Digital Morphometrics: A Tool for Leaf Morpho- Taxonomical Studies

Leaves are most important part of the plant and can be used for the identification of a taxon. An appropriate understanding of leaf development in terms of shape and responsible abiotic factors is necessary for improvement in plant. Leaf shape variation could be evaluated successfully, and the symmetrical and asymmetrical elements of the overall shape variation could be detected. The aim of the present study was to establish a quantitative analysis method of leaf shape by elliptic Fourier descriptors and principal component analysis (EF-PCA). EF-PCA describes an overall shape mathematically by transforming coordinate information concerning its contours into elliptic Fourier descriptors (EFDs) and summarizing the EFDs by principal component analysis. We can be able to extract six variables by using leaf specimen images from field and herbarium specimens. In the present study, total leaf area with respect to notch area is more variable within species. Within a species the major source of the symmetrical elements may be governed by genotypic features and the asymmetrical elements are strongly affected by the environment. We could discuss the value of morphometrics to detect subtle morphological variation which may be undetectable by human eye.

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

Grapevine 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.

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.

Discrimination of the species of the Crassiphycus corneus/C. usneoides complex (Gracilariaceae, Rhodophyta) through geometric morphometric analysis

The results of the discrimination by geometric morphometry of the species within the Crassiphycus corneus/C. usneoides complex is presented, from the shape of its cortical, subcortical and medullary cells in the apical, medium and basal portions of thallus. Principal component analysis, based on the elliptic Fourier descriptors of cellular outline shapes and NP-MANOVA analysis, show that only the cortical cells in the medium portion were significantly wider in C. corneus than in C. usneoides. The isoperimetric quotients (Q) indicated that these cells were significantly more circular in C. corneus than in C. usneoides. We conclude that the outline analyses efficiently recovered phenotypic differences between the species defined by molecular systematics and considered to be cryptic, so far.

Elliptic Fourier based analysis and multivariate approaches for size and shape distinctions of walnut (Juglans regia L.) cultivars

Size and shape data of agricultural crops provide great sources for food processing technologies. The physical attributes of different fruits should be known for the design, developing and innovation of food technologies. In this study, the size and shape distinctions of fifteen national and international walnut cultivars (Midland, Sütyemez-1, Serr, Maraş-18, Maraş-12, Sütyemez-2, Kaman-1, Kaman-5, Pedro, Howard, Chandler, Şebin, Şen-2, Bilecik and KR-1) were determined using elliptic Fourier and multivariate approaches. Firstly, the gravitational features of walnut cultivars were determined, and their dimensional, area and shape attributes were revealed by image processing. Cluster analysis was used to designate the walnut cultivars. Elliptic Fourier descriptors obtained from walnut outlines provided the comparisons among walnut cultivars in shape. The shape index indicated that Serr, Sütyemez-2, Midland and Şen-2 cultivars were oval-shaped, and the others were spherical. The cluster analysis divided the walnut cultivars into four subgroups. Elliptic Fourier descriptors perfectly distinguished the walnut cultivars according to shape.