Fully Automatic Cell Segmentation with Fourier Descriptors

Cell segmentation is a fundamental problem in biology for which convolutional neural networks yield the best results nowadays. In this paper, we present HarmonicNet, a network, which is a modification of the popular StarDist and SplineDist architectures. While StarDist and SplineDist describe an object by the lengths of equiangular rays and control points respectively, our network utilizes Fourier descriptors, predicting a coefficient vector for every pixel on the image, which implicitly define the resulting segmentation. We evaluate our model on three different datasets, and show that Fourier descriptors can achieve a high level of accuracy with a small number of coefficients. HarmonicNet is also capable of accurately segmenting objects that are not star-shaped, a case where StarDist performs suboptimally according to our experiments.

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.

Echocardiography Segmentation by Fractional Differential and Improved Canny, Analysis by Fourier Descriptor

The omnidirectional M-mode echocardiogram provides a new method for human heart functional analyses. In this article, to sharpen object edges, we designed image processing kernel based on Fractional differential for image enhancement. After that, the contour of the left ventricle in a short axis is first extracted using both an improved Canny edge detection algorithm and the gray level searching algorithm in the radial direction as auxiliary. The modified Canny edge detection algorithm with the matching method between adjacent frames then is adopted for the subsequent frames to extract the left ventricular contours. The non-functional movements in the B-ultrasonic plane are determined by using the movement extracting method based on Fourier descriptors and the mass center with the inertia axis method, and the movements are removed from a compound motion. The Fourier descriptors are applied to get a series of image contour curves with the principal translation and rotation. Hence the curve of the cardiac motion can accurately show functional movements in any location of the heart. Using our technique, we can reduce multi-lines and excursion, as well as correct the omnidirectional M-mode echocardiography.

Growth stanza in fish life history using otoliths shape: the protandric Centropomus case (Carangaria: Centropomidae)

ABSTRACT Morphoanatomical or physiological changes coupled with changes in body size are known as allometric relationships. The objective of this study was to identify the points of growth changes in Centropomus based on otolith morphometry and morphogeometry. For this purpose, 455 individuals of C. undecimalis and 176 of C. parallelus were collected from artisanal fishermen of the coast of the state of Alagoas, Brazil. The sagittal otoliths were measured for length, height, perimeter, area and weighed. The potential and polyphasic models were fitted between total fish length and otolith length. The morphotypes otoliths wen describe by form Fourier descriptors and shape indices. The polyphasic model detected three growth phases. The first stanza for C. undecimalis was at 46.8 cm and the second at 75.9 cm. For C. parallelus, it was at 18.8 cm and at 41.2 cm. Each stanza has a specific otoliths morphotype in both species. The otoliths of C. undecimalis and C. parallelus exhibited ontogenetic allometric changes in their growth pattern with two stanzas changing points. The stanzas corresponded to specific lengths reached by individuals over their life cycles, such as their size at maturity and length at sexual reversion.

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.