Application – what we can do

Camera Calibration from a Single Image based on Coupled Line Cameras and Rectangle ConstraintJoo-Haeng Lee* * Robot and Cognitive Systems Dept., ETRI, KOREA

ICPR 2012, TuPSAT2.5

(1) Assume a simple camera model with unknown parameters.

• Square pixel: fx= fy

• No skew: s = 0• Image center on principal axis

• Square pixel: fx= fy

• No skew: s = 0• Image center on principal axis

(3) We can determine if that quadrilateral Qg is the image of any scene rectangle.

• Determinant: D• Determinant: D

D ± =

A 0 + A 1 ± 2 A 0 A 1

A 1 − A 0

> 0

(4) If so, we can reconstruct the scene rectangle Gg in a metric sense without camera calibration. Gg

(2) When an image quadrilateral Qg is given, Qg

(5) Finally, we can calibrate camera parameters:

• focal length: f• external params: [R|T]

Theory - how we do it

(1) An analytic solution for pose estimation of a 2D line camera is proposed.

(3) Based on this observation, we can derive an analytic solution for projective reconstruction.

(2) The rectangle constraint can be modelled with two coupled lines cameras.

cv0v2 m

tanθ0

2=

A 0 + A 1 ± 2 A 0 A 1

A 1 − A 0

= D ±

(4) It can be applied to a general quadrilateral since the virtual centered quadrilateral can be found.

(5) The proposed method is numerically stable for pixel poises and singular cases.