Elliptic Fourier Descriptors Research Articles

Strawberry fruit shape: quantification by image analysis and QTL detection by genome-wide association analysis.

Fruit shape of cultivated strawberry (Fragaria × ananassa Duch.) is an important breeding target. To detect genomic regions associated with this trait, its quantitative evaluation is needed. Previously we created a multi-parent advanced-generation inter-cross (MAGIC) strawberry population derived from six founder parents. In this study, we used this population to quantify fruit shape. Elliptic Fourier descriptors (EFDs) were generated from 2 969 two-dimensional binarized fruit images, and principal component (PC) scores were calculated on the basis of the EFD coefficients. PC1–PC3 explained 96% of variation in shape and thus adequately quantified it. In genome-wide association study, the PC scores were used as phenotypes. Genome wide association study using mixed linear models revealed 2 quantitative trait loci (QTLs) for fruit shape. Our results provide a novel and effective method to analyze strawberry fruit morphology; the detected QTLs and presented method can support marker-assisted selection in practical breeding programs to improve fruit shape.

Disentangling Leaf Morphology in Daustinia montana (Convolvulaceae)

Abstract—Daustinia montana (Convolvulaceae) is the only species of the genus, and is notable for its wide leaf variability. To understand whether this plasticity is correlated with the distribution of the species, linear morphometric and leaf contour analyses were performed. Specimens from herbaria were photographed, and pre-established linear measurements were made. A multivariate analysis was then performed to test the strength of associations among morphological characteristics, climatic variables, and distribution of the species. Elliptic Fourier analysis based on 20 harmonics was used to generate shape descriptors, resulting in nine main components. With elliptic Fourier descriptors, a grouping tree was created that suggests the existence of six morphotypes in D. montana. Moreover, clustering analysis revealed two large groups distinguished mainly by leaf width. The present findings indicate that the morphotypes are strongly related to latitude and that other characteristics such as the type of indumentum are related to climatic variables.

Analysis of the grapevine (Vitis vinifera L.) berry shape by using elliptic Fourier descriptors

AbstractGrapevine berry shape has important marketing value in the table grape commerce, hence variability evaluation of this characteristic is highly important. In this study berry shape of 5 table grape genotypes: “Fanny”, “Lidi”, “Hamburgi muskotály”, “Moldova”, and “Orsi” were compared. To evaluate the shape variability graphic reconstruction and elliptic Fourier analysis have been carried out. Shape outlines have been investigated and Principal Component Analysis (PCA) has been performed with the SHAPE software package. PCA of the contours showed that 6 out of the 77 principal components were effective to describe shape attributes. The first 6 PCs explained 94.51% of the total variance. PC1 associated with the width and length of the berry. PC2 related to the shape of the top and bottom of the berries, while PC3 linked to the ratio of the top and the bottom width. ANOVA of the principal component scores revealed significant difference among the genotypes. Results suggest that morphology of the berry is a variable not only among but within the accessions. Our findings confirmed that elliptic Fourier descriptors (EFDs) would be a powerful tool for quantifying grapevine berry morphological diversity.

Differences in otolith shape and fluctuating-asymmetry between reared and wild gilthead seabream (Sparus aurata Linnaeus, 1758).

Otolith structure is a useful tool in discrimination among fish populations as it is a permanent record of the influence of endogenous and exogenous factors. In the present study we examined otolith morphology and fluctuating asymmetry (FA) for differences between wild-caught (by bottom trawl) and reared specimens of Gilthead seabream (Sparus aurata). Based on the frequency of regenerated scales (degree of scale regeneration, SRD) on each specimen, a threshold of 30% SRD was used to assign wild-caught fish individuals as wild (≤30% SRD, LR group) or as possible aquaculture escapees (>30% SRD, HR group). Based on the analysis of elliptic Fourier descriptors, significant differences were found in otolith shape between reared (Rr) and the wild-caught groups (LR, HR). Reared fish had otoliths with significantly larger perimeter (OP ) than wild-caught fish. Furthermore, FA was significantly higher in the Rr than the LR group for OP and all except one shape descriptors (harmonics 2-7). The HR group exhibited intermediate levels of FA between the low and high FA levels observed in the LR and Rr groups. Results are discussed in terms of the value of combining otolith and scale morphology for the identification of escapees in wild Gilthead seabream stocks.

