A Linear Extrinsic Calibration of Kaleidoscopic Imaging System from Single 3D Point

Abstract

This paper proposes a new extrinsic calibration of kaleidoscopic imaging system by estimating normals and distances of the mirrors. The problem to be solved in this paper is a simultaneous estimation of all mirror parameters consistent throughout multiple reflections. Unlike conventional methods utilizing a pair of direct and mirrored images of a reference 3D object to estimate the parameters on a permirror basis, our method renders the simultaneous estimation problem into solving a linear set of equations. The key contribution of this paper is to introduce a linear estimation of multiple mirror parameters from kaleidoscopic 2D projections of a single 3D point of unknown geometry. Evaluations with synthesized and real images demonstrate the performance of the proposed algorithm in comparison with conventional methods.

Global calibration of non-overlapping cameras: State of the art

“…The experimental results show that the system achieves 0.1 mm measurement accuracy in the range of 1353 mm. Other works based on combined techniques are described in [91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106] to implement global calibration. Fig.…”

Structure of Multiple Mirror System from Kaleidoscopic Projections of Single 3D Point

“…Compared with the earlier version of this work [18], we parameterize the p 0 and minimize their reprojection errors explicitly by following the bundle adjustment manner presented in [35].…”

“…In addition to the above methods, we also compared the proposed method with its earlier version [18] in which the 3D points were restricted to be on the line through its 2D observations in the base chamber, while the proposed method does not have this limitation as described in Section 5.3.…”

“…The yellow and cyan dashed lines are the results by the orthogonality constraint-based approach [23] and the baseline with the same five points for the red and magenta dashed lines. The orange line shows the result of the earlier version of this work [18] with five input points. Note that the baseline and the orthogonality constraint-based approach [23] without the final non-linear optimization could not achieve comparable results (typically E rep 10 pixels).…”

“…An earlier version of this study was presented in [18]. Compared with [18], this paper provides a novel algorithm of chamber assignment based on the kaleidoscopic projection constraint, while [18] assumes that the chamber labels are assigned by hand beforehand. This chamber assignment algorithm realizes a fully automatic calibration of the kaleidoscopic imaging system.…”