A spectral framework for sperm shape characterization
Introduction
Aimed at optimizing the speed and accuracy while avoiding the intrinsic subjectivity of human operators, computational semen analysis has been increasingly considered as a routine procedure in several research and diagnostic laboratories. Originally oriented to sperm motility, several software applications can be found currently that are capable of performing additional morphological analysis in automated or semi-automated fashion. While many such programs concentrate on the geometric properties of the sperm head, some of them also allow the characterization of alterations in the sperm tail, identifying total length, irregular shapes (bent and coiled tail), as well as the presence of cytoplasm droplets [1], [2], [3].
Several measurements have been considered for sperm morphology characterization and analysis. Typically, off-the-shelf programs estimate traditional basic features such as area, perimeter, length and width, as well as derived measurements including width–length ratio, roundness, ellipticity and shape factor, among others. More sophisticated geometrical features such as Fourier descriptors and symmetry have also been considered [4].
As human sperm heads are predominantly elliptical, little attention is generally given to the placement of tail implantation. Because several of the currently available software programs for animal sperm analysis are adaptations of human sperm analysis software, few resources are usually available for the characterization of tail implantation. At the same time, several commercial species such as bovine, rams and ovine present an oval head with a plan extremity (head basis) with characteristic central tail implantation. Displaced implantations (abaxial) generally interfere with sperm motility, with obvious implications for fertility [5]. Another typical abnormality is the narrowing of the head basis [5]. As a consequence of difficulties for properly identifying the basal region and the tail implantation position, the estimation of geometrical measurements characterizing such important alterations is seldom available in commercial software.
Morphometric characterization of the sperm head is frequently used for male fertility evaluation in human and veterinary medicine, being frequently enhanced by application of computational means. Detailed study of these features suggests the existence of correlations between the phylogeny and sperm shape [6]. Combinations of the morphometric features make possible separation of spermatozoa of different species. Such combinations generally possess high sensitivity in the identification of the carrying spermatozoa morphologic abnormalities, therefore representing an important resource for the evaluation of male fertility.
Introduced by Costa [7], [8], the spectral approach to multiscale curvature estimation provides a natural means for the identification and characterization of sperm morphology. The method is based on the derivative property of the Fourier transform, which is applied over smoothed (i.e. low-pass filtered) versions of the contour of the object. As a Gaussian function is used as low-pass filter kernel, its standard deviation defines a spatial scale parameter that can be used to control the level of detail considered in the analysis, allowing effective removal of small scale noise implied by the spatial quantization of the object when captured as a digital image. The special importance of the curvature for vertex identification stems from the fact that these features of the object contour are characterized by peaks of curvature [9]. As such, the technique allows a natural means to identify not only the placement of the tail implantation, but also the two vertices characterizing the sperm head basal region. In addition, the multiscale bending energy [10] of the frontal portion of the sperm head contour can be obtained as an immediate byproduct of the methodology. The bending energy provides an interesting conceptual interpretation as being proportional to the amount of energy one has to apply to a circle in order to transform it into the object under analysis.
The present article describes how the multiscale curvature and the closely related multiscale bending energy, numerically estimated by a spectral method, can be used for sperm shape analysis, more specifically as a means of quantifying the tail implantation, width of basal region, and energy of the frontal portion of the sperm head.
This paper starts with a description of the multiscale curvature and its application to sperm morphometric characterization (Section 2.1), making possible the vertex head detection (Section 2.2). Then we present new morphometric measures (Section 2.3) that, when applied to bovine, caprine, ovine and canine sperm are evaluated considering diverse combinations. These measurements allowed the descrimination of several species of spermatozoa, as well as respective subpopulations.
Section snippets
Spectral curvature estimation
The sperm contour is henceforth assumed to be represented as the parametric curve defined by the Cartesian coordinates (x(s),y(s)) of each of its elements, where s is the arc-length parameter. Such a representation can be obtained by using standard cell segmentation and contour following algorithms such as those described in [9], [11]. The curvature of a parametric contour is formally defined as in Eq. (1), which is irrespective of the adopted parameterization
Experimental results
The methods used for identification of the sperm head vertices are verified to be generally effective, as demonstrated in Fig. 1. The results were plotted considering two-by-two combinations of the measurements, as shown in Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8. Fig. 3 shows the cluster distribution obtained considering ε(σ=3) and ε(σ=5), allowing good separation between the species, mainly along the y-axis (related to ε(σ=5)), as well as the presence of spermatozoa displaced from the
Conclusions
This article reports on the application of a spectral approach for multiscale curvature estimation to the characterization of animal sperm head geometry, with special attention given to the width of the basal portion, centralization of tail implantation, and energy of the frontal portion of the head. Given their potential for diagnosis and phylogenetic investigations, such measures can assist investigations on animal fertility, which had been previously constrained by most of the existing
Summary
The characterization of sperm morphology is of great importance for objective and quantitative analysis of fertility of individuals, as well as for phylogenetic studies. The present work describes how a spectral approach to derivative estimation has been used to obtain particularly relevant measurements of sperm head morphology. The methodology involves extracting the sperm head outlines and using the Fourier transform to estimate its first and second derivatives, from which the respective
Acknowledgements
Luciano da F. Costa and Marcelo E. Beletti are grateful to Conselho Nacional de Desenvolvimento Cientı́fico e Tecnológico - CNPq (308231/03-1, 150020/02-3 and 350058/03-2) and Fundação de Amparo à Pesquisa do Estado de São Paulo - FAPESP (99/12765-2) for financial support.
