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Distortion of Stereoscopic Visual Space
, 1997
"... A stereo vision system requires accurate knowledge of the internal parameters of its two cameras and of the relative orientation between them in order to faithfully reconstruct a scene from corresponding image points. When incorrect values for the parameters of the stereo system are used, the result ..."
Abstract

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A stereo vision system requires accurate knowledge of the internal parameters of its two cameras and of the relative orientation between them in order to faithfully reconstruct a scene from corresponding image points. When incorrect values for the parameters of the stereo system are used, the resulting reconstruction is distorted in a systematic way. The transformation between the true scene structure and its distorted reconstruction, which we call the shape distortion transformation, is a quadratic Cremona transformation  a rational transformation that is onetoone almost everywhere, but that does not, in general, preserve collinearity. Our distortion framework describes and enables the analysis of situations where insufficient information is available to compute even a weak calibration of a stereo rig. It also makes possible a thorough error analysis of systematic errors in computing structure from motion. The global, qualitative, behavior of the shape distortion is studied by ...
AlgorithmIndependent Stability Analysis of Structure from Motion
, 1996
"... The stability analysis for the structure from motion problem presented in this paper investigates the optimal relationship between the errors in the estimated translational and rotational parameters of a rigid motion that results in the estimation of a minimum number of negative depth values. No par ..."
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The stability analysis for the structure from motion problem presented in this paper investigates the optimal relationship between the errors in the estimated translational and rotational parameters of a rigid motion that results in the estimation of a minimum number of negative depth values. No particular estimators are used and no specific assumptions about the scene are made. The input used is the value of the flow along some direction, which is more general than optic flow or correspondence. For a planar retina it is shown that the optimal configuration is achieved when the projections of the translational and rotational errors on the image plane are perpendicular. For a spherical retina, given a rotational error, the optimal translation is the correct one, while given a translational error the optimal rotational error is normal to the translational one at an equal distance from the real and estimated translations. The proofs, besides illuminating the confounding of translation and...
Distortions of Stereoscopic Visual Space and Quadratic Cremona Transformations
"... . When incorrect values for the extrinsic and intrinsic parameters of the two cameras of a stereo rig are used in the reconstruction of a threedimensional scene from image correspondences, the resulting reconstruction is distorted in a systematic way. We show here that the transformation betwee ..."
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. When incorrect values for the extrinsic and intrinsic parameters of the two cameras of a stereo rig are used in the reconstruction of a threedimensional scene from image correspondences, the resulting reconstruction is distorted in a systematic way. We show here that the transformation between the true scene structure and its distorted reconstruction is a quadratic Cremona transformation  a rational transformation which is onetoone almost everywhere, but which does not in general preserve collinearity. We study the distortion of points in the fixation plane on a global, qualitative, level, and on a local, quantitative level. Both global and local viewpoints provide evidence of severe nonlinear distortions in the vicinity of the camera centers, thereby indicating that their consideration is of particularly high relevance for near regions of the stereo rig. This is consistent with experimental evidence from psychophysics, which shows that distortions in the near rang...