Camera model) Intrinsic parameters I extrinsic parameters I projection Examples, center of CCD is at image center (right hand coordinate system with ideal CCD) v(pixels) 768 OO (512,384) in pixels CCD u(pixels 1024 1,1 Ch2. Cameras v0.b2 21
Camera model | Intrinsic parameters | extrinsic parameters | projection Examples, center of CCD is at image center (right hand coordinate system with ideal CCD) CCD u (pixels) v (pixels) (Ox ,Oy )= (512,384) in pixels y x Z 1024 1,1 768 Ch2. Cameras v.0.b2 21
Camera model) Intrinsic parameters I extrinsic parameters I projection A summary The focal length can be expressed in pixels f=f/Sx (assume Sx=Sy A 3D feature point is at P=Xc Yc, Zc) The center of the ccd sensor is placed at O, Oy in pixels of the image The projected image point of p=(Xc, yc, Z c is at u, v) We can use Intrinsic parameters to represent all the ese Ch2. Cameras v0.b2
Camera model | Intrinsic parameters | extrinsic parameters | projection A summary • The focal length can be expressed in pixels, f=F/Sx (assume Sx=Sy) • A 3D feature point is at P=(Xc,Yc,Zc) • The center of the CCD sensor is placed at Ox,Oy in pixels of the image. • The projected image point of P=(Xc,Yc,Zc) is at (u,v) • We can use Intrinsic parameters to represent all these. Ch2. Cameras v.0.b2 22
Camera model Intrinsic parameters extrinsic parameters I projection Camera parameters trinsiC parameters Focal length(F)in meters pixel width, height are sx Sy, in meters, resp image(or principal) center(ox o in pixels lens-distortion(k)(assign no distortion ignored here) ° Extrinsic parameters Position of the camera such as (RC--rotation, Tc--translation) Ch2. Cameras v0.b2
Camera model | Intrinsic parameters | extrinsic parameters | projection Camera parameters • Intrinsic parameters – Focal length (F) in meters, – pixel width, height are sx sy in meters, resp. – image (or principal) center (ox ,oy ) in pixels – lens-distortion (K) (assign no distortion , ignored here). • Extrinsic parameters – Position of the camera such as (Rc -- rotation, Tc -- translation) Ch2. Cameras v.0.b2 23
Camera model Intrinsic parameters extrinsic parameters I projection Intrinsic parameters from camera coordinates to image coordinates Mint a 3x3 matrix Current discussion assumes center of camera=center of world Ch2. Cameras v0.b2
Camera model | Intrinsic parameters | extrinsic parameters | projection Intrinsic parameters from camera coordinates to image coordinates Mint ( a 3x3 matrix) (Current discussion assumes center of camera=center of world) Ch2. Cameras v.0.b2 24
Camera model Intrinsic parameters extrinsic parameters I projection Typical webcam Intrinsic parameters ixed: by manufacturer E.g. S, =s, 5.46um(1um=1x10A-6 m=1 micron) For a CCD of 1024x768, the image center or principa center is at(0,o=(512X384) lens-distortion(k) for fixed lens. ignore to make life easier Variable focal length(eg f 5mm), may be varied zoom lens lens-distortion(k) may follow f Ch2. Cameras v0.b2
Camera model | Intrinsic parameters | extrinsic parameters | projection Typical webcam Intrinsic parameters • Fixed: by manufacturer – E.g. sx =sy 5.46um (1um=1x10^-6 m=1 micron) – For a CCD of 1024x768 , the image center or principal center is at (ox ,oy )=(512x384) – lens-distortion (K) for fixed lens. (ignore to make life easier) • Variable : – focal length (e.g. f 5mm) , may be varied (zoom lens), – lens-distortion (K) may follow f. Ch2. Cameras v.0.b2 25