Marcelo Emı́lio Beletti is an Adjunct Professor at the Federal University at Uberlândia, MG, PhD at the Cell Biology, and has 5 papers in international journals. His principal interests include Theriogenology, Biological Morphology and Image Analysis.
References (12)
- et al.
Piecewise linear segmentation of digital contours in O(N.LOG(N)) trough technique based on effective digital curvature estimation
Real-Time Imaging
(1995) - et al.
Comparison of the Sperm Quality Analyzer IIC variables with the computer-aided sperm analysis estimates
Int. J. Androl.
(2002) - et al.
Variation in semen parameters derived from computer-aided semen analysis, within donors and between donors
J. Androl.
(2001) - et al.
Relationship of bull fertility to sperm nuclear shape
J. Androl.
(2001) - et al.
Measurements of bovine sperm nuclear shape using Fourier harmonic amplitudes
J. Androl.
(2001) - et al.
Reproduction in Farm Animals
(2000)
Cited by (14)
Automatic classification of human sperm head morphology
2017, Computers in Biology and MedicineCitation Excerpt :About morphological characterization of sperm heads, Beletti et al. [33] described the morphology of sperm heads using features such as: head area, perimeter, width, length, aspect ratio, ellipticity, shape factor, width of sperm basis, the three first Fourier values, side and anterior-posterior symmetry and hydrodynamic coefficient. In [32], the authors characterized the animal sperm head shape using a multiscale curvature estimation. They showed how a spectral approach to estimate the derivative property of the Fourier transform is useful for extracting relevant features for sperm head morphology assessment.
Assessment of acrosome state in boar spermatozoa heads using n-contours descriptor and RLVQ
2013, Computer Methods and Programs in BiomedicineCitation Excerpt :Following this idea, a number of digital image processing methods have been suggested for the segmentation, description and classification of sperm cells. Examples of this are the publications of Beletti et al., where the authors describe the spermatozoa head's morphology [9], while in [10], they characterize the animal sperm shape using a multiscale curvature estimation. Other authors, such as Linneberg et al. [11] describe the human sperm head morphology using invariant Fourier descriptors grouped in energy bands classifying them by means of neural networks.
Texture and moments-based classification of the acrosome integrity of boar spermatozoa images
2012, Computer Methods and Programs in BiomedicineCitation Excerpt :These approaches were first designed for human semen analysis [1], but they have been currently adapted to other species [2]. These systems are essentially based on parameters such as motility or morphometry [3–6], as they are directly related to the semen quality. However, up to our knowledge, the evaluation of the acrosome integrity of the spermatozoon heads is carried out manually, using stains and there are not any computer assisted tools for that analysis.
Automatic classification of the acrosome status of boar spermatozoa using digital image processing and LVQ
2008, Computers in Biology and MedicineCut-off values for normal sperm morphology and toxicology for automated analysis of rat sperm morphology and morphometry
2018, Biotechnic and HistochemistryUsing sperm morphometry and multivariate analysis to differentiate species of gray Mazama
2016, Royal Society Open Science
Marcelo Emı́lio Beletti is an Adjunct Professor at the Federal University at Uberlândia, MG, PhD at the Cell Biology, and has 5 papers in international journals. His principal interests include Theriogenology, Biological Morphology and Image Analysis.
Luciano da Fontoura Costa is an Associate Professor at the Institute of Physics at São Carlos, University of São Paulo, where he coordinate the Cybernetic Vision Research Group, which he founded in 1993. He has about 100 papers in international journals and belongs to the editorial board of Journal of Real-Time Imaging (Elsevier), EURASIP Applied Signal Processing (EURASIP-Hindawi), Journal of Intelligent and Fuzzy Systems (IOS), Psyche (The MIT Press), Neuroinformatics (Humana Press) and Journal of Integrative Neuroscience (World Scientific), being one of the Associate Editors of the latter. He has authored, jointly with Roberto M. Cesar Jr, the book Shape Analysis and Classification (CRC Press, 2001). His main interests include Neuroinformatics, Bioinformatics, Computer Vision, Signal Processing, Physical Modeling and Pattern Recognition.
Matheus Palhares Viana is an undergrad student at the Physics Department, Federal University at São Carlos, and is interested in Image Analysis and Physical Applications.