Calibration of a moving camera using a planar pattern: Optimal computation, reliability evaluation, and stabilization by the geometric AIC

Abstract

SUMMARYWe propose a simultaneous calibration scheme for computing the parameters of a continuously moving and continuously zooming camera by placing a planar pattern behind the object. We describe a procedure for computing an analytical solution which is exact in the absence of noise, estimating an optimal solution that attains the theoretical accuracy bound in the presence of noise, and evaluating the reliability of the computed solution. Finally, we show that degenerate configurations in which the solution is indeterminate and statistical fluctuations of computation can be avoided by model selection. This is done by comparing the model predicted from the history of the camera motion with the actually computed model by the geometric AIC. We confirm the effectiveness of our method by simulations and show real image examples. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(7): 1221, 2001

Do we really have to consider covariance matrices for image feature points?

“…Computing the homography from images is a necessary step in many vision applications such as image mosaicking and camera calibration [6,8]. In the presence of image noise, a statistically optimal estimate of H is obtained by minimizing the following function [3]:…”

“…Since it is defined only up to a scale factor, we normalize it to ||H|| = 1 [the norm of a matrix A = (A ij ) is defined by ||A|| = √  Σ i,j=1 3 A ij 2 ]. Computing the homography from images is a necessary step in many vision applications such as image mosaicking and camera calibration [6,8]. In the presence of image noise, a statistically optimal estimate of H is obtained by minimizing the following function [3]:…”

“…The authors have presented various optimization techniques for feature-based problems, such as 3D reconstruction, camera calibration, and image mosaicking, using the covariance matrix of a feature point as the measure of its uncertainty [4,6,8,9]. In most cases, we have assumed isotropic homogeneous noise for the covariance matrix.…”