Morpho-chronology of monogenetic scoria cones from their level contour curves. Applications to the Chichinautzin monogenetic field, Central Mexico

The genesis, distribution and hazards associated with monogenetic volcanic fields pose particular difficulties derived from their dispersed character. Establishing a relationship between the spatial and the age distributions of volcanic cones is necessary both to understand the nature of monogenetic field formation and evolution and to set supported hazard-assessment criteria. We present here a new method –specifically developed to quantify the degree of age-dependent erosion of individual scoria cones– aimed to estimate the relative ages of undated scoria cones in a monogenetic volcanic field from a contour level morphometric analysis of the field digital elevation model (DEM). This method is based on the hypothesis that age and the degree and type of erosion causing significant morphological changes on scoria cones are markedly correlated. It is assumed that, at the time of their formation, monogenetic volcanoes have diverse, yet smooth shapes, which mechanical processes of wearing gradually change in different spatial scales. This evolution is largely evidenced both as changes of the volcano slopes and as height-dependent undulations of the cone surface generated by the hydrometeorological ablation in the otherwise uniform elevation contour lines. Here, we characterize the time-dependence of the shape and size of the altitude isoline undulations by means of the Elliptical Fourier Descriptor spectra of the contour curves of volcanic cones. To test the effects of the DEM data type and resolution on this morpho-chronological dating, we analyze the correlations of published radiometric ages of cones with two datasets of contour curves from the Sierra Chichinautzin monogenetic volcanic field in Central Mexico (SCVF): one obtained from airborne LIDAR surveys (INEGI, Mexico) and the other from a satellite radar mission (DLR, Germany).

Shape difference of mud clasts depending on depositional facies: application of newly modified elliptic Fourier analysis to hybrid event beds

ABSTRACT Hybrid event beds are the deposits from sediment gravity flows that change their rheological behavior through their passage, entraining muddy sediments and damping turbulence. Muddy facies of hybrid event beds are often associated with abundant mud clasts which show a wide variety of size and shape. The variation of clast occurrence in hybrid event beds is expected to preserve the information of entrainment and transport processes of muddy sediments in submarine density currents. However, previous analyses of hybrid event beds have focused on describing the overall clast occurrence rather than the statistical size and shape analyses because traditional shape parameters are incapable of characterizing the complex shape of mud clasts. Here, a new quantitative grain-shape analysis of mud clasts is conducted and allows visualization of the spatial variation of clast size and shape, which suggests the wide variety of origin and transport systems of entrained mud clasts. This new method revises the traditional elliptic Fourier analysis, substituting Fourier power spectra (FPS) for traditional elliptic Fourier descriptors to overcome the mirror-wise shape problem. Further, principal-component analysis is shown to capture significant shape attributes more effectively than traditional shape parameters. The proposed method is applied to mud clasts in sediment-gravity-flow deposits in the lower Pleistocene Otadai Formation, central Japan. Results imply that there are distinctive shape and size differences of mud clasts that are strongly associated with depositional facies rather than the distance from the source. The clasts have a higher angularity than other facies in the debrite intervals in hybrid event beds. It is also shown that clasts in sandy, structureless facies have different characteristics in shapes based on elongation and convexity compared to laminated facies. Comparison between different shape-analysis methods demonstrates that none of the traditional methods are able to visualize these trends as effectively as the method presented herein. These results highlight the importance of the quantitative shape analysis of sediment grains and the effectiveness of FPS-based elliptic Fourier analysis.

Fourier-Based Automatic Transformation between Mapping Shapes—Cadastral and Land Registry Applications

Sometimes it is necessary to know the transformation to apply to a mapping shape in order to locate its true place. Such an operation can be computed if a corresponding reference object exists and we can identify corresponding points in both shapes. Nevertheless our approach does not need to match any corresponding point beforehand. The method proposed defines a polygon in the frequency domain—two periodic functions are derived from a polygonal or polygon. According to the theory of elliptic Fourier descriptors those two periodic functions can be expressed by Fourier expansions. The transformation can be computed using the coefficients of the harmonics from the corresponding shapes without taking into account where each polygon vertex is placed in the spatial domain. The transformation parameters will be derived by a least squares approach. The geomatics and geosciences applications of this method go from photogrammetry, geographic information system, computer vision, to cadaster and real estates.

