Geometric analysis of planar shapes with applications to cell deformations

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

Análisis de desempeño de segmentación sobre imágenes de muestras de sangre periférica

La sicklemia es una enfermedad con alta incidencia en la población cubana. Se caracteriza por la deformación del eritrocito y puede estudiarse empleando técnicas automatizadas para análisis de imágenes de sangre, que dependen de la calidad de los bordes detectados. En este trabajo se propone un estudio comparativo sobre el desempeño de cuatro métodos de segmentación (Umbralización, Mean-Shift, Level-Set y Chan-Vese) aplicados a este tipo de imágenes. La experimentación permitió demostrar la superioridad del método Mean-Shift, los resultados fueron evaluados empleando métricas de media, varianza, distancia de Baddeley e índice de Jaccard y Dice

Measure of Segments which Intersect a Convex Body from Rotational Formulae

Classical problems in integral geometry and geometric probability involve the kinematic measure of congruent segments of fixed length within a convex body in ℝ3. We give this measure from rotational formulae; that is, from isotropic plane sections through a fixed point. From this result we also obtain a new rotational formula for the volume of a convex body; which is proved to be equivalent to the wedge formula for the volume

Shape description from generalized support functions

The generalized support function is considered to be a representation of shape properties of compact connected sets in R2. Some interesting properties are studied and several parameters are defined for use in shape description and classification. When these parameters are applied to describe convex figures, they are closely related with the measure of congruent segments of fixed length within the convex figure. Finally, an experimental study is conducted to show the goodness obtained when using the generalized support function in shape classification

Erythrocyte shape classification using integral-geometry-based methods

Erythrocyte shape deformations are related to different important illnesses. In this paper, we focus on one of the most important: the Sickle cell disease. This disease causes the hardening or polymerization of the hemoglobin that contains the erythrocytes. The study of this process using digital images of peripheral blood smears can offer useful results in the clinical diagnosis of these illnesses. In particular, it would be very valuable to find a rapid and reproducible automatic classification method to quantify the number of deformed cells and so gauge the severity of the illness. In this paper, we show the good results obtained in the automatic classification of erythrocytes in normal cells, sickle cells, and cells with other deformations, when we use a set of functions based on integral-geometry methods, an active contour-based segmentation method, and a k-NN classification algorithm. Blood specimens were obtained from patients with Sickle cell disease. Seventeen peripheral blood smears were obtained for the study, and 45 images of different fields were obtained. A specialist selected the cells to use, determining those cells which were normal, elongated, and with other deformations present in the images. A process of automatic classification, with cross-validation of errors with the proposed descriptors and with other two functions used in previous studies, was realized.Work supported by the UJI project P11B2012-24

Clasificación morfológica de células endoteliales de venas de cordón umbilical humano (HUVEC) en imágenes digitales

El análisis de la morfología celular en imágenes de muestras microscópicas es una cuestión relevante, pues los cambios morfológicos pueden representar una respuesta a situaciones ante las cuales sean sometidas las células. En este trabajo nos centramos en la posibilidad de obtener, de forma automatizada, una clasificación morfológica celular en imágenes de culturas in vitro 2D de células endoteliales de venas de cordón umbilical humano (HUVEC) para estudio de la angiogénesis. Se realizó la clasificación supervisada de las células en tres clases: circulares, deformadas alargadas (elongadas) y deformadas poco alargadas (otras deformaciones) usando los coeficientes de formas elíptico (ESF) y circular (CSF), lo que permitió identificar formas celulares relevantes para la evaluación de este proceso. Todos los algoritmos fueron implementados en Plataforma Matlab®. Los resultados obtenidos demuestran la factibilidad de la aplicación de esta propuesta y que la misma puede ser empleada para facilitar el estudio de eventos precoces bajo los efectos del empleo de agentes inhibidores de la angiogénesis