and morphological characters

AbstractWe evaluated the validity of the subspecific designation for Schistocerca gregaria gregaria (Forskål) and Schistocerca gregaria flaviventris (Burmeister), isolated in distinct regions along the north–south axis of Africa. Towards this goal, we assessed the variation of multiple morphological and molecular traits within species. We first used elliptic Fourier and landmark‐based relative warps analyses to compare the size and shape of two internal and two external structures of male genitalia. We provide a discriminant function which classified the specimens with 100% accuracy and selected shape elements of the external structures only (cercus and epiproct). We also tested eight molecular markers, and because of either absence of variation or contamination by mitochondrial DNA (mtDNA)‐like sequences, we used a clone‐and‐sequence analysis of the standard cytochrome c oxidase subunit I mitochondrial DNA barcode only. We differentiated 185 true mitochondrial sequences from 66 mitochondrial DNA‐like sequences, most of which were from S. g. gregaria specimens. On the dataset of mitochondrial origin, we identified three characteristic point mutations that diagnosed the two allopatric subspecies with 94% accuracy. Minimum spanning network and parsimony tree analyses identified S. g. flaviventris as a monophyletic lineage distinct from the nominate subspecies. Accordingly, microsatellite data indicate rarely occurring admixture events only, showing that independent evolutionary history is the norm.

Application of elliptic discrete Fourier transform type (I) in denoising and receiver design

In this paper, two various applications of elliptic discrete Fourier transform type I (EDFT_I) are presented in the communication area. In the first application, EDFT_I is applied to reduce the additive uniform and Gaussian noise in the sinusoidal signal. The noise reduction is independent from the type of noise and the corresponding amplitude. In the second application, an EDFT_I-based receiver has been proposed which improves the signal to noise at least about 2 dB for the same error-probability as compared with the optimum receiver considering an additive non-Gaussian noise. In this approach, a binary orthogonal signaling is created using the EDFT_I, which cosine and sine signals are used as carrier for 0 and 1 information. Moreover, for an additive non-Gaussian noise, the proper choice of this transform's parameters as well as the decision threshold, results in improving the accuracy of digital information's transmission.

Geometric Morphometrics on Gene Expression Patterns Within Phenotypes: A Case Example on Limb Development.

How the genotype translates into the phenotype through development is critical to fully understand the evolution of phenotypes. We propose a novel approach to directly assess how changes in gene expression patterns are associated with changes in morphology using the limb as a case example. Our method combines molecular biology techniques, such as whole-mount in situ hybridization, with image and shape analysis, extending the use of Geometric Morphometrics to the analysis of nonanatomical shapes, such as gene expression domains. Elliptical Fourier and Procrustes-based semilandmark analyses were used to analyze the variation and covariation patterns of the limb bud shape with the expression patterns of two relevant genes for limb morphogenesis, Hoxa11 and Hoxa13. We devised a multiple thresholding method to semiautomatically segment gene domains at several expression levels in large samples of limb buds from C57Bl6 mouse embryos between 10 and 12 postfertilization days. Besides providing an accurate phenotyping tool to quantify the spatiotemporal dynamics of gene expression patterns within developing structures, our morphometric analyses revealed high, non-random, and gene-specific variation undergoing canalization during limb development. Our results demonstrate that Hoxa11 and Hoxa13, despite being paralogs with analogous functions in limb patterning, show clearly distinct dynamic patterns, both in shape and size, and are associated differently with the limb bud shape. The correspondence between our results and already well-established molecular processes underlying limb development confirms that this morphometric approach is a powerful tool to extract features of development regulating morphogenesis. Such multilevel analyses are promising in systems where not so much molecular information is available and will advance our understanding of the genotype–phenotype map. In systematics, this knowledge will increase our ability to infer how evolution modified a common developmental pattern to generate a wide diversity of morphologies, as in the vertebrate limb.

Methods of converting multidimensional measuring information to a number by means of differential equations in partial derivatives

We have proved that finite difference representation of differential equations in partial derivatives is the most effective method of converting multidimensional measuring information to a single number. The devised conversion methods use Laplace’s elliptic equations and Fourier’s parabolic equations. To convert information,we have solved a number of tasks. We have devised a method of elliptic conversion of static images of the measured object by means of finite difference representation of Laplace’s differential equation in the second-order partial derivatives, which means a change of the current value of the pixel brightness to a new one that has two gradations of brightness––black and white. Pixel summation turns the relative number of black pixels into a single number as a result of elliptic conversion. We have improved the method of parabolic conversion of dynamic images of the measured object by means of finite difference representation of Fourier’s differential equation in the second-order partial derivatives,which means a change of the current value of the pixel brightness to a new one that has two gradations of brightness––black and white. Pixel summation turns the relative number of black pixels into a single number as a result of parabolic conversion. We have used the devised methods of industrial testing of metrological support for the technological process of continuous casting of copper ingots. The testing has proved technical and economic effectiveness of the approach. The paper contains examples of technical and economic effectiveness of the devised methods in metallurgical production.

