tsai摄像机标定源代码下载

########################################################### Tsai Camera Calibration FAQ - Reg Willson Date: Oct 27, 1995 If you have any questions, comments, or suggestions about this document, the software, or camera calibration in general, please read item 5. --------------------------- Table of contents --------------------------- 1 - What is Tsai's camera model? 2 - Where can I find the required intrinsic camera constants? 2.1 - Why is the calibrated focal length not the same as the number printed on the lens? 3 - How do I collect calibration data? 3.1 - Coplanar and non-coplanar data 3.2 - Distribution of data points 3.3 - Placement of world coordinate origin 3.4 - Perspective projection effects (or lack thereof) 3.5 - Subpixel measurement of image features 4 - What are some of the nonlinear optimization issues? 5 - Where can I find more information on Tsai's algorithm? 6 - Comments and thanks --------------------------- Contents --------------------------- 1 - What is Tsai's camera model? Tsai's camera model is based on the pin-hole model of 3D-2D perspective projection with 1st order radial lens distortion. The model has 11 parameters: five internal (also called intrinsic or interior) parameters: f - effective focal length of the pin-hole camera, kappa1 - 1st order radial lens distortion coefficient, Cx, Cy - coordinates of center of radial lens distortion -and- the piercing point of the camera coordinate frame's Z axis with the camera's sensor plane, sx - scale factor to account for any uncertainty in the framegrabber's resampling of the horizontal scanline. and six external (also called extrinsic or exterior) parameters: Rx, Ry, Rz - rotation angles for the transform between the world and camera coordinate frames, Tx, Ty, Tz - translational components for the transform between the world and camera coordinate frames. In addition to the 11 variable camera parameters Tsai's model has six fixed intrinsic camera constants: Ncx - number of sensor elements in camera's x direction (in sels), Nfx - number of pixels in frame grabber's x direction (in pixels), dx - X dimension of camera's sensor element (in mm/sel), dy - Y dimension of camera's sensor element (in mm/sel), dpx - effective X dimension of pixel in frame grabber (in mm/pixel), and dpy - effective Y dimension of pixel in frame grabber (in mm/pixel). 2 - Where can I find the required intrinsic camera constants? Commercial and industrial cameras often list Ncx, dx, and dy in their user guides. With consumer cameras you will generally need to contact the manufacturer. You don't need to know the actual values of the intrinsic constants to calibrate an "accurate" camera model. For most applications "accurate" simply means that given the 3D world coordinates of a point P the camera model will accurately predict the 2D position of the point's image P' in the frame buffer. In these cases the true intrinsic constants aren't necessary. To get the camera calibration to converge to a solution you only need the aspect ratio of the camera/frame grabber set up, i.e. the ratio between dpx and dpy. You can get a good estimate for this from a straight-on image of a rectangular target. Measuring the rectangle, the ratio (pixels from side-to-side in image) / (mm from side-to-side on target) ------------------------------------------------------------------------ (pixels from top-to-bottom in image) / (mm from top-to-bottom on target) should be an accurate enough estimate of dpx / dpy to allow the calibration to converge. The calibration algorithms (with the exception of the basic Tsai coplanar calibration) will adjust the sx parameter to automatically compensate for any error in the ratio of dpx / dpy. Given the ratio of dpx to dpy, simply pick some value for dpy, say 10um (or if you know it you can use the actual vertical pixel pitch) and use that to back calculate dpx, dx, and dy. Set Ncx = Nfx, sx = 1.0, and Cx and Cy to be the center of the frame buffer. When you calibrate the model the algorithm will adjust sx, Cx, and Cy to give a best fit set of intrinsic parameters. Observe if you double dpx and dpy, all the extrinsic parameters, Cx, Cy, and sx, and the calibration error should remain the same. The calibrated camera model will be just as accurate. The only thing that will change is f and k1. 2.1 - Why is the calibrated focal length not the same as the number printed on the lens? Even if you use the exact intrinsic camera parameters specified by the manufacturer, the calibrated value of the effective focal length f is unlikely to be the same as the focal length specified on the lens. In these calibration algorithms the effective focal length is a parameter in a pin-hole camera model. The focal length printed on the lens is a parameter in a thick-lens camera model. While the two parameters have similar effects on the image they are actually quite different quantities. 3 - How do I collect calibration data? Calibration for the model consists of the 3D (x,y,z) world coordinates of a feature point (in mm) and the corresponding coordinates (Xf,Yf) (in pixels) of the feature point in the image. The 3D coordinates must be specified in a right-handed coordinate system. Once a camera has been calibrated, subsequent calibrations at different poses (i.e. with the camera rotated and/or translated) can be speeded up by using the intrinsic parameters from the first calibration as a starting point. 3.1 - Coplanar and non-coplanar data Tsai's algorithm has two variants: one for coplanar data and one for non-coplanar data. For coplanar data Tsai's algorithm requires the z component of the 3D coordinates to be 0. Basic coplanar calibration requires at least five data points. Basic non-coplanar calibration requires at least seven data points. Fully optimized calibration requires at least 11 data points for either coplanar and non-coplanar data. The sx camera parameter cannot be calibrated for using coplanar data. Its value is left unchanged in the coplanar calibration routines. 3.2 - Distribution of data points To accurately estimate the radial lens distortion and image center parameters the calibration data should be distributed broadly across the field of view. The distribution of data points should, if possible, span the range of depths that you expect to use the model over. 3.3 - Placement of world coordinate system origin Tsai's algorithm fails if the origin of the world coordinate system is near the center of the camera's field of view or near the Y axis of the camera coordinate system. The Y axis requirement ensures Ty is not exactly zero which is an explicit requirement in Tsai's algorithm. If your calibration data doesn't meet the above criteria you can simply create a new, artificial coordinate frame for the data that is offset from the world coordinate frame that you plan on working with. Just add the offset into the data before you calibrate with it. 3.4 - Perspective projection effects (or lack thereof) To be able to separate the effects of f and Tz on the image there needs to be perspective distortion (foreshortening) effects in the calibration data. For useable perspective distortion the distance between the calibration points nearest and farthest from the camera should be on the same scale as the distance between the calibration points and the camera. This applies both to coplanar and non-coplanar calibration. For co-planar calibration the worst case situation is to have the 3D points lie in a plane parallel to the camera's image plane (all points an equal distance away). Simple geometry tells us we can't separate the effects of f and Tz. A relative angle of 30 degrees or more is recommended to giv