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STEREO IMAGING (continued)

STEREO IMAGING (continued). RIGHT IMAGE PLANE. LEFT IMAGE PLANE. FOCAL LENGTH f. RIGHT FOCAL POINT. LEFT FOCAL POINT. BASELINE d. BINOCULAR STEREO SYSTEM.

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STEREO IMAGING (continued)

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  1. STEREO IMAGING(continued)

  2. RIGHT IMAGE PLANE LEFT IMAGE PLANE FOCAL LENGTH f RIGHT FOCAL POINT LEFT FOCAL POINT BASELINE d BINOCULAR STEREO SYSTEM • GOAL: Passive 2-camera system for triangulating 3D position of points in space to generate a depth map of a world scene. • Example of a depth-map: z=f(x,y) where x,y coordinatizes one of the image planes and z is the height above the respective image plane. (2D topdown view)

  3. RIGHT IMAGE PLANE LEFT IMAGE PLANE FOCAL LENGTH f RIGHT FOCAL POINT LEFT FOCAL POINT BASELINE d BINOCULAR STEREO SYSTEM • Correspondence Problem is a key issue for binocular stereo -- namely identify image features in respective images that correspond to exactly the same world object point. • Clearly localization of image features (e.g., edges) is of critical importance to 3D measurement accuracy. (2D topdown view)

  4. LIMITED FIELD OF VIEW OCCLUSION SOME OTHER MAJOR PROBLEMS WITH CORRESPONDENCE (2D VIEW)

  5. BINOCULAR STEREO SYSTEM(2D VIEW Verged Stereo System Nonverged Stereo System

  6. Z Z=f (0,0) (d,0) X XL XR df Z = (XL - XR) BINOCULAR STEREO SYSTEM DISPARITY (XL - XR) Z = (f/XL) X Z= (f/XR) (X-d) (f/XL) X = (f/XR) (X-d) X = (XR d) / (XL - XR)

  7. Points of closest approach LEFT IMAGE RIGHT IMAGE BINOCULAR STEREO SYSTEM(3D VIEW) • Rays of projection in 3D may not intersect at all.

  8. (XR,YR) (XL,YL) (0,0,0) (d,0,0) Z Y Points of closest approach X BINOCULAR STEREO SYSTEM

  9. (XR,YR) (XL,YL) (0,0,0) (d,0,0) Points of closest approach =(XL,YL,f) - (0,0,0) ^ ^ u = v = =(XR+d,YL,f) - (d,0,0) v u u v v u v u = (d,0,0) - (0,0,0) D D ^ ^ FIND a and b that minimizes| au - (D + bv) | where norm | | is Euclidean Norm. BINOCULAR STEREO SYSTEM

  10. (XR,YR) (XL,YL) Best Geometric Computation is: (0,0,0) (d,0,0) ^ ^ a u + (D + b v) o o 2 Points of closest approach 2 2 ^ ^ ^ ^ 1 - (u.v) 1 - (u.v) u v D ^ ^ FIND a and b that minimizes| au - (D + bv) | where norm | | is Euclidean Norm. BINOCULAR STEREO SYSTEM ^ ^ ^ ^ u .D - (u.v)(v.D) a = o ^ ^ ^ ^ (v.u)(u.D) - v.D b = o

  11. Points of closest approach C A B EPIPOLAR GEOMETRY • For an image point C in the left image plane consider the plane determined by the left image focal point A the right image focal point B and the point C. Call this the epipolar plane for image point C with respect to a particular binocular stereo configuration.

  12. Points of closest approach C A B EPIPOLAR GEOMETRY • In order to guarantee intersection of projective rays produced from the left and right image planes, the point in the right image plane corresponding to C must lie on the intersection of the epipolar plane with the right image plane. EPIPOLAR LINE EPIPOLAR PLANE

  13. EPIPOLAR GEOMETRY(‘SCANLINE COHERENT’ STEREO SYSTEM)

  14. EPIPOLAR GEOMETRY(VERGED IN)

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