@article{a4feea7bd8da4b2ab7530a9473658a59,
title = "Stochastic Analysis of Stereo Quantization Error",
abstract = "The designer of a stereo imaging system often needs to know how the various system parameters affect the range estimation error. The probability density function of the range estimation error and the expected value of the range error magnitude are derived in terms of the various design parameters. In addition, the relative range error is proposed as a better way of quantifying the range resolution of a stereo imaging system.",
keywords = "Estimation theory, image digitization, quantization error, stereoscopy",
author = "Rodriguez, {Jeffrey J.} and Aggarwal, {J. K.}",
note = "Funding Information: Stereoscopy is a common technique for passively computing range information about a scene. A nonconvergent stereo imaging system consists of two fixed cameras, separated by some baseline distance, and having parallel optical axes. With this set-up, a left image and a right image are obtained. By computing the displacement, or disparity, between two corresponding feature points in the left and right images, the three-dimensional coordinates of an imaged point in the scene can be found. Designing a stereo system involves choosing several parameters: the focal length of the cameras, the image sampling interval, the baseline distance, and the distance from the cameras to the scene. Unfortunately, one must compromise to meet the conflicting requirements of accurate feature matching and accurate range estimation. In order to match feature points accurately and to avoid as much occlusion as possible, the product, baseline X focal length, must be small. However, accurate range estimation requires that this product be large. Alternatively, the range estimation accuracy can be improved by decreasing the sampling interval, but this is usually constrained by the physical limitations of the imaging device. Therefore, one typically decides how much range estimation error is acceptable, and then attempts to choose the design parameters to meet this requirement. This leads to the need for a way to predict the range estimation error due to quantization, given the stereo system parameters. Although matching errors also contribute to the range error, it is as- sumed that appropriate error modeling for a particular feature extraction method could be formulated in terms of a spatial quantization of the image plane. Let there be one stereo image pair from which depths are to be estimated. (That is, we do not have a sequence of images to which block adjustment or sequential estimation methods could be applied.) Blostein and Huang [ 11 derived an equation for the probability that the percent range error is less Manuscript received April 2, 1988; revised October 19, 1989. Recommended for acceptance by 0. D. Faugeras. This work was supported in part by the National Science Foundation under Grant DCR-8517583, Army Research Office Contract DAAL03-87-K-0089, and by a National Science Foundation Graduate Fellowship. The authors are with the Computer and Vision Research Center, Department of Electrical Engineering, University of Texas at Austin, Austin, TX 78712. IEEE Log Number 8933759.",
year = "1990",
month = may,
doi = "10.1109/34.55106",
language = "English (US)",
volume = "12",
pages = "467--470",
journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence",
issn = "0162-8828",
publisher = "IEEE Computer Society",
number = "5",
}