A Hybrid Wind Load Estimation Method for Container Ship Based on Computational Fluid Dynamics and Neural Networks

The estimation of wind loads on ships and other marine objects represents a continuous challenge because of its implication for various aspects of exposed structure exploitation. An extended method for estimating the wind loads on container ships is presented. The method uses the Generalized Regression Neural Network (GRNN), which is trained with Elliptic Fourier Descriptors (EFD) of sets of frontal and lateral closed contours as inputs. Wind load coefficients (Cx, Cy, CN), used as outputs for network training, are derived from 3D steady RANS CFD analysis. This approach is very suitable for assessing wind loads on container ships wherever there is a wind load database for a various container configuration. In this way, the cheaper and faster calculation can bridge the gap for the container configurations for which calculations or experiments have not already been made. The results obtained by trained GRNN are in line with available experimental measurements of the wind loads on various container configuration on the deck of a 9000+ TEU container ship obtained through a series of wind tunnel tests, as well as with performed CFD simulation for the same conditions.

Identifying Chagas disease vectors using elliptic Fourier descriptors of body contour: a case for the cryptic dimidiata complex

BackgroundTriatoma dimidiata (Reduviidae: Triatominae) is an important vector of Chagas disease in various countries in the Americas. Phylogenetic studies have defined three lineages in Mexico and part of Central America. While there is a marked genetic differentiation, methods for identifying them using morphometric analyses with landmarks have not yet been fully resolutive. Elliptical Fourier descriptors (EFDs), which mathematically describe the shape of any closed two-dimensional contours, could be a potentially useful alternative method. Our objective was to validate the use of EFDs for the identification of three lineages of this species complex.MethodA total of 84 dorsal view images of individuals of the three lineages were used. Body contours were described with EFDs using between 5 and 30 harmonics. The number of obtained coefficients was reduced by a principal components analysis and the first axis scores were used as shape variables. A linear discriminant function analysis and an ordination plot of the discriminant analysis were performed using the shape variables. A confusion matrix of the ordination plot of the discriminant analysis was obtained to estimate the classification errors, the first five PC scores were statistically compared, and a neural network were then performed using the shape variables.ResultsThe first principal component explained 50% of the variability, regardless the number of harmonics used. The results of discriminant analysis get improved by increasing the number of harmonics and components considered. With 25 harmonics and 30 components, the identification of haplogroups was achieved with an overall efficiency greater than 97%. The ordering diagram showed the correct discrimination of haplogroups, with only one error of discrimination corroborated by the confusion matrix. When comparing the first five PC scores, significant differences were found among at least two haplogroups. The 30 multilayer perceptron neural networks were also efficient in identification, reaching 91% efficiency with the validation data.ConclusionsThe use of EFD is a simple and useful method for the identification of the main lineages of Triatoma dimidiata, with high values of correct identification.

Comparative analysis of otolith morphology in icefishes (Channichthyidae) applying different statistical classification methods

The genus Chionodraco includes three morphologically similar species, two of them (C. hamatus and C. myersi) living sympatrically in the Eastern Antarctica, and the third one (C. rastrospinosus) being distributed in the Western Antarctica along the southern Scotia Arc. The few overlapping diagnostic characters are often useless for the right taxonomic identification of three species, complicated by the presence of hybrids between them. In the present study, we tested the discrimination power of sagittal otolith shape as a tool to distinguish among these closely related species. An array of shape indices and elliptic Fourier descriptors were individually obtained from sagittal otoliths and analysed using three different models for species classification: Linear Discriminant Analysis (LDA), Random Forest (RF) and K-nearest neighbour (KNN). According to the characteristics of the adopted metric (precision), none of the methods resulted to be the absolute best approach as the performance largely varied with the species. The overall precision was 63 %, 66 % and 70 % for LDA, RF and KNN respectively, so that KNN can be considered the best classifier model. As expected, C. myersi was the best recognized species by all classifier models, consistently with its morphological and phylogenetic difference from the other two species. Taking into account the observed pattern of otolith morphology of the three species and their own geographical distribution, we were able to evaluate the role of genetic, endogenous or environmental components in influencing otolith size and shape.

