Dimensional curvature identities on pseudo-Riemannian geometry

The curvature tensor of a pseudo-Riemannian metric, and its covariant derivatives, satisfy certain identities that hold on any manifold of dimension less or equal than $n$. In this paper, we re-elaborate recent results by Gilkey-Park-Sekigawa regarding $p$-covariant dimensional curvature identities, for $p=0,2$. To this end, we use the classical theory of natural operations, that allows us to simplify some arguments and to generalize the description of Gilkey-Park-Sekigawa. Thus, our main result describes the first space of $p$-covariant dimensional curvature identities, for any even $p$.Comment: Polished version. 15 page

Automorphisms of classical geometries in the sense of Klein

In this note, we compute the group of automorphisms of Projective, Affine and Euclidean Geometries in the sense of Klein. As an application, we give a simple construction of the outer automorphism of S_6.Comment: 8 page

Lovelock's theorem revisited

Let (X, g) be an arbitrary pseudo-riemannian manifold. A celebrated result by Lovelock gives an explicit description of all second-order natural (0,2)-tensors on X, that satisfy the conditions of being symmetric and divergence-free. Apart from the dual metric, the Einstein tensor of g is the simplest example. In this paper, we give a short and self-contained proof of this theorem, simplifying the existing one by formalizing the notion of derivative of a natural tensor.Comment: 9 page

Planar PØP: feature-less pose estimation with applications in UAV localization

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We present a featureless pose estimation method that, in contrast to current Perspective-n-Point (PnP) approaches, it does not require n point correspondences to obtain the camera pose, allowing for pose estimation from natural shapes that do not necessarily have distinguished features like corners or intersecting edges. Instead of using n correspondences (e.g. extracted with a feature detector) we will use the raw polygonal representation of the observed shape and directly estimate the pose in the pose-space of the camera. This method compared with a general PnP method, does not require n point correspondences neither a priori knowledge of the object model (except the scale), which is registered with a picture taken from a known robot pose. Moreover, we achieve higher precision because all the information of the shape contour is used to minimize the area between the projected and the observed shape contours. To emphasize the non-use of n point correspondences between the projected template and observed contour shape, we call the method Planar PØP. The method is shown both in simulation and in a real application consisting on a UAV localization where comparisons with a precise ground-truth are provided.Peer ReviewedPostprint (author's final draft

Using microelectrode models for real time cell-culture monitoring

This paper proposes a cell-microelectrode model for cell biometry applications, based on the area overlap as main parameter. The model can be applied to cell size identification, cell count, and their extension to cell growth and dosimetry protocols. Experiments performed with comercial electrodes are presented, illustrating a procedure to obtain cell number in both growth and dosimetry processes. Results obtained for the AA8 cell line are promising.Junta de Andalucía P0-TIC-538