Camera Calibration with Two Arbitrary Coaxial Circles

Abstract

Abstract. We present an approach for camera calibration from the image of at least two circles arranged in a coaxial way. Such a geometric configuration arises in static scenes of objects with rotational symmetry or in scenes including generic objects undergoing rotational motion around a fixed axis. The approach is based on the automatic localization of a surface of revolution (SOR) in the image, and its use as a calibration artifact. The SOR can either be a real object in a static scene, or a "virtual surface" obtained by frame superposition in a rotational sequence. This provides a unified framework for calibration from single images of SORs or from turntable sequences. Both the internal and external calibration parameters (square pixels model) are obtained from two or more imaged cross sections of the SOR, whose apparent contour is also exploited to obtain a better calibration accuracy. Experimental results show that this calibration approach is accurate enough for several vision applications, encompassing 3D realistic model acquisition from single images, and desktop 3D object scanning.

Accurate camera calibration using iterative refinement of control points

“…Circular control points were introduced as an alternative to the square control points for camera calibration [16,7,4,3,24,21,19]. Heikkila in [7] performed a minimization over the weighted sum of squared differences between the observation and the camera model using Levenberg-Marquardt [14].…”

“…Due to their ease of use, calibration algorithms that use planar patterns have gained widespread acceptance. In addition to the square planar pattern, circle and ring patterns have also been used [16,7,4,3,24,21,11,9]. The calibration procedure typically consists of either localizing the calibration pattern control points (square corners, circle or ring centers) [18,22,7,9] and then solving for the camera parameters, or using some geometric property of the pattern itself to solve for the camera parameters directly [4,3,24,21,11].…”

Seeing Glassware: from Edge Detection to Pose Estimation and Shape Recovery

“…The modeling of projected SORs for pose estimation and reconstruction has been addressed as a single-view problem, where pose and camera calibration can be recovered either from bi-tangent points on the apparent contour [31], [29], imaged cross-sections detected as ellipses [4], [5], [10], or both bi-tangent points and cross-sections [3]. Methods have been proposed for the projective [27] and metric [5] reconstruction of an SOR from a single calibrated view when the pose in known, as well as image contours.…”

“…Closest to this work are approaches on SOR reconstruction and pose estimation, using two views and manually segmented contours [23], or automatically segmenting contours in a single view before applying reconstruction [3]. The goal of this work is to jointly segment and reconstruct the object in an effort to achieve more robustness.…”

“…5 b, assuming the object is seen from above (l ∞ appears above the object in the image), a negative ρ (h) (object getting thinner as h increases) will cause the occluding 3D point to lie further away from the camera than the cross-section center (θ < 0), whereas a positive ρ (h) will have the opposite effect (θ > 0). For a given height h, a possible radius ρ(h) and tangent ρ (h), there is a unique point on Γ at height h, and a unique corresponding point on the apparent contour γ [3]. This enables the definition of the function, γ A (h, ρ(h), ρ (h)) mapping h and possible ρ(h), ρ (h) to a unique point in the image space and edge score map supporting the choice of ρ(h), ρ (h).…”