Camera re-calibration after zooming based on sets of conics

We describe a method to compute the internal parameters (focal and principal points) of a camera with known position and orientation, based on the observation of two or more conics on a known plane. The conics can even be degenerate (e.g. pairs of lines). The proposed method can be used to re-estimate the internal parameters of a fully calibrated camera after zooming to a new, unknown, focal length. It also allows estimating the internal parameters when a second, fully calibrated camera observes the same conics. The parameters estimated through the proposed method are coherent with the output of more traditional procedures that require a higher number of calibration images. A deep analysis of the geometrical configurations that influence the proposed method is also reported

Linear pose estimate from corresponding conics

We propose here a new method to recover the orientation and position of a plane by matching at least three projections of a conic lying on the plane itself. The procedure is based on rearranging the conic projection equations such that the non linear terms are eliminated. It works with any kind of conic and does not require that the shape of the conic is known a-priori. The method was extensively tested using ellipses, but it can also be used for hyperbolas and parabolas. It was further applied to pairs of lines, which can be viewed as a degenerate case of hyperbola, without requiring the correspondence problem to be solved first. Critical configurations and numerical stability have been analyzed through simulations. The accuracy of the proposed algorithm was compared to that of traditional algorithms and of a trinocular vision system using a set of landmarks

On special quadratic birational transformations of a projective space into a hypersurface

We study transformations as in the title with emphasis on those having smooth connected base locus, called "special". In particular, we classify all special quadratic birational maps into a quadric hypersurface whose inverse is given by quadratic forms by showing that there are only four examples having general hyperplane sections of Severi varieties as base loci.Comment: Accepted for publication in Rendiconti del Circolo Matematico di Palerm

A baby steps/giant steps Monte Carlo algorithm for computing roadmaps in smooth compact real hypersurfaces

International audienceWe consider the problem of constructing roadmaps of real algebraic sets. The problem was introduced by Canny to answer connectivity questions and solve motion planning problems. Given $s$ polynomial equations with rational coefficients, of degree $D$ in $n$ variables, Canny's algorithm has a Monte Carlo cost of $s^n\log(s) D^{O(n^2)}$ operations in $\mathbb{Q}$; a deterministic version runs in time $s^n \log(s) D^{O(n^4)}$. The next improvement was due to Basu, Pollack and Roy, with an algorithm of deterministic cost $s^{d+1} D^{O(n^2)}$ for the more general problem of computing roadmaps of semi-algebraic sets ($d \le n$ is the dimension of an associated object). We give a Monte Carlo algorithm of complexity $(nD)^{O(n^{1.5})}$ for the problem of computing a roadmap of a compact hypersurface $V$ of degree $D$ in $n$ variables; we also have to assume that $V$ has a finite number of singular points. Even under these extra assumptions, no previous algorithm featured a cost better than $D^{O(n^2)}$

Conic Based Camera Re-calibration after Zooming

We describe here a method to compute the internal parameters of a camera whose position and orientation are known. The method is based on the observation of at least three conics on a known plane; these can be easily extracted in a real scenario from a tiled floor or other regular structures. The method estimates the principal point and focal length using a unique image of the conics when these are observed by an additional calibrated camera. Differently from other methods, no assumptions is made on the conics used for calibration. The experimental results demonstrate that the accuracy of the method is comparable to that of more traditional (and time consuming) approaches. It can find applications in systems of Pan-Zoom-Tilt (PZT) or traditional cameras, that are nowadays widely employed, for instance in the surveillance domain, and require frequent re-calibration

Tracking 3D orientation through corresponding conics

We propose here a new method to recover the 3D orientation of a rigid body by matching corresponding conics embedded in the object itself. The method is based on writing the projective equations of the conics and rearranging them in a suitable way. This leads to a very simple linear system. Results from simulated experiments show good accuracy and suggest that this method could be used for instance in augmented reality surgery to effectively track surgery instruments inside the operating room

Un nuovo tipo di apparecchio ARTVA basato sulla geometria delle linee del campo magnetico

Il brevetto descrive un nuovo tipo di apparecchio ARTVA, opportunamente modificato rispetto a quelli ora in uso, che consente di muoversi in direzione di un disperso sotto una valanga seguendo una linea retta, anzich\ue9 tangenzialmente lungo le linee curve dei campi magnetici, come accade attualmente. La corretta direzione di marcia viene individuata tramite un semplice calcolo, basato sulle propriet\ue0 geometriche delle linee del campo magnetico e sull'inclinazione dell'antenna dell'apparecchio del disperso, rispetto ad un comune sistema di riferimento, informazione che viene trasmessa al ricercatore