Autocalibration with the Minimum Number of Cameras with Known Pixel Shape

In 3D reconstruction, the recovery of the calibration parameters of the cameras is paramount since it provides metric information about the observed scene, e.g., measures of angles and ratios of distances. Autocalibration enables the estimation of the camera parameters without using a calibration device, but by enforcing simple constraints on the camera parameters. In the absence of information about the internal camera parameters such as the focal length and the principal point, the knowledge of the camera pixel shape is usually the only available constraint. Given a projective reconstruction of a rigid scene, we address the problem of the autocalibration of a minimal set of cameras with known pixel shape and otherwise arbitrarily varying intrinsic and extrinsic parameters. We propose an algorithm that only requires 5 cameras (the theoretical minimum), thus halving the number of cameras required by previous algorithms based on the same constraint. To this purpose, we introduce as our basic geometric tool the six-line conic variety (SLCV), consisting in the set of planes intersecting six given lines of 3D space in points of a conic. We show that the set of solutions of the Euclidean upgrading problem for three cameras with known pixel shape can be parameterized in a computationally efficient way. This parameterization is then used to solve autocalibration from five or more cameras, reducing the three-dimensional search space to a two-dimensional one. We provide experiments with real images showing the good performance of the technique.Comment: 19 pages, 14 figures, 7 tables, J. Math. Imaging Vi

On the Non-Linear Optimization of Projective Motion Using Minimal Parameters

655, av. de l’Europ

Triangulation for Points on Lines

Triangulation consists in finding a 3D point reprojecting the best as possible onto corresponding image points. It is classical to minimize the reprojection error, which, in the pinhole camera model case, is nonlinear in the 3D point coordinates. We study the triangulation of points lying on a 3D line, which is a typical problem for Structure-From- Motion in man-made environments. We show that the reprojection error can be minimized by finding the real roots of a polynomial in a single variable, which degree depends on the number of images. We use a set of transformations in 3D and in the images to make the degree of this polynomial as low as possible, and derive a practical reconstruction algorithm. Experimental comparisons with an algebraic approximation algorithm and minimization of the reprojection error using Gauss-Newton are reported for simulated and real data. Our algorithm finds the optimal solution with high accuracy in all cases, showing that the polynomial equation is very stable. It only computes the roots corresponding to feasible points, and can thus deal with a very large number of views – triangulation from hundreds of views is performed in a few seconds. Reconstruction accuracy is shown to be greatly improved compared to standard triangulation methods that do not take the line constraint into account

A New Autocalibration Algorithm: Experimental Evaluation

Abstract. A new autocalibration algorithm has been recently presented by Mendonça and Cipolla which is both simple and nearly globally convergent. Analysis of convergence is missing in the original article. This paper fills the gap, presenting an extensive experimental evaluation of the Mendonça and Cipolla algorithm, aimed at assessing both accuracy and sensitivity to initialization. Results show that its accuracy is fair, and – remarkably – it converges from almost everywhere. This is very significant, because most of the existing algorithms are either complicated or they need to be started very close to the solution

Negative capacitance tunnel F£Ts: Experimental demonstration of outstanding simultaneous boosting of on-current, transconductance, overdrive, and swing

This paper demonstrates and experimentally reports the highest ever performance boosting in strained silicon-nanowire homojunction TFETs with negative capacitance, provided by matched PZT capacitors. Outstanding enhancements of I on , g m , and overdrive are analyzed and explained by most effective reduction of body factor, m V T , which greatly amplify the control on the surface potential TFET, which dictates a highly non-linear BTBT regime. We achieve a full non-hysteretic negative-capacitance switch configuration, suitable for logic applications, and report non-current increase by a factor of 500x, voltage overdrive of IV, transconductance increase of up to 5× 10 3 x, and subthreshold swing improvement

Practical autocalibration

As it has been noted several times in literature, the difficult part of autocalibration efforts resides in the structural non-linearity of the search for the plane at infinity. In this paper we present a robust and versatile autocalibration method based on the enumeration of the inherently bounded space of the intrinsic parameters of two cameras in order to find the collineation of space that upgrades a given projective reconstruction to Euclidean. Each sample of the search space (which reduces to a finite subset of \u211d2 under mild assumptions) defines a consistent plane at infinity. This in turn produces a tentative, approximate Euclidean upgrade of the whole reconstruction which is then scored according to the expected intrinsic parameters of a Euclidean camera. This approach has been compared with several other algorithms on both synthetic and concrete cases, obtaining favourable results