Morphological Analysis of Cells by Means of an Elastic Metric in the Shape Space
DOI:
https://doi.org/10.5566/ias.2183Keywords:
elastic metric, erythrocyte deformation, geodesics, planar closed curves, shape space, SRVFAbstract
Shape analysis is of great importance in many fields, such as computer vision, medical imaging, and computational biology. This analysis can be performed considering shapes as closed planar curves in the shape space. This approach has been used for the first time to obtain the morphological classification of erythrocytes in digital images of sickle cell disease considering the shape space S1, which has the property of being isometric to an infinite-dimensional Grassmann manifold of two-dimensional subspaces (Younes et al., 2008), without taking advantage of all the features offered by the elastic metric related to the possibility of stretching and bending of the curves. In this paper, we study this deformation in the shape space, S2, which is based on the representation of closed planar curves by means of the square-root velocity function (SRVF) (Srivastava et al., 2011), using the elastic metric of this space to obtain more efficient geodesics and geodesic lengths between planar curves. Supervised classification with this approach achieved an accuracy of 94.3%, classification using templates achieved 94.2% and unsupervised clustering in three groups achieved 94.7%, considering three classes of erythrocytes: normal, sickle, and with other deformations. These results are better than those previously achieved in the morphological analysis of erythrocytes and the method can be used in different applications related to the treatment of sickle cell disease, even in cases where it is necessary to study the process of evolution of the deformation, something that can not be done in a natural way in the feature space.
References
Aziz Toma S (2013). Using aspect ratio to classify red blood images. IOSR J Comput Eng13:30-33.
Bauer M, Bruveris M, Marsland S, Michor PW (2014). Constructing reparametrization invariant metrics on spaces of plane curves. Differ Geom Appl, 34C:139-65.
Bauer M, Bruveris M, Harms P, Møller-Andersen J (2017). A numerical framework for Sobolev metrics on the space of curves. SIAM J. Imaging Sci. 10 (1):47–73.
Bauer M, Bruveris M, Charon N, Møller-Andersen J (2019). A relaxed approach for curve matching with elastic metrics. ESAIM: COCV. 25 (72):1-24.
Dalvi PT, Vernekar N (2016). Computer aided detection of abnormal red blood cells. In Proceedings 2016 IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology (RTEICT), Bangalore:1741-46.
Delgado-Font W, González-Hidalgo M, Herold-Garcia S, Jaume-i-Capó A, Mir A (2016). Erythrocytes morphological classification through HMM for sickle cell detection. International Conference on Articulated Motion and Deformable Objects (AMDO), LNCS: 9756:88-97.
Durant TJS, Olson EM, Schulz WL, Torres R (2017). Very deep convolutional neural networks for morphologic classification of erythrocytes. Clin Chem 63:1847-55.
Fernández K, Herold-Garcia S, Fern ández A, Escobedo M, Coello G, Marrero P (2013). Estudio Morfológico en Muestras de Sangre Periférica. In V Latin American Congress on Biomedical Engineering CLAIB 2011, Cuba. IFMBE Proceedings 33:543-46. Reading: Springer, Berlin, Heidelberg.
Frejlichowski D (2010). Pre-processing, extraction and recognition of binary erythrocyte shapes for computer-assisted diagnosis based on MGG images. In International Conference on Computer Vision and Graphics, Poland 2010, Part I. LNCS 6374:368–75.
Gonzalez-Hidalgo M, Guerrero-Pena FA, Herold-Garcia S, Jaume-i-Capó A, Marrero-Fernandez P (2015). Red blood cell cluster separation from digital images for use in sickle cell disease. IEEE J Biomed Health Inform 19:1514-25.
Gual-Arnau X, Herold-Garcia S, Simó A (2013). Shape description from generalized support functions. Pattern Recogn Lett 34:619-26.
Gual-Arnau X, Herold-Garcia S, Sim ó A (2015a). Erythrocyte shape classification using integral-geometry-based methods. Med Biol Eng Comput 53:623-33.
Gual-Arnau X, Herold-Garcia S, Sim ó A (2015b). Geometric analysis of planar shapes with applications to cell deformations. Image Anal Stereol 34(3):171-82.
Joshi SH, Srivastava A, Klassen E, Jermyn I (2007). A Novel Representation for Computing Geodesics Between n-Dimensional Elastic Curves. In 2007 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Minneapolis.
Kurtek S, Needham T (2020). Simplifying transforms for general elastic metrics on the space of plane curves. SIAM J Imaging Sci (to appear). Arxiv:1803.10894.
Laga H, Kurtek S, Srivastava A, Golzarian M, Miklavcic SJ (2012). A Riemannian Elastic Metric for Shape-Based Plant Leaf Classification. In 2012 International Conference on Digital Image Computing Techniques and Applications (DICTA), Fremantle, WA:1-7.
Mazalan SM, Mahmood NH, Razak MAA (2013). Automated red blood cells counting in peripheral blood smear image using circular Hough transform. In 2013 IEEE 1stInternational Conference on Artificial Intelligence, Modelling and Simulation:320-24.
Mio W, Srivastava A, Joshi S (2007). On shape of plane elastic curves. Int J Comput Vision. 73(3):307-24.
Neretin YA (2001). On Jordan angles and the triangle inequality in Grassmann manifold. Geometriae Dedicata 86:81–92.
Pennec X (2006). Intrinsic statistics on Riemannian manifolds: basic tools for geometric measurements. J Math Imaging Vis 25:127–54.
Rahmat RF, Wulandari FS, Faza S, Muchtar MA, Siregar I (2018). The morphological classification of normal and abnormal red blood cell using self-organizing map. IOPConf Series: Mater Sci Eng 308:012015.
Sarrafzadeh O, Dehnavi AM. Rabbani H, Ghane N, Talebi A (2015). Circlet based framework for red blood cells segmentation and counting. In 2015 IEEE Workshop Signal Processing Systems:16. Reading: IEEE.
Srivastava A, Klassen E, Joshi SH, Jermyn IH (2011). Shape analysis of elastic curves in Euclidean spaces. IEEE Trans. on Pattern Analysis and Machine Intelligence.33:1415–28.
Srivastava A, Klassen E (2016). Functional and Shape Data Analysis. Reading: Springer-Verlag, New York.
Wheeless L, Robinson R, Lapets OP, Cox C, Rubio A, Weintraub M, Benjamin LJ (1994). Classification of red-blood-cells as normal, sickle, or other abnormal, using a single image-analysis feature. Cytometry 17:159-66.
Younes L, Michor PW, Shah J, Mumford D (2008). A Metric on Shape Space with Explicit Geodesics. Rend Lincei Mat Appl 39:25–5.
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