333 research outputs found
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
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
A Fisher-Rao metric for paracatadioptric images of lines
In a central paracatadioptric imaging system a perspective camera takes an image of a scene reflected in a paraboloidal mirror. A 360° field of view is obtained, but
the image is severely distorted. In particular, straight lines in the scene project to circles in the image. These distortions make it diffcult to detect projected lines using standard image processing algorithms. The distortions are removed using a Fisher-Rao metric which is defined on the space of projected lines in the paracatadioptric image. The space of projected lines is divided into subsets such that on each subset the Fisher-Rao metric is closely approximated by the Euclidean metric. Each subset is sampled at the vertices of a square grid and values are assigned to the sampled points using an adaptation of the trace transform. The result is a set of digital images to which standard image processing algorithms can be applied.
The effectiveness of this approach to line detection is illustrated using two algorithms, both of which are based on the Sobel edge operator. The task of line detection is reduced to the task of finding isolated peaks in a Sobel image. An experimental comparison is made between these two algorithms and third algorithm taken from the literature and
based on the Hough transform
Vision-Based Navigation III: Pose and Motion from Omnidirectional Optical Flow and a Digital Terrain Map
An algorithm for pose and motion estimation using corresponding features in
omnidirectional images and a digital terrain map is proposed. In previous
paper, such algorithm for regular camera was considered. Using a Digital
Terrain (or Digital Elevation) Map (DTM/DEM) as a global reference enables
recovering the absolute position and orientation of the camera. In order to do
this, the DTM is used to formulate a constraint between corresponding features
in two consecutive frames. In this paper, these constraints are extended to
handle non-central projection, as is the case with many omnidirectional
systems. The utilization of omnidirectional data is shown to improve the
robustness and accuracy of the navigation algorithm. The feasibility of this
algorithm is established through lab experimentation with two kinds of
omnidirectional acquisition systems. The first one is polydioptric cameras
while the second is catadioptric camera.Comment: 6 pages, 9 figure
04251 -- Imaging Beyond the Pinhole Camera
From 13.06.04 to 18.06.04, the
Dagstuhl Seminar 04251 ``Imaging Beyond the Pin-hole Camera. 12th Seminar on Theoretical Foundations of Computer Vision\u27\u27 was held
in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Fast Central Catadioptric Line Extraction
International audienceLines are particularly important features for different tasks such as calibration, structure from motion, 3D reconstruction in computer vision. However, line detection in catadioptric images is not trivial because the projection of a 3D line is a conic eventually degenerated. If the sensor is calibrated, it has been already demonstrated that each conic can be described by two parameters. In this way, some methods based on the adaptation of conventional line detection methods have been proposed. However, most of these methods suffer from the same disadvantages than in the perspective case (computing time, accuracy, robustness, ...). In this paper, we then propose a new method for line detection in central catadioptric image comparable to the polygonal approximation approach. With this method, only two points of a chain allows to extract with a very high accuracy a catadioptric line. Moreover , this algorithm is particularly fast and is applicable in realtime. We also present experimental results with some quantitative and qualitative evaluations in order to show the quality of the results and the perspectives of this method
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