General case cameras can be arbitrary locations and orientations Binocular stereo Special case cameras are parallel to each other and translated along X axis Z axis X axis Stereo with rectified cameras ID: 1007145
Download Presentation The PPT/PDF document "Binocular stereo Binocular stereo" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
1. Binocular stereo
2. Binocular stereoGeneral case: cameras can be arbitrary locations and orientations
3. Binocular stereoSpecial case: cameras are parallel to each other and translated along X axisZ axisX axis
4. Stereo with rectified camerasSpecial case: cameras are parallel to each other and translated along X axisZ axisX axis
5. Stereo headKinect / depth cameras
6. Stereo with “rectified cameras”
7. Perspective projection in rectified camerasWithout loss of generality, assume origin is at pinhole of 1st camera
8. Perspective projection in rectified camerasWithout loss of generality, assume origin is at pinhole of 1st camera
9. Perspective projection in rectified camerasWithout loss of generality, assume origin is at pinhole of 1st camera
10. Perspective projection in rectified camerasWithout loss of generality, assume origin is at pinhole of 1st camera
11. Perspective projection in rectified camerasWithout loss of generality, assume origin is at pinhole of 1st camera
12. Perspective projection in rectified camerasWithout loss of generality, assume origin is at pinhole of 1st camera
13. Perspective projection in rectified camerasWithout loss of generality, assume origin is at pinhole of 1st camera
14. Perspective projection in rectified camerasWithout loss of generality, assume origin is at pinhole of 1st cameraY coordinate is the same!X coordinate differs by tx/Z
15. Perspective projection in rectified camerasX coordinate differs by tx/ZThat is, difference in X coordinate is inversely proportional to depthDifference in X coordinate is called disparity Translation between cameras (tx) is called baselinedisparity = baseline / depth
16. The disparity imageFor pixel (x,y) in one image, only need to know disparity to get correspondenceCreate an image with color at (x,y) = disparityright imageleft imagedisparity
17. Perspective projection in rectified camerasFor rectified cameras, correspondence problem is easierOnly requires searching along a particular row.
18. NCC - Normalized Cross CorrelationLighting and color change pixel intensitiesExample: increase brightness / contrastSubtract patch mean: invariance to Divide by norm of vector: invariance to similarity = Why not SIFT?
19. Cross-correlation of neighborhoodtranslate so that mean is zero
20. left image bandright image bandcross correlation100.5x
21. left image bandright image bandcross correlation10x0.5target region
22. The NCC cost volumeConsider M x N imageSuppose there are D possible disparities. For every pixel, D possible scoresCan be written as an M x N x D arrayTo get disparity, take max along 3rd axis
23. Computing the NCC volumeFor every pixel (x, y)For every disparity dGet normalized patch from image 1 at (x, y)Get normalized patch from image 2 at (x + d, y)Compute NCC
24. Computing the NCC volumeFor every disparity dFor every pixel (x, y)Get normalized patch from image 1 at (x, y)Get normalized patch from image 2 at (x + d, y)Compute NCCAssume all pixels lie at same disparity d (i.e., lie on same plane) and compute cost for eachPlane sweep stereo
25. NCC volumeDisparity
26. Perspective projection in rectified camerasWithout loss of generality, assume origin is at pinhole of 1st cameraY coordinate is the same!X coordinate differs by tx/Z
27. Perspective projection in rectified camerasdisparity = tx/ZIf tx is known, disparity gives ZOtherwise, disparity gives Z in units of txSmall-baseline, near depth = large-baseline, far depth
28. Perspective projection in rectified camerasFor rectified cameras, correspondence problem is easierOnly requires searching along a particular row.
29. Rectifying camerasGiven two images from two cameras with known P, can we rectify them?Can we create new images corresponding to a rectified setup?
30. Rectifying camerasCan we rotate / translate cameras?Do we need to know the 3D structure of the world to do this?
31. Rotating camerasAssume K is identityAssume coordinate system at camera pinhole
32. Rotating camerasAssume K is identityAssume coordinate system at camera pinhole
33. Rotating camerasWhat happens if the camera is rotated?
34. Rotating camerasWhat happens if the camera is rotated?No need to know the 3D structureRotation matrixHomogenous coordinates of original pixelHomogenous coordinates of mapped pixel
35. Rotating cameras
36. Rectifying cameras
37. Rectifying cameras
38. Rectifying cameras
39. Rectifying cameras
40.