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**1 - 1**of**1**### Computing Rigorous Bounds to the Accuracy of Calibrated Stereo Reconstruction

, 2004

"... We deal with the problem of computing rigorous bounds to the position of 3-D points obtained by stereo triangulation when both the camera matrix and the coordinates of image points are affected by measurement errors. By “rigorous bounds ” we mean that the true unknown 3-D points are guaranteed to li ..."

Abstract
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We deal with the problem of computing rigorous bounds to the position of 3-D points obtained by stereo triangulation when both the camera matrix and the coordinates of image points are affected by measurement errors. By “rigorous bounds ” we mean that the true unknown 3-D points are guaranteed to lie within the intervals computed by our method with mathematical certainty. To this end, we first model the calibration process by assuming a bounded error in the localization of the reference points in the image, then we compute narrow intervals for the entries of the camera matrix by using numerical methods based on Interval Analysis. Finally, we apply triangulation and obtain cuboids that bound point coordinates. We employed two state-of-the-art methods for the solution of linear systems of interval equations, namely Rump’s and Shary’s methods. Our conclusion is that a careful selection of numerical techniques allows to use Interval Analysis as a tool for obtaining realistic bounds on the output error even in presence of significant errors in the input data. I.