matlab相機定標工具箱程序的算法原理

1、 Camera Calibration Toolbox for MatlabDescription of the calibration parametersAfter calibration, the list of parameters may be stored in the matab file Calib_Results by clicking on Save. The list of variables may be se

2、parated into two categories: Intrinsic parameters and extrinsic parameters. Intrinsic parameters (camera model): The internal camera model is very similar to that used by Heikkil 伯 a> and Silven at the University of O

3、ulu in Finland. Visit their online calibration page, and their publication page. We specifically recommend their CVPR'97 paper: A Four-step Camera Calibration Procedure with Implicit Image Correction. The list of int

4、ernal parameters: ? Focal length: The focal length in pixels is stored in the 2x1 vector fc. ? Principal point: The principal point coordinates are stored in the 2x1 vector cc. ? Skew coefficient: The skew coefficient de

5、fining the angle between the x and y pixel axes is stored in the scalar alpha_c. ? Distortions: The image distortion coefficients (radial and tangential distortions) are stored in the 5x1 vector kc. Definition of the int

6、rinsic parameters: Let P be a point in space of coordinate vector XXc = [Xc;Yc;Zc] in the camera reference frame. Let us project now that point on the image plane according to the intrinsic parameters (fc,cc,alpha_c,kc).

7、 Let xn be the normalized (pinhole) image projection: Let r2 = x2 + y2. After including lens distortion, the new normalized point coordinate xd is defined as follows:Commented [微軟用戶 微軟用戶 1]: 四個內(nèi)參，包括焦距 fc，原點坐標 cc， 相機坐標系中

8、 x 和 y 軸夾角 alpha_c（接近 90°） ，幾何畸變系數(shù) kcBoth components of the vector fc are usually very similar. The ratio fc(2)/fc(1), often called “aspect ratio“, is different from 1 if the pixel in the CCD array are not square. T

9、herefore, the camera model naturally handles non-square pixels. In addition, the coefficient alpha_c encodes the angle between the x and y sensor axes. Consequently, pixels are even allowed to be non-rectangular. Some au

10、thors refer to that type of model as “affine distortion“ model. In addition to computing estimates for the intrinsic parameters fc, cc, kc and alpha_c, the toolbox also returns estimates of the uncertainties on those par

11、ameters. The matlab variables containing those uncertainties are fc_error, cc_error, kc_error, alpha_c_error. For information, those vectors are approximately three times the standard deviations of the errors of estimati

12、on. Here is an example of output of the toolbox after optimization: In this case fc = [657.30254 ; 657.74391] and fc_error = [0.28487 ; 0.28937], cc = [302.71656 ; 242.33386], cc_error = [0.59115 ; 0.55710], ... Importan

13、t Convention: Pixel coordinates are defined such that [0;0] is the center of the upper left pixel of the image. As a result, [nx-1;0] is center of the upper right corner pixel, [0;ny-1] is the center of the lower left co

14、rner pixel and [nx-1;ny-1] is the center of the lower right corner pixel where nx and ny are the width and height of the image (for the images of the first example, nx=640 and ny=480). One matlab function provided in the

15、 toolbox computes that direct pixel projection map. This function is project_points2.m. This function takes in the 3D coordinates of a set of points in space (in world reference frame or camera reference frame) and the i

16、ntrinsic camera parameters (fc,cc,kc,alpha_c), and returns the pixel projections of the points on the image plane. See the information given in the function. The inverse mapping: The inverse problem of computing the norm

17、alized image projection vector xn from the pixel coordinate x_pixel is very useful in most machine vision applications. However, because of the high degree distortion model, there exists no general algebraic expression f

18、or this inverse map (also called normalization). In the toolbox however, a numerical implementation of inverse mapping is provided in the form of a function: normalize.m. Here is the way the function should be called: xn

19、 = normalize(x_pixel,fc,cc,kc,alpha_c). In that syntax, x_pixel and xn may consist of more than one point coordinates. For an example of call, see the matlab function compute_extrinsic_init.m. Commented [微軟用戶 微軟用戶 4]: Fc

20、_error,cc_error,kc_error,alpha_c_error 這四個變量記錄四個內(nèi)參的不確定度，大小設(shè)定為三倍 標準差Commented [微軟用戶 微軟用戶 5]: 注意：圖像左上角默認為原 點[0;0] 左下角為[0;ny-1] 右上角為[nx-1;0] 右下角為[nx-1;ny-1]Commented [微軟用戶 微軟用戶 6]: 函數(shù) project_points2.m 將相機 坐標系下的三維點陣按照內(nèi)參轉(zhuǎn)化