(1) The document proposes a method for camera calibration from a single image based on modeling the image as two coupled line cameras and applying rectangle constraints. (2) It presents an analytic solution for estimating the pose of a 2D line camera and models a rectangle constraint using two coupled line cameras. (3) Based on this, the method derives an analytic solution for projective reconstruction that allows reconstructing the scene rectangle in a metric sense without full camera calibration.

1. ICPR 2012, TuPSAT2.5
Camera Calibration from a Single Image based on Coupled Line Cameras and Rectangle Constraint
Joo-Haeng Lee* * Robot and Cognitive Systems Dept., ETRI, KOREA
Application – what we can do Theory - how we do it
(1) Assume a simple camera •• Square pixel: fxf==fyfy
Square pixel: x (1) An analytic solution for pose
model with unknown •• No skew: s s==00
No skew: estimation of a 2D line
parameters. •• Image center on principal axis
Image center on principal axis camera is proposed.
(2) When an image v2 m v0 c
quadrilateral Qg is given, Qg (2) The rectangle constraint can
be modelled with two
coupled lines cameras.
(3) We can determine if that • • Determinant: D
Determinant: D
quadrilateral Qg is the image (3) Based on this observation,
A 0 + A 1 ± 2 A 0A 1 θ0 A 0 + A 1 ± 2 A 0A 1
of any scene rectangle. D = >0 we can derive an analytic tan =
±
A1−A 0 2 A1−A 0
solution for projective
reconstruction. = D
(4) If so, we can reconstruct ±
the scene rectangle Gg in a
metric sense without camera (4) It can be applied to a
calibration. Gg general quadrilateral
since the virtual centered
quadrilateral can be found.
(5) Finally, we can calibrate
camera parameters: (5) The proposed method is
• focal length: f numerically stable for pixel
• external params: [R|T] poises and singular cases.