Population structure and habitat connectivity of Genidens genidens (Siluriformes) in tropical and subtropical coasts from Southwestern Atlantic

We use otolith trace element-to-calcium element concentraton ratios (Ba:Ca, Cu:Ca, Mg:Ca, Mn:Ca, Ni:Ca, Sr:Ca and Zn:Ca) and shape to evaluate the degree of segregation and presence of different nursery areas and fish stocks of Genidens genidens in the Brazilian coastal area. Otolith core (juvenile stage) and edge (adult stage) element:Ca fingerprints (N = 89), as well as otolith elliptic Fourier descriptors (N = 147) were compared between four estuaries. Several element:Ca ratios were significantly different between estuaries for otolith core and edge (p < 0.05). MANOVA, PERMANOVA, linear and quadratic discriminant analyses based on Fourier descriptors (12 harmonics) and microchemistry were effective for discriminating between all sampling sites (p < 0.05), except Itapanhaú River and Paranaguá Bay (p > 0.05). The discriminant analyses showed jackknifed classification from 54.1% to 100% considering young (core microchemistry) and adult life stages (edge microchemistry and shape). When otolith microchemistry and shape were combined, the jackknifed classification increased in relation to the separates methods, ranged from 89.5 to 100% (mean 95.2%). The high degree of segregation (low connectivity) in juvenile and adult stages between the estuaries is consistent with the presence of isolated populations, and advocates for estuary-specific management strategies.

Detecting prostate cancer using deep learning convolution neural network with transfer learning approach.

Prostate Cancer in men has become one of the most diagnosed cancer and also one of the leading causes of death in United States of America. Radiologists cannot detect prostate cancer properly because of complexity in masses. In recent past, many prostate cancer detection techniques were developed but these could not diagnose cancer efficiently. In this research work, robust deep learning convolutional neural network (CNN) is employed, using transfer learning approach. Results are compared with various machine learning strategies (Decision Tree, SVM different kernels, Bayes). Cancer MRI database are used to train GoogleNet model and to train Machine Learning classifiers, various features such as Morphological, Entropy based, Texture, SIFT (Scale Invariant Feature Transform), and Elliptic Fourier Descriptors are extracted. For the purpose of performance evaluation, various performance measures such as specificity, sensitivity, Positive predictive value, negative predictive value, false positive rate and receive operating curve are calculated. The maximum performance was found with CNN model (GoogleNet), using Transfer learning approach. We have obtained reasonably good results with various Machine Learning Classifiers such as Decision Tree, Support Vector Machine RBF kernel and Bayes, however outstanding results were obtained by using deep learning technique.

Cultivar discrimination of litchi fruit images using deep learning

Litchi (Litchi chinensis Sonn.) originated from China and many of its cultivars have been produced in China so far during the long history of cultivation. One problem in litchi production and research is the worldwide confusion regarding litchi cultivar nomenclature. Because litchi cultivars can be described in terms of cultivar-dependent fruit appearance, it should be possible to discriminate cultivars of postharvest fruits. In this study, we explored this possibility using recently developed deep learning technology for four common Taiwanese cultivars 'Gui Wei', 'Hei Ye', 'No Mai Tsz', and 'Yu Her Pau'. First, we quantitatively evaluated litchi fruit shapes using elliptic Fourier descriptors and characterized the relationship between cultivars and fruit shapes. Results suggest that 'Yu Her Pau' can be clearly discriminated from others mainly based on its higher length-to-diameter ratio. We then fine-tuned a pre-trained VGG16 to construct a cultivar discrimination model. Relatively few images were sufficient to train the model to classify fruit images with 98.33% accuracy. We evaluated our model using images of fruits collected in different seasons and locations and found the model could identify 'Yu Her Pau' fruits with 100% accuracy and 'Hei Ye' fruits with 84% accuracy. A Grad-CAM visualization reveals that this model uses different cultivar-dependent regions for cultivar recognition. Overall, this study suggests that deep learning can be used to discriminate litchi cultivars from images of the fruit.

