Elliptic Fourier descriptors of cell and nuclear shapes

1997 ◽  
pp. 307-321 ◽  
Author(s):  
Giacomo Diaz ◽  
Corrado Cappai ◽  
Maria Dolores Setzu ◽  
Silvia Sirigu ◽  
Andrea Diana
Keyword(s):  
Fourier Descriptors ◽  
Elliptic Fourier Descriptors

scholarly journals On the evaluation of chicken egg shape variability

2008 ◽  
Vol 56 (5) ◽  
pp. 69-74 ◽  
Author(s):  
Miroslav Havlíček ◽  
Šárka Nedomová ◽  
Jana Simeonovová ◽  
Libor Severa ◽  
Ivo Křivánek
Keyword(s):  
Shape Index ◽  
Width Ratio ◽  
Geometrical Parameters ◽  
Fourier Descriptors ◽  
Shape Variation ◽  
Egg Volume ◽  
Maximum Width ◽  
Chicken Egg ◽  
Egg Shape ◽  
Elliptic Fourier Descriptors

Although recently reported models for determining egg shape are highly accurate, certain com­pli­ca­ted measurements or computations are to be performed. Thus relatively simple and attainable analysis methods of chicken egg shape variability were chosen and used for the purpose of presented research. Sample of 250 eggs of ISA BROWN strain was examined. Geometrical parameters were measured and calculated with following expression of their coefficient of variation – namely egg length 3.56 %, egg maximum width 2.84 %, shape index 3.80 %, surface area 5.08 %, and egg volume 7.23 %. The second method consisted in shape quantitative measuring by the score of the principal components of elliptic Fourier descriptors (EFDs). The first four principles components which could explain over 99 % of the egg shape variations were found to be very good measures of the monitored phenomenon. It was found that 87.41 % of the total shape variation can be accounted to length to width ratio. Usefulness and relevance of the shape index usage was confirmed.

Shape Discrimination of Almond Cultivars by Elliptic Fourier Descriptors

2019 ◽  
Vol 61 (3) ◽  
pp. 245-256 ◽  
Author(s):  
Bünyamin Demir ◽  
Bahadır Sayinci ◽  
Necati Çetin ◽  
Mehmet Yaman ◽  
Ruçhan Çömlek
Keyword(s):  
Fourier Descriptors ◽  
Shape Discrimination ◽  
Elliptic Fourier Descriptors

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

2020 ◽  
Vol 9 (8) ◽  
pp. 482
Author(s):  
Juan Francisco Reinoso-Gordo ◽  
Rocío Romero-Zaliz ◽  
Carlos León-Robles ◽  
Jesús Mataix-SanJuan ◽  
Marcelo Antonio Nero
Keyword(s):  
Computer Vision ◽  
Information System ◽  
Geographic Information System ◽  
Least Squares ◽  
Reference Object ◽  
Fourier Descriptors ◽  
Periodic Functions ◽  
Fourier Expansions ◽  
Elliptic Fourier Descriptors ◽  
Least Squares Approach

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.

scholarly journals The Evaluation of Genotype × Environment Interactions of Citrus Leaf Morphology Using Image Analysis and Elliptic Fourier Descriptors

2002 ◽  
Vol 52 (4) ◽  
pp. 243-251 ◽  
Author(s):  
Hiroyoshi Iwata ◽  
Hirohisa Nesumi ◽  
Seishi Ninomiya ◽  
Yasushi Takano ◽  
Yasuo Ukai
Keyword(s):  
Image Analysis ◽  
Leaf Morphology ◽  
Fourier Descriptors ◽  
Citrus Leaf ◽  
Elliptic Fourier Descriptors

scholarly journals Diallel Analysis of Root Shape of Japanese Radish (Raphanus sativus L.) Based on Elliptic Fourier Descriptors.

2000 ◽  
Vol 50 (2) ◽  
pp. 73-80 ◽  
Author(s):  
Hiroshi Iwata ◽  
Satoshi Niikura ◽  
Seiji Matsuura ◽  
Yasushi Takano ◽  
Yasuo Ukai
Keyword(s):  
Raphanus Sativus ◽  
Diallel Analysis ◽  
Fourier Descriptors ◽  
Japanese Radish ◽  
Raphanus Sativus L ◽  
Elliptic Fourier Descriptors

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

2018 ◽  
Vol 69 (4) ◽  
pp. 271
Author(s):  
B. Demir ◽  
B. Sayıncı ◽  
N. Çetin ◽  
M. Yaman ◽  
R. Çömlek ◽  
...  
Keyword(s):  
Cluster Analysis ◽  
Juglans Regia ◽  
Shape Index ◽  
Fourier Descriptors ◽  
Processing Technologies ◽  
Size And Shape ◽  
Physical Attributes ◽  
Elliptic Fourier Descriptors ◽  
Multivariate Approaches ◽  
Shape Data

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.

scholarly journals Digital Morphometrics: A Tool for Leaf Morpho- Taxonomical Studies

2021 ◽  
Vol 1 (2) ◽  
pp. 1-7
Author(s):  
Kavi K. Oza ◽  
Rinku J. Desai ◽  
Vinay M. Raole*
Keyword(s):  
Principal Component Analysis ◽  
Abiotic Factors ◽  
Leaf Shape ◽  
Principal Component ◽  
Component Analysis ◽  
Herbarium Specimens ◽  
Fourier Descriptors ◽  
Shape Variation ◽  
Quantitative Analysis Method ◽  
Elliptic Fourier Descriptors

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.

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