On plane-based camera calibration: A general algorithm, singularities, applications

Abstract

We present a general algorithm for plane-based calibration that can deal with arbitrary numbers of views and calibration planes. The algorithm can simultaneously calibrate different views from a camera with variable intrinsic parameters and it is easy to incorporate known values of intrinsic parameters. For some minimal cases, we describe all singularities, naming the parameters that can not be estimated. Experimental results of our method are shown that exhibit the singularities while revealing good performance in non-singular conditions. Several applications of plane-based 3D geometry inference are discussed as well.

An Enhanced Structure-from-Motion Paradigm Based on the Absolute Dual Quadric and Images of Circular Points

“…The CP-pair consists of two complex conjugate points at infinity [3] whose images, easily derived from the geometry of any planar shape like [15,16,11], define the well-known plane-based calibration constraints [16]. Our key idea is that incorporating the images of CPpairs into the SfM algorithm sequence, namely (i) in projective factorization scheme mixing images of natural points and images of CP as well and (ii) in the Euclidean update of the obtained projective reconstruction.…”

“…Note that, in the general case, the four equations brought by constraints (10,11) are linearly independent w.r.t. Q * ∞ .…”

“…What is the link between the circular-point constraints (10,11) and the "original" linear self-calibration constraints (7,8)? In the light of the insights given in the previous section, we suggest to revisit (7,8) by first complexifying them to get algebraically equivalent equations (superscripts are omitted)…”

“…In this case, constraints (10,11) hold with Π = P (1, i, 0) and P q = P (0, 0, 1) respectively represent the line tangent to ω at I o and the image plane's line at infinity.…”

Interpreting Sphere Images Using the Double-Contact Theorem

“…The intrinsic parameters describe the camera's imaging geometric characteristics, and the extrinsic parameters represent the camera's orientation and position with respect to the world coordinate system. Many approaches to camera calibration have been proposed and they can be classified into two categories: using calibration objects [6,13,16,11,1,2,8,12,14,15], and self-calibration [7,5,9]. As we know, the occluding contour of a sphere is projected to a conic in the perspective image [1,2,5,12,14].…”