Metric 3D reconstruction and texture acquisition of surfaces of revolution from a single uncalibrated view

Abstract

Image analysis and computer vision can be effectively employed to recover the three-dimensional structure of imaged objects, together with their surface properties. In this paper, we address the problem of metric reconstruction and texture acquisition from a single uncalibrated view of a surface of revolution (SOR). Geometric constraints induced in the image by the symmetry properties of the SOR structure are exploited to perform self-calibration of a natural camera, 3D metric reconstruction, and texture acquisition. By exploiting the analogy with the geometry of single axis motion, we demonstrate that the imaged apparent contour and the visible segments of two imaged cross sections in a single SOR view provide enough information for these tasks. Original contributions of the paper are: single view self-calibration and reconstruction based on planar rectification, previously developed for planar surfaces, has been extended to deal also with the SOR class of curved surfaces; self-calibration is obtained by estimating both camera focal length (one parameter) and principal point (two parameters) from three independent linear constraints for the SOR fixed entities; the invariant-based description of the SOR scaling function has been extended from affine to perspective projection. The solution proposed exploits both the geometric and topological properties of the transformation that relates the apparent contour to the SOR scaling function. Therefore, with this method, a metric localization of the SOR occluded parts can be made, so as to cope with them correctly. For the reconstruction of textured SORs, texture acquisition is performed without requiring the estimation of external camera calibration parameters, but only using internal camera parameters obtained from self-calibration.

Camera Calibration with Two Arbitrary Coaxial Circles

“…provides four linear constraints on ω, whose coefficients can be computed from (the visible portions of) two imaged ellipses as shown in [12]. In that paper, it is demonstrated that only three out of the four constraints above are actually independent.…”

“…Another desktop approach appears in [9]: by exploiting the image of two arbitrary coplanar circles, the focal length of the camera and its extrinsic parameters are obtained. Being quite common in man-made environments, surfaces of revolution (SORs) were also proposed for desktop internal calibration purposes [10] and single view metric reconstruction [11], [12]. Thanks to their symmetry properties, SORs can be conveniently used as multiple camera calibration artifacts.…”

“…In [10], the apparent contour alone is used to calibrate the camera; this method requires that that two SORs are present in the same image, or that two or more images of SORs taken from the same camera are available. In [12] it is shown that the visible portions of two manually segmented imaged cross-sections are enough for calibrating from one view the focal length and the principal point provided that the camera has square pixels (a constraint always met by the modern devices), even when a single SOR object is present in the image.…”

“…1(c, d)). As in [12], calibration of a square pixel camera is achieved from a single SOR view. However, that calibration approach is extended here to both internal and external parameters, and is completely automatic, thanks to a homology-based curve segmentation strategy.…”

“…However, that calibration approach is extended here to both internal and external parameters, and is completely automatic, thanks to a homology-based curve segmentation strategy. In addition, our approach combines both the calibration primitives exploited in [12] (imaged cross-sections) and those used in [10] (apparent contour) so as to add robustness and accuracy to the calibration task. Besides, the approach offers a new solution to the problem of camera calibration from turntable sequences, differing from previous solutions (see e.g.…”