3D computer vision techniques v.4b2 1

●●● ●●●● ●●●●● ●●●● How to obtain 3D information? 3:8 ● Cameras-2D Range sensors 3D 3D computer vsion techniques v 4

3D computer vision techniques v.4b2 6 How to obtain 3D information? ⚫ Cameras-2D ⚫ Range sensors-3D

●●● ●●●● ●●●●● ●●●● ●●●●● Challenges ●●●● o obtain 3d information for tasks in a 3d world o 2D-to-3D reconstruction from a camera 3d directly- laser range sensor, kinect sensor ● Novel sensors Camera array/ multiple camera ° One pixel camera ight field camera 3D computer vsion techniques v 4

3D computer vision techniques v.4b2 7 Challenges ⚫ Obtain 3D information for tasks in a 3D world. ⚫ 2D-to-3D reconstruction from a camera ⚫ 3D directly— laser range sensor, kinect sensor ⚫ Novel sensors ⚫ Camera array/ multiple camera ⚫ One pixel camera ⚫ light field camera

●●● 2D-to-3D reconstruction ●●●● ●●●●● ●●●● ●●●●● (feature based method) ●●●● Camera(perspective projection Features-extraction and correspondences ● Methods ° One-image method TWO-image(Stereo) method ° Three-image method N-image method Bundle adjustment ● Kalman filter 3D computer vsion techniques v 4

3D computer vision techniques v.4b2 8 2D-to-3D reconstruction (feature based method) ⚫ Camera (perspective projection) ⚫ Features-extraction and correspondences ⚫ Methods ⚫ One-image method ⚫ Two-image (Stereo) method ⚫ Three-image method ⚫ N-image method ⚫ Bundle adjustment ⚫ Kalman filter

●●● http://upload.wikimediaorg/wikipedia/en/8/81/pinhole-camera.png3... ●●●● ●●●●● Camera: 3D to 2D projection ●●●● Pinhole Camera Perspective model u=FX/Z(nonlinear relation V=FRY/Z Virtual World Screen or cCd center Y sensor Screen Or Thin lens CC or a pin he sensor

3D computer vision techniques v.4b2 9 Camera: 3D to 2D projection Perspective model u=F*X/Z (nonlinear relation) v=F*Y/Z F Z Y v World center F Thin lens or a pin hole Virtual Screen or CCD sensor Real Screen Or CCD sensor Pinhole Camera http://upload.wikimedia.org/wikipedia/en/8/81/Pinhole-camera.png

●●● ●●●● Perspective ●●●● Wod● Projective Coordinates Zw XW Rc. TC Modelmat t=l image XYZ v-aXIs XC-axis Camera u Coordinates Zc-axis Principal axis≤- c(Image center,(0,0, 0) Camera center u-aXIs F=focal length Yc-axis (0,0)of image plane 3D computer vsion techniques v 4b

3D computer vision techniques v.4b2 10 Perspective Projective ⚫ Model M at t=1 c (Image center, ox ,oy ) F=focal length image Oc= (0,0,0) (Camera center) Xc-axis Zc-axis Yc-axis v-axis u-axis X,Y,Z (u,v) (0,0) of image plane Camera Coordinates. World Coordinates Zw Yw Xw Rc,Tc Principal axis