Recognising mollusc shell contours with enlarged spines: Wavelet vs Elliptic Fourier analyses

Gastropod shells may present large spines and sharp shapes that vary according to environmental, taxonomic, and evolutionary factors. In these cases, classic morphometric methods used to study shell contour might not provide a clear representation of morphological shell based on angular decomposition of contour. The present study analyzed and compared for the first time the robustness of the contour analysis using wavelet transformed and Elliptic Fourier descriptors for gastropod shells including enlarged spines. For that, we analyzed two geographical and ecological separated populations of Bolinus brandaris from the NW Mediterranean Sea. Results showed that contour analysis of gastropod shells with enlarged spines can be analyzed using both methodologies, but the wavelet analysis provided a better local discrimination. From an ecological perspective, shells with spines of different sizes were observed in both localities suggesting a wide plasticity of the species.

Long-term temporal stability of Northeast Arctic cod (Gadus morhua) otolith morphology

Abstract Otolith shape analysis provides a robust tool for the discrimination of many fish stocks in the context of fisheries management. However, there has been little research to examine within-stock temporal stability of otolith morphology in relation to changes in the environment and stock conditions. This study investigated the variability of Northeast Arctic (NEA) cod (Gadus morhua) otolith shape between 1933 and 2015, using elliptical Fourier descriptors extracted from archived material of 2968 mature fish. Series of hierarchical multivariate models were developed to relate shape to the identified optimal windows of some environmental drivers. Differences between years accounted for &amp;lt;3% of the observed variation and no significant differences were found between the average cohort shapes. The models not only confirmed that fish growth was the strongest driver of shape differences, but also highlighted effects of temperature and biomass-related variables at different life stages. Extrinsic factors described only a small fraction of the observed variance, which indicates that environmental changes over time likely account for less than the natural inter-individual variability in otolith shape. These results suggest that overall shape remains relatively stable through time within NEA cod, which further contributes towards a consensus on the biological interpretation of shape differences.

Reprint of: Morphometric approaches to promote the use of exotic germplasm for improved food security and resilience to climate change: A kura clover example

Adaptation of agriculture to climate change and its associated ecological pressures will require new crops, novel trait combinations, and previously unknown phenotypic attributes to deploy in climate resilient cropping systems. Genebanks, a primary source of exotic germplasm for novel crops and breeding materials, need comprehensive methods to detect novel and unknown phenotypes without a priori information about the species or trait under consideration. We demonstrate how persistent homology (PH) and elliptical fourier descriptors (EFD), two morphometric techniques easily applied to image-based data, can serve this purpose by cataloging leaf morphology in the USDA NPGS kura clover collection and demarcating a leaf morphospace for the species. Additionally, we identify a set of representative accessions spanning the leaf morphospace and propose they serve as a kura clover core collection. The core collection will be a framework for monitoring the effects of climate change on kura clover in situ diversity and determining the role of ex situ accessions in modern agriculture.

CHOG Based EFD for Geometric Shape Retrieval of Images for Cloth and Object Invariant Gait Recognition

Gait refers to person identification based on the observation of human walking style. One of the prominent hurdles in gait recognition is, the challenges posed by change in apparels like clothes and object held by the subject. The paper explores the feature extraction techniques like CHOG and Elliptical Fourier Descriptors in spatial and frequency domain respectively to mitigate this negative impact on gait recognition. The CHOG behavioural feature extraction technique is used to capture the effective distribution of local gradient on gait sequence images. Further the Elliptical Fourier Descriptor (EFD) is found in frequency domain to access the geometric characteristics of a spatial domain image. The work is carried out on 36 subjects with 5 different apparels and 3 different objects each with 6 gait cycles from standard dataset CASIA SET – B and CMU - MoBo. SVM classifier is used to effectively discriminate the gait cycle patterns using optimal hyper plane. The results obtained have given an improvement of 7% to 24% increase in gait recognition over earlier techniques like GEI, CDA, LDA, ENTROPY, static and dynamic region splitting.

