《图像处理与计算机视觉 Image Processing and Computer Vision》课程教学资源（PPT课件讲稿）Chapter 02 Image processing and computer vision（Camera models and parameters）

Camera model Intrinsic parameters extrinsic parameters I projection Intrinsic parameters Mint (an upper-triangular matrix) 3D=Xc YC. Zc in meters Image=u, v in pixels Sty s=arbitrary rating factor Exercise. Show equations 3)(4 are the same as this F/S30 matrix form eq 5) Recal∥ 0 F/s O nt U=(FS*Xz+0x-(3) 0 V=(E/5 *(Y/ Z3+0v-(4) image center=(0,,O,)in pixels Answer: from(5) use matrix multiplication F=focal length in meters s+u=(5)*(x)+a2*z-() s*v=(F5y+oy+z-间 f= focal length in pixels Set s=z------. xsD=pixel size in meters (iii, hence u=(F/Sx *(X/ Z2+Ox, same as(3) (ii/ii, hence v=(F/SV*(Y/Z5+Ov, same as(4) ( proved Ch2. Cameras v0.b2

Camera model | Intrinsic parameters | extrinsic parameters | projection Intrinsic parameters Mint (an upper-triangular matrix) • 3D=Xc,Yc,Zc in meters • Image=u,v in pixels • s= arbitrary rating factor • Exercise: • Show equations (3) (4) are the same as this matrix form eq(5). • Recall: • u=(F/sx )*(Xc /Zc ) + ox --(3) • v=(F/sy )*(Yc /Zc ) + oy --(4) • Answer: from (5) use matrix multiplication • s*u=(F/sx )*(Xc ) + ox *Zc --(i) • s*v=(F/sy )*(Yc ) + oy *Zc --(ii) • Set s= Zc -------------------------(iii) • (i)/(iii), hence u=(F/sx )*(Xc /Zc ) + ox , same as (3) • (ii)/(iii), hence v=(F/sy )*(Yc /Zc ) + oy , same as (4) (proved!) , _ in meters _ in pixels _ in meters _ ( , ) in pixels 0 0 1 0 / / 0 * (5) * int c c c int S S pixel size f focal length F focal length image center o o F s o F s o M Z Y X M s s v s u x y x y y y x x = = = =           = − − − −           =           Ch2. Cameras v.0.b2 26

Camera model Intrinsic parameters extrinsic parameters I projection Simplified Intrinsic parameters Mint in pixels Sx=Sy and F/sx=f in pixels 3D=X..Z in meters C Image=u, v in pixels C s= arbitrary rating factor x int f 001 image center=(0,,o,(in pixels) f=focal length (in pixels) Ch2. Cameras v0.b2 27

Camera model | Intrinsic parameters | extrinsic parameters | projection Simplified Intrinsic parameters Mint in pixels Sx=Sy and F/sx= f in pixels • 3D=Xc ,Yc ,Zc in meters • Image=u,v in pixels • s= arbitrary rating factor _ (in pixels) _ ( , )(in pixels) 0 0 1 0 0 * * int int f focal length image center o o f o f o M Z Y X M s s v s u x y y x c c c = =           =           =           Ch2. Cameras v.0.b2 27

Examples, center of CCd is at image center (right hane on Camera model Intrinsic parameters) extrinsic parameters I projecti coordinate system with ideal ccD) f 0 v(pixels) 768 001 OX, Oy)= (512,384) in pixels CCD u(pixels 1024 1,1 Ch2. Cameras v0.b2 28

Camera model | Intrinsic parameters | extrinsic parameters | projection Examples, center of CCD is at image center (right hand coordinate system with ideal CCD)           = 0 0 1 0 0 int y x f o f o M CCD u (pixels) v (pixels) (Ox,Oy)= (512,384) in pixels y x Z 1024 1,1 768 Ch2. Cameras v.0.b2 28

Camera model Intrinsic parameters extrinsic parameters I projection Worksheet 2,3 The camera ccd has 1024 768 pixels and the size of the ccd is 5mm x3 75mm What are Sx, Sy(pixel size)? Ans: Ch2. Cameras v0.b2

Camera model | Intrinsic parameters | extrinsic parameters | projection Worksheet 2.3 • The camera CCD has 1024 x 768 pixels and the size of the CCD is 5mm x 3.75mm • What are Sx,Sy (pixel size)? • Ans:____________ Ch2. Cameras v.0.b2 29

Camera model Intrinsic parameters extrinsic parameters I projection Worksheet 2. 4, 3D projection on image S=S,=54 ( Ch1 el.m) (o,ov=(512, 384)in pixels f=4.3mm/5.4um=800 pixels ⅨYz=[0.02,0.05,1.2] meters s u X(8000512)0.02 MY 08003840.05 Int [uv]=? 001‖1.2 Answer: Write a pseudo code(or matlab) program to calculate the projected point [u v] t tom [X y on the above camera intrinsic parameters. c)C Ch2. Cameras v0.b2

Camera model | Intrinsic parameters | extrinsic parameters | projection Worksheet 2.4, 3D projection on image (Ch1_e1.m ) • sx =sy=5.4um • (ox ,oy )=(512,384) in pixels • f=4.3mm/5.4um=800 pixels • [Xc ,Yc ,Zc ] T =[0.02,0.05,1.2]Tmeters • [u v]’=? • Answer: ___________ • Write a pseudo code (or matlab) program to calculate the projected point [u v] T from [Xc ,Yc ,Zc ] T based on the above camera intrinsic parameters.                     =           =           1.2 0.05 0.02 0 0 1 0 800 384 800 0 512 * * int Z Y X M s s v s u Ch2. Cameras v.0.b2 30