807 research outputs found
Extrinisic Calibration of a Camera-Arm System Through Rotation Identification
Determining extrinsic calibration parameters is a necessity in any robotic
system composed of actuators and cameras. Once a system is outside the lab
environment, parameters must be determined without relying on outside artifacts
such as calibration targets. We propose a method that relies on structured
motion of an observed arm to recover extrinsic calibration parameters. Our
method combines known arm kinematics with observations of conics in the image
plane to calculate maximum-likelihood estimates for calibration extrinsics.
This method is validated in simulation and tested against a real-world model,
yielding results consistent with ruler-based estimates. Our method shows
promise for estimating the pose of a camera relative to an articulated arm's
end effector without requiring tedious measurements or external artifacts.
Index Terms: robotics, hand-eye problem, self-calibration, structure from
motio
Relating vanishing points to catadioptric camera calibration
This paper presents the analysis and derivation of the geometric relation between vanishing points and camera parameters of central catadioptric camera systems. These vanishing points correspond to the three mutually orthogonal directions of 3D real world coordinate system (i.e. X, Y and Z axes). Compared to vanishing points (VPs) in the perspective projection, the advantages of VPs under central catadioptric projection are that there are normally two vanishing points for each set of parallel lines, since lines are projected to conics in the catadioptric image plane. Also, their vanishing points are usually located inside the image frame. We show that knowledge of the VPs corresponding to XYZ axes from a single image can lead to simple derivation of both intrinsic and extrinsic parameters of the central catadioptric system. This derived novel theory is demonstrated and tested on both synthetic and real data with respect to noise sensitivity
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
Geometric Properties of Central Catadioptric Line Images and Their Application in Calibration
In central catadioptric systems, lines in a scene are projected to conic
curves in the image. This work studies the geometry of the central catadioptric
projection of lines and its use in calibration. It is shown that the conic curves where
the lines are mapped possess several projective invariant properties. From these
properties, it follows that any central catadioptric system can be fully calibrated from
an image of three or more lines. The image of the absolute conic, the relative pose
between the camera and the mirror, and the shape of the reflective surface can be
recovered using a geometric construction based on the conic loci where the lines
are projected. This result is valid for any central catadioptric system and generalizes
previous results for paracatadioptric sensors. Moreover, it is proven that systems
with a hyperbolic/elliptical mirror can be calibrated from the image of two lines. If
both the shape and the pose of the mirror are known, then two line images are
enough to determine the image of the absolute conic encoding the camera’s
intrinsic parameters. The sensitivity to errors is evaluated and the approach is used
to calibrate a real camer
Understanding fast macroscale fracture from microcrack post mortem patterns
Dynamic crack propagation drives catastrophic solid failures. In many
amorphous brittle materials, sufficiently fast crack growth involves
small-scale, high-frequency microcracking damage localized near the crack tip.
The ultra-fast dynamics of microcrack nucleation, growth and coalescence is
inaccessible experimentally and fast crack propagation was therefore studied
only as a macroscale average. Here, we overcome this limitation in
polymethylmethacrylate, the archetype of brittle amorphous materials: We
reconstruct the complete spatio-temporal microcracking dynamics, with
micrometer / nanosecond resolution, through post mortem analysis of the
fracture surfaces. We find that all individual microcracks propagate at the
same low, load-independent, velocity. Collectively, the main effect of
microcracks is not to slow down fracture by increasing the energy required for
crack propagation, as commonly believed, but on the contrary to boost the
macroscale velocity through an acceleration factor selected on geometric
grounds. Our results emphasize the key role of damage-related internal
variables in the selection of macroscale fracture dynamics.Comment: 9 pages, 5 figures + supporting information (15 pages
On a discretization of confocal quadrics. I. An integrable systems approach
Confocal quadrics lie at the heart of the system of confocal coordinates
(also called elliptic coordinates, after Jacobi). We suggest a discretization
which respects two crucial properties of confocal coordinates: separability and
all two-dimensional coordinate subnets being isothermic surfaces (that is,
allowing a conformal parametrization along curvature lines, or, equivalently,
supporting orthogonal Koenigs nets). Our construction is based on an integrable
discretization of the Euler-Poisson-Darboux equation and leads to discrete nets
with the separability property, with all two-dimensional subnets being Koenigs
nets, and with an additional novel discrete analog of the orthogonality
property. The coordinate functions of our discrete nets are given explicitly in
terms of gamma functions.Comment: 37 pp., 9 figures. V2 is a completely reworked and extended version,
with a lot of new materia
Reconstruction of surface of revolution from multiple uncalibrated views: a bundle-adjustment approach
This paper addresses the problem of recovering the 3D shape of a surface of revolution from multiple uncalibrated perspective views. In previous work, we have exploited the invariant properties of the surface of revolution and its silhouette to recover the contour generator and hence the meridian of the surface of revolution from a single uncalibrated view. However, there exists one degree of freedom in the reconstruction which corresponds to the unknown orientation of the revolution axis of the surface of revolution. In this paper, such an ambiguity is removed by estimating the horizon, again, using the image invariants associated with the surface of revolution. A bundle-adjustment approach is then proposed to provide an optimal estimate of the meridian when multiple uncalibrated views of the same surface of revolution are available. Experimental results on real images are presented, which demonstrate the feasibility of the approach.postprintThe 6th Asian Conference on Computer Vision (ACCV 2004), Jeju, Korea, 27-30 January 2004. In Proceedings of the 6th Asian Conference on Computer Vision, 2004, v. 1, p. 378-38
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