Morphometric approaches to promote the use of exotic germplasm for improved food security and resilience to climate change: a kura clover example

Adaptation of agriculture to climate change and its associated ecological pressures will require new crops, novel trait combinations, and previously unknown phenotypic attributes to deploy in climate resilient cropping systems. Genebanks, a primary source of exotic germplasm for novel crops and breeding materials, need comprehensive methods to detect novel and unknown phenotypes without a priori information about the species or trait under consideration. We demonstrate how persistent homology (PH) and elliptical Fourier descriptors (EFD), two morphometric techniques easily applied to image-based data, can serve this purpose by cataloging leaf morphology in the USDA NPGS kura clover collection and demarcating a leaf morphospace for the species. Additionally, we identify a set of representative accessions spanning the leaf morphospace and propose they serve as a kura clover core collection. The core collection will be a framework for monitoring the effects of climate change on kura clover in situ diversity and determining the role of ex situ accessions in modern agriculture.

Population structure of Chelidonichthys lucerna in Portugal mainland using otolith shape and elemental signatures

ABSTRACTThe tub gurnard, Chelidonichthys lucerna, is considered the most important commercial fish species of the family Triglidae captured by the Portuguese traditional fisheries. However, the data available about its population structure, movement patterns and habitat connectivity is, at present, scarce. In this study, otolith chemistry and shape analyses of 90 individuals captured, between March and June 2016, in the three main fishing grounds of the Portuguese mainland coast (Matosinhos, Aveiro and Peniche) were investigated. Otolith morphological (shape indices and elliptic Fourier descriptors) and elemental (Ba:Ca, Fe:Ca, Mg:Ca, Mn:Ca, Sr:Ca and Zn:Ca) signatures of individuals with similar length range were assessed through uni and multivariate statistical tests. The overall combination of otolith elemental chemistry and morphology techniques revealed the highest re-classification success (74%) of samples to their original location and the existence of significant differences among sampling regions. However, linear discrimination function analyses and canonical analyses of principal coordinates did not fully discriminate C. lucerna individuals from the three sampling regions of Portugal. Moreover, the hereby data revealed a partial overlap among individuals from the different sampling regions. The obtained shape and chemical signatures suggest that C. lucerna is apparently a unique, although not necessarily homogenous, single population-unit in Portugal mainland, and that these fish populations should not be managed separately for fisheries purposes.

Two new methodological approaches for assessing skeletal maturity in archeological human remains based on the femoral distal epiphysis

This study presents two new methodological approaches for estimating skeletal age from maturational changes in the femoral distal epiphysis. In the first approach, five maturity stages were coded based on morphological changes in the epiphysis that encompass the overall developmental process. Data were presented as age ranges for the different maturity stages in the reference sample. As this approach has a number of shortcomings for age assessment, a probabilistic approach was also used. Cross-validation was then used to compare the accuracy of the age estimation from the maturity stages with that from Pyle and Hoerr’s atlas. This study’s findings showed that Pyle and Hoerr’s atlas is more precise than our qualitative method in the oldest age categories. Nonetheless, results from the test of agreement between methods showed that skeletal age estimates from both methods are interchangeable. In the second approach, the overall shape of the femoral distal epiphyses was first analyzed based on elliptical Fourier descriptors (EFDs). Since the number of EFDs is excessively large, a principal component analysis (PCA) of these EFDs was carried out. PC1 scores were used to model the relationship between age and overall shape in a sample of 110 cases of the femoral distal epiphysis. Inverse and classical regression methods of calibration were used to explore the relationship. Based on our results, we recommend the use of a classical calibration model for those cases in which we suspect that the growth and development of the target individual is advanced or delayed relative to those of the Portuguese sample. Otherwise, the inverse calibration model is preferable. Both, quantitative and qualitative methods presented herein notably improve our abilities to estimate skeletal age using incomplete femora from skeletal samples.