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Photogrammetry (Camera Models)

Photogrammetry (Camera Models). The basic pinhole model. Euclidean 3-space R3 to Euclidean 2-space R2. Central projection using homogeneous coordinates. Homogeneous 4-vector. Homogeneous Camera Projection Matrix. Principal point offset. Principal point offset.

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Photogrammetry (Camera Models)

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  1. Photogrammetry(Camera Models)

  2. The basic pinhole model Euclidean 3-space R3 to Euclidean 2-space R2

  3. Central projection using homogeneous coordinates Homogeneous 4-vector Homogeneous Camera Projection Matrix

  4. Principal point offset

  5. Principal point offset • K=Camera Calibration Matrix

  6. Camera Rotation & Translation The two coordinate frames are related via a rotation and a translation

  7. Camera Rotation & Translation X is now in a world coordinate frame

  8. CCD cameras The number of pixels per unit distance in image coordinate The general form of the calibration matrix of a CCD camera

  9. Finite projective camera The added parameter s is reffered to as the skew parameter.

  10. Camera anatomy A general projective camera may be decomposed into blocks according to Where M is a 3*3 matrix.

  11. Camera center Consider the line containing C and any other point A in 3-space.

  12. Column vectors • p1, p2, p3 are the vanishing points of the world coordinate x, y, and z axes respectively

  13. Row vectors

  14. Point at infinity of the image P3 is principal plane C lies on the principal plane The principal plane The principal plane is the plane through the camera center parallel to the image plane

  15. The principal point The principal axis is the line passing through the camera centre C, with direction perpendicular to the principal plane The axis intersects the image plane at the principal point.

  16. The principal axis vector • Vector points in the direction of the direction axis. • This leaves an ambiguity as to whether or points in the positive direction. x=PX , , is the third row of M. The is the direction vector. is unaffected by scaling of P, which is a vector in the direction of the principal axis, directed towards the front of the camera.

  17. Depth of points A camera matrix ,projecting a point in 3-space to the image point .since PC=0 where is the principal ray direction. If the camera matrix is normalized so that det M>0 and , then is a unit vector pointing in the positive axial direction.

  18. Projective Camera (Matrix)

  19. Computation of the Camera Matrix P

  20. The Direct Linear Transformation (DLT) Algorithm

  21. The Direct Linear Transformation (DLT) Algorithm

  22. The Direct Linear Transformation (DLT) Algorithm

  23. The Direct Linear Transformation (DLT) Algorithm • Obtain the SVD of A. • The unit singular vector corresponding to the smallest value is the solution h, then h is the last column of V The matrix H is determined form h.

  24. Euclidean vs projective spaces The transformation between the camera and world coordinate frame is again represented between by a 4*4 homogeneous matrix, and the resulting map from projective 3-space to the image is still represensted by a 3*4 matrix P with rank3

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