Using otolith microchemistry and shape to assess the habitat value of oil structures for reef fish

Over 7500 oil and gas structures (e.g. oil platforms) are installed in offshore waters worldwide and many will require decommissioning within the next two decades. The decision to remove such structures or turn them into reefs (i.e. ‘rigs-to-reefs’) hinges on the habitat value they provide, yet this can rarely be determined because the residency of mobile species is difficult to establish. Here, we test a novel solution to this problem for reef fishes; the use of otolith (earstone) properties to identify oil structures of residence. We compare the otolith microchemistry and otolith shape of a site-attached coral reef fish (Pseudanthias rubrizonatus) among four oil structures (depth 82–135 m, separated by 9.7–84.2 km) on Australia's North West Shelf to determine if populations developed distinct otolith properties during their residency. Microchemical signatures obtained from the otolith edge using laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) differed among oil structures, driven by elements Sr, Ba and Mn, and to a lesser extent Mg and Fe. A combination of microchemical data from the otolith edge and elliptical Fourier (shape) descriptors allowed allocation of individuals to their ‘home’ structure with moderate accuracy (overall allocation accuracy: 63.3%, range: 45.5–78.1%), despite lower allocation accuracies for each otolith property in isolation (microchemistry: 47.5%, otolith shape: 45%). Site-specific microchemical signatures were also stable enough through time to distinguish populations during 3 separate time periods, suggesting that residence histories could be recreated by targeting previous growth zones in the otolith. Our results indicate that reef fish can develop unique otolith properties during their residency on oil structures which may be useful for assessing the habitat value of individual structures. The approach outlined here may also be useful for determining the residency of reef fish on artificial reefs, which would assist productivity assessments of these habitats.

Geometric Morphometric Analysis of Population Differentiation in Two Species of Stem Borers from Bohol, Philippines

Stem borers are one of the most important insect pests that could infest rice plants from seedling to maturity and thus play a major role in crop losses. The study of its mandible that is used in feeding of stem borer would help understand the mechanisms and variations that could affect the adaptation and modification affecting severity of infestation. In this study, the mandible of two population of stem borers, the yellow stem borer (Scirpophaga incertulas and the striped stemborer (Chilo suppressalis) in three rice varieties IR-66, Pioneer 77 and Bigante were used to analyze the adaptation with regards to mandible shape in relation to rice variety in the same geographical location using outline-based (elliptic Fourier) geometric morphometric (GM) analysis to determine the shape variations in the left and right mandible of two population of stem borers. Further, scatter plot method was used to illustrate variations in the shapes of the mandibles between populations. Results of this study showed symmetrical shape variations in the right and left mandible of the two species of stem borers and their accumulation to the kind of rice plant varieties were not selective. Keywords - Animal ecology, stem borer, mandible, geometric morphometric analysis,Philippines

Vision-Based Hand Gesture Spotting and Recognition Using CRF and SVM

In this paper, a novel gesture spotting and recognition technique is proposed to handle hand gesture from continuous hand motion based on Conditional Random Fields in conjunction with Support Vector Machine. Firstly, YCbCr color space and 3D depth map are used to detect and segment the hand. The depth map is to neutralize complex background sense. Secondly, 3D spatio-temporal features for hand volume of dynamic affine-invariants like elliptic Fourier and Zernike moments are extracted, in addition to three orientations motion features. Finally, the hand gesture is spotted and recognized by using the discriminative Conditional Random Fields Model. Accordingly, a Support Vector Machine verifies the hand shape at the start and the end point of meaningful gesture, which enforces vigorous view invariant task. Experiments demonstrate that the proposed method can successfully spot and recognize hand gesture from continuous hand motion data with 92.50% recognition rate.

