Camera Calibration with Accuracy Evaluation and Real-time Evaluation in the Use of Vision Robot

In order to calibrate a wide-angle camera in real-time and find the precious position of the target object which could help the robot to find to location where they are, new method which uses the center iteration method and the regional interpolation method based on the distortion correction table is proposed. With this method, the world coordinates of the target object could be calculated accurately. The experimental results show that the theory is effective enough to get the world coordinates of objects with good accuracy for industrial application. Introduction With the developing of image processing technology and camera manufacturing technology, machine vision applications in the use of robotics get more attentions. Owning to the inflexible of the robot mechanical structure in many industrial conditions, a wide-angle camera which can obtain a larger field will be used to get the position of the target object. Because of the distortion which is caused by the wide-angle lens, the accuracy of the positioning result of the target object will be impacted. [1] has introduced a good way for camera calibration. [2] has proposed the lens distortion model. And [3] [6] have provided many different ways to complete the camera calibration. But these algorithms of camera calibration are too complex for a robot system to realize. So, this paper will propose an available method which could get the accuracy world coordinates with the center iteration method and the regional interpolation method. Wide-angle camera model Wide-angle camera model can be divided into the pinhole camera model and the lens distortion model. Consideredthese two different models, the paper proposes a method that could get the actual coordinate of target object is divided into two steps: First, with the lens distortion model, the distortion of the pixel coordinate will be eliminated. And second, the world coordinates will be calculated with the pinhole camera model. A Pinhole camera model With the pinhole model, the relationship between the pixel coordinates and the world coordinates could be obtained as 0 0 f X u u du Z f Y v v dv Z ⎧ = + ⎪⎪ ⎨ ⎪ = + ⎪⎩ , where f is the focal length of the camera, du dv are the length of International Conference on Information Science and Computer Applications (ISCA 2013) © 2013. The authors Published by Atlantis Press 269 a pixel in the direction of u v. Two variables, Ku = f / du and Kv = f / dv, will be introduced. And Ku Kv u0 v0 are intrinsic parameters of a certain camera and they would not be changed after a camera is produced completely. So, the matrix form of the pinhole model can be described as (1). 0 0 0 0 0 0 1 ut Ku u X vt Kv v Y t Z ⎛ ⎞ ⎛ ⎞⎛ ⎞ ⎜ ⎟ ⎜ ⎟⎜ ⎟ = ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠ (1) B Lens distortion model There are mainly two main lens distortions in this model, radial distortion and tangential distortion. (u, v) is the ideal pixel coordinates in image plane without distortion, (u d ,v d ) is the pixel coordinates with distortion. Similarly, (x, y) are the ideal image coordinates without distortion in image plant and (xd ,yd)is the distortional image coordinates. The distortion camera model [2] can be described by formula (2): d u u v (r)+ (r) ( )+ (r) d v u u T B v v T r B ⎧ = + ⎨ = + ⎩ (2) Where 2 4 6 u 0 1 2 3 2 4 6 v 0 1 2 3 (r)=(u-u )(k r +k r +k r ) (r)=(v-v )(k r +k r +k r ) T T ⎧ ⎨ ⎩ , 2 2 u 1 2 2 2 v 1 2 (r)=2 ( 2 ) (r)= ( 2 ) 2 d d d d d d B p x y p r x B p r y p x y ⎧ + + ⎨ + + ⎩ . Equation (2) can be written in matrix form is shown as (3) d =P -P AJ (3) Where d [ ,v ] d d T P u = , [ ,v] P u = , 2 4 6 2 2 2 4 6 2 2 2 r +2x =[ ] r +2y 2 d d d d d d d d d d d d x x x r r r x y du du du A y y y r r r x y du du du , 1 2 3 1 2 =[k ,k ,k ,p ,p ] T J 2 2 2 r x y = + , 1 2 3 , , k k k are radial distortion coefficients, 1 2 , p p are the tangential distortion coefficients. Positioning method To obtain the world coordinates of target object, the positioning method is divided into four steps. First, calculate the distortion correspondence table. Secondly, obtain the pixel coordinates of the target object in the picture with distortion. Thirdly, eliminate the distortion of the pixel coordinates. And lastly, calculate the world coordinates of the target object with the pinhole camera model. A Distortion correspondence table With (3), the non-distortional pixel coordinates will be converted to the coordinates with distortion and then, the distortion correspondence tables could be obtained. Two double-precision floating point buffer, used to save the contents of the corresponding table, will be defined in this paper which are named Fu and Fv. With the following equation, one of the distortion correspondence tables could be obtained and stored in Fu. W and H are defined as the width and height of the image size.