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| Givan: Localizing 3D straight lines from single 2D images |
We present an algorithm that can be used to localize the position in the space of straight lines from a single 2D image. This reconstruction is possible if the image is retrieved using a special camera apparatus. In particular this work focuses on axial catadioptric cameras since for this kind of cameras it is possible to demonstrate that the straight lines localization is always possible with the only exception of particular lines as, for example, those coplanar with the camera axis. The work, then, presents how to cope with the error present in the image that represents the contours of the original image. This is done by applying an optimization algorithm using a particular error function. In the end we present an algorithm used to simulate the image retrieval and the equation of a set of mirrors used in conjunction with the camera.
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This work was produced at the department of Electronic and Information at "Politecnico di Milano" , Italy under the supervison of professor Vincenzo Caglioti. The thesis was presented both in Milan in december 2004 and in may 2005 in Chicago at University of Illinois Share this article        |
The algorithms developed were implemented as part of a simulator (thi image is a screen shoot of a running session) in order to test different kind of mirror surfaces. The program allows to draw an initial set of 3d lines in the environment and propose a couple of alghoritms to siumulate the image generated in front of the camera. From this image then it is possible to test the main contribute of the thesis by reconstructing the position of those lines. The program allow to test different mirror profile (paabolic, spheric, conic, ...) and to simulate also the presence of error in the captured image.
As you can see from this image the program is capable of detecting the source line that project itself on the input curve given.
One of the running example used to test the algorithm is the representation of this room geometry. Initially a simulated images is generated using the mirror and camera characteristics. Then the original lines position is discarded and the alghoritms used. As it is possible to see the camera-mirror axis is not coplanar to any of the line represented. If this was the case, in fact, the recovery wouldn't be possible (as it is clearly stated in the thesis).
Comparison between the reconstructed room (left image) and the correct one (right image). Notice that part of the original room is not detected since these parts do not reflect on the particular mirror used (in this case a parabolic mirror) .
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