Silhouette differences among cats do not suggest a general selection for paedomorphosis

Abstract : Paedomorphosis is the retention of juvenile morphology at maturity and is important in generatingevolutionary change in domestic species and species in the wild. This preliminary study compared morphologicalcharacteristics of seven domestic cat pure breeds and felid species from around the world. An original procedure basedon elliptical Fourier (EF) methods was applied to head lateral views of specimens and were assessed in order to analysehead profile. For comparative purposes three domestic kittens of different ages and three species of genus Lynx werealso used. EF descriptors, allowed for the quantification of the head profile. Using the Fourier transform, reconstructionof the mean head profile revealed that there was a general shape difference between wild cats, domestic cats andkittens. Results suggested that variability in head profile differentiate quite well between adult cats and kittens, butdomestic and wild cats appeared grouped into a similar cluster. The similarity between breeds can thus be attributedmore to the general head profile than to flatness, i.e. to the general conformation rather than facial profile. Therefore,no effect of paedomorphism on the studied breeds can be undertaken. The present approach opens interestingethnological perspectives for the aloidic characterisation for domestic breeds.Keywords : aloidism, elliptic Fourier descriptors, morphology, skull

Two Classes of Elliptic Discrete Fourier Transforms: Properties and Examples

This paper analyzes the block structure of the matrix of the N-point discrete Fourier transform (DFT) in the real space R 2N . Each block of this matrix corresponds to the Givens transformation, or elementary rotation describing the multiplications by twiddle coefficients. Such rotations around the circle can be substituted by other kinds of rotations, for instance rotations around ellipses, while reserving the block-wise representation of the matrix and main properties of the DFT. To show that, we present two classes of the elliptic discrete Fourier transforms (EDFT), that are defined by different types of the Nth roots of the identity matrix 2×2, whose groups of motion move points around different ellipses. These two classes (the N-block EDFT of types I and II) are parameterized and exist for any order N. Properties and examples of application of the proposed elliptic EDFTs in signal and image processing are given.

Identifying hybridizing taxa within the Daphnia longispina species complex: a comparison of genetic methods and phenotypic approaches

Daphnia galeata Sars, D. longispina O. F. Muller and D. cucullata Sars (Crustacea: Cladocera) are closely related species which often produce interspecific hybrids in natural populations. Several marker systems are available for taxon determination in this hybridizing complex, but their performance and reliability has not been systematically assessed. We compared results from identifications by three molecular methods. More than 1,200 individuals from 10 localities in the Czech Republic were identified as parental species or hybrids by allozyme electrophoresis and the analysis of the restriction fragment length polymorphism of the internal transcribed spacer (ITS-RFLP); over 440 of them were additionally analyzed and identified by 12 microsatellite loci. Identification by microsatellite markers corresponded well with allozyme analyses. However, consistent discrepancies between ITS-RFLP and other markers were observed in two out of 10 studied localities. Although some marker discrepancies may have been caused by occasional recent introgression, consistent deviations between ITS-RFLP and other markers suggest a long-term maintenance of introgressed alleles. These results warn against its use as a sole identification method in field studies. Additionally, we quantitatively evaluated the discriminatory power of geometric morphometric (elliptic Fourier) analysis of body shapes based on photos of over 1,300 individuals pre-classified by allozyme markers. Furthermore, a randomly selected subset of 240 individuals was independently determined from photos by several experts. Despite a tendency for morphological divergence among parental Daphnia species, some taxa (especially D. galeata, D. longispina, and their hybrids) substantially overlapped in their body shapes. This was reflected in different determination success for particular species and hybrids in discriminant analysis based on shape data as well as from photographs.

Comparison of morphometric techniques for shapes with few homologous landmarks based on machine-learning approaches to biological discrimination

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 (&lt;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.

Elliptic Fourier analysis on the tympanic bullae in three Meriones species (Rodentia, Mammalia): its application in biosystematics

Abstract. The size and shape of the auditory bullae are investigated across three species of Meriones, in order to determine the biosystematic value of bulla characteristics in species recognition. This study is based on outline (geometric morphometric) with elliptical Fourier and eigenshape analysis of tympanic bullae in: (a) the suprameatal triangle, (b) the mastoid, (c) the auditory meatus, and (d) the ventral view of bullae. The results show that characters of the auditory meatus separate these three species from each other. The shape of different parts of the bullae within each species is also shown to vary such as in two populations of M. persicus. The shape of organs is important in the interaction between the organism and its environment. Tympanic bullae variation is similar in the Geno population of M. persicus (Geno is located in south of Iran), and in M. libycus which lives in similar climates. The results of this analysis of tympanic bullae differ from the characters described by CORBET (1978).