GEOMETRIC ANALYSIS OF PLANAR SHAPES WITH APPLICATIONS TO CELL DEFORMATIONS

Ximo Gual-Arnau, Silena Herold-García, Amelia Simó

Abstract

Shape analysis is of great importance in many fields such as computer vision, medical imaging, and computational biology. In this paper we focus on a shape space in which shapes are represented by means of planar closed curves. In this shape space a new metric was recently introduced with the result that this shape space has the property of being isometric to an infinite-dimensional Grassmann manifold of 2-dimensional subspaces. Using this isometry it is possible, from Younes et al. (2008), to explicitly describe geodesics, a task that previously was not at all easy. Our aim is twofold, namely: to use this general theory in order to show some applications to the study of erythrocytes, using digital images of peripheral blood smears, in the treatment of sickle cell disease; and, since normal erythrocytes are almost circular and many Sickle cells have elliptical shape, to particularize the computation of geodesics and distances between shapes using this metric to planar objects considered as deformations of a template (circle or ellipse). The applications considered include: shape interpolation, shape classification, and shape clustering.

Keywords
cell deformation; geodesics; planar closed curves; radius-vector function; shape space

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DOI: 10.5566/ias.1151

Image Analysis & Stereology
EISSN 1854-5165 (Electronic version)
ISSN 1580-3139 (Printed version)