1,013 research outputs found
3D Reconstruction with Uncalibrated Cameras Using the Six-Line Conic Variety
We present new algorithms for the recovery of the Euclidean structure from a projective calibration of a set of cameras with square pixels but otherwise arbitrarily varying intrinsic and extrinsic parameters. Our results, based on a novel geometric approach, include a closed-form solution for the case of three cameras and two known vanishing points and an efficient one-dimensional search algorithm for the case of four cameras and one known vanishing point. In addition, an algorithm for a reliable automatic detection of vanishing points on the images is presented. These techniques fit in a 3D reconstruction scheme oriented to urban scenes reconstruction. The satisfactory performance of the techniques is demonstrated with tests on synthetic and real data
Hierarchical structure-and-motion recovery from uncalibrated images
This paper addresses the structure-and-motion problem, that requires to find
camera motion and 3D struc- ture from point matches. A new pipeline, dubbed
Samantha, is presented, that departs from the prevailing sequential paradigm
and embraces instead a hierarchical approach. This method has several
advantages, like a provably lower computational complexity, which is necessary
to achieve true scalability, and better error containment, leading to more
stability and less drift. Moreover, a practical autocalibration procedure
allows to process images without ancillary information. Experiments with real
data assess the accuracy and the computational efficiency of the method.Comment: Accepted for publication in CVI
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
Line geometry and camera autocalibration
We provide a completely new rigorous matrix formulation of the absolute quadratic complex (AQC), given by the set of lines intersecting the absolute conic. The new results include closed-form expressions for the camera intrinsic parameters in terms of the AQC, an algorithm to obtain the dual absolute quadric from the AQC using straightforward matrix operations, and an equally direct computation of a Euclidean-upgrading homography from the AQC. We also completely characterize the 6×6 matrices acting on lines which are induced by a spatial homography. Several algorithmic possibilities arising from the AQC are systematically explored and analyzed in terms of efficiency and computational cost. Experiments include 3D reconstruction from real images
Camera Autocalibration using Plücker Coordinates
We present new results on the Absolute Line Quadric (ALQ), the geometric object representing the set of lines that intersect the absolute conic. We include new techniques for the obtainment of the Euclidean structure that lead to an efficient algorithm for the autocalibration of cameras with varying parameters
Autocalibration of Cameras with Known Pixel Shape
We present new algorithms for the recovery of the Euclidean structure
from a projective calibration of a set of cameras of known pixel shape but otherwise
arbitrarily varying intrinsic and extrinsic parameters. The algorithms have a geometrical
motivation based on the properties of the set of lines intersecting the absolute conic.
The theoretical part of the paper contributes with theoretical results that establish the
relationship between the geometrical object corresponding to this set of lines and other
equivalent objects as the absolute quadric. Finally, the satisfactory performance of the
techniques is demonstrated with synthetic and real data
Design of a Low-cost GPS/magnetometer System for Land-based Navigation: Integration and Autocalibration Algorithms
The land-based navigation, paying attention to precision farming, is the research topic: the final purpose is the design and development of a guidance-aided system focusing on a low-cost GPS receiver able to provide a pseudorange-based solution only. Specific tests have been carried out to reproduce the trajectories followed by the vehicle in agricultural applications, whose accuracy target is typically 1 m. Results show that the investigated low-cost receiver is affected by a drift in time which is mainly detected while turning and causing a deviation from the optimal reference solution. Thus, the goal is to correct this behavior because the deviation accumulates during time and causes a not optimal treatment of the field (waste of material and money).
Paying attention to the cost of the system, a new idea is proposed: the integration between the low-cost GPS with a magnetometer/digital compass. A dedicated algorithm has been also implemented, taking the heading provided by th
e magnetometer and using it to correct the deviation in turns. Unluckily a magnetometer is deeply influenced by ferrous materials and the sensor is supposed to be installed on the vehicle, which is mainly made by metal. As a
consequence, the sensed measurements are affected by a deviation from the actual magnetic field. Those disturbances need to be properly reduced by an autocalibration procedure. A new approach for the autocalibration problem has been developed and implemented; then the comparison with respect to the traditional method has been also performed in order to test and validate the new idea. A comprehensive and detailed description of all the algorithms will be
produced concerning both the sensors integration (GPS and magnetometer) along with the magnetometer autocalibration. Particular attention will be focused on results and performances of the autocalibration procedure, which appears to provide very interesting results. The new approach, which is simply based on the covariance matrix, appears to be more successful than the traditional one. Several tests have been analyzed: the stand-alone
low-cost GPS provides solutions which are not acceptable for precision farming applications, while the integration with a magnetometer slightly increases the accuracy. Furthermore, the innovation of the research is connected to the autocalibration algorithm itself. The final goal was the design of a low-cost system for supporting the guidance in land-based navigation; improvements are still required but the goal is close to be achieved
The Absolute Line Quadric and Camera Autocalibration
We introduce a geometrical object providing the same information as the absolute conic: the absolute line quadric (ALQ). After the introduction of the necessary exterior algebra and Grassmannian geometry tools, we analyze the Grassmannian of lines of P^3 from both the projective and Euclidean points of view. The exterior algebra setting allows then to introduce the ALQ as a quadric arising very naturally from the dual absolute quadric. We fully characterize the ALQ and provide clean relationships to solve the inverse problem, i.e., recovering the Euclidean structure of space from the ALQ. Finally we show how the ALQ turns out to be particularly suitable to address the Euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters, providing new linear and non-linear algorithms for this problem. We also provide experimental results showing the good performance of the techniques
Recursive Camera Autocalibration with the Kalman Filter
Given a projective reconstruction of a 3D scene, we address the problem of recovering the Euclidean structure of the scene in a recursive way. This leads to the application of Kalman filtering to the problem of camera autocalibration and to new algorithms for the autocalibration of cameras with varying parameters. This has benefits in saving memory and computational effort, and obtaining faster updates of the 3D Euclidean structure of the scene under consideration
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