The study of cell morphology is an important aspect of the diagnosis of some diseases, such as sickle cell disease, because red blood cell deformation is caused by these diseases. Due to the elongated shape of the erythrocyte, ellipse adjustment and concave point detection are applied widely to images of peripheral blood samples, including during the detection of cells that are partially occluded in the clusters generated by the sample preparation process. In the present study, we propose a method for the analysis of the shape of erythrocytes in peripheral blood smear samples of sickle cell disease, which uses ellipse adjustments and a new algorithm for detecting notable points. Furthermore, we apply a set of constraints that allow the elimination of significant image preprocessing steps proposed in previous studies. We used three types of images to validate our method: artificial images, which were automatically generated in a random manner using a computer code; real images from peripheral blood smear sample images that contained normal and elongated erythrocytes; and synthetic images generated from real isolated cells. Using the proposed method, the efficiency of detecting the two types of objects in the three image types exceeded 99.00%, 98.00%, and 99.35%, respectively. These efficiency levels were superior to the results obtained with previously proposed methods using the same database, which is available at http://erythrocytesidb.uib.es/. This method can be extended to clusters of several cells and it requires no user inputs.

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.

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We present an algorithm in the Conformal Geometric Algebra framework which computes the transformation (rotation and translation) relating the coordinate system of an endoscopic camera, with the coordinate system of the markers placed on it. Such markers are placed in order to track the camera's position in real time by using an optical tracking system. The problem is an adaptation of the so-called handeye calibration, well known in robotics; however we name it the endoscope-tracking system calibration. By this way, we can relate the preoperative data (3D model and planing of the surgery), with the data acquired in real time during the surgery by means of the optical tracking system and the endoscope. Results obtained with our approach are compared with other approach which computes separately (in a two-step algorithm) the rotation and translation, and they are promising.