Camera Calibration. CS485/685 Computer Vision Prof. Bebis. f/s y. f/s x. Camera Calibration - Goal. Estimate the extrinsic and intrinsic camera parameters. f/s y. f/s x. Camera Calibration - How.
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CS485/685 Computer Vision
(1) A 3D object of known geometry.
(2) Located in a known position in space.
(3) Yields image features which can be located accurately.
equally spaced black squares.
reference frame is centered at
the lower left corner of the
right grid, with axes parallel to
the three directions identified by
the calibration pattern.
Compute the extrinsic and intrinsic camera
parameters from N corresponding pairs of points:
and (xim_i, yim_i), i = 1, . . . , N.
(1) Indirect camera calibration
(1.1) Estimate the elements of the projection matrix.
(1.2) If needed, compute the intrinsic/extrinsic camera parameters from the entries of the projection matrix.
(2) Direct camera calibration
Direct recovery of the intrinsic and extrinsic camera parameters.
Note: replaced (xim,yim) with (x,y) for simplicity.
N x 12 matrix
(Method 1) Step 2: find intrinsic/extrinsic parameters
(1) Assuming that oxand oyare known, estimate all other parameters.
(2) Estimate oxand oy
divide by f y and re-arrange terms:
we obtain the following equation:
N x 8 matrix
or xTz+fx(r11Xw+r12Yw+r13Zw+Tx) = -x(r31Xw+r32Yw+r33Zw)
Using SVD, the (least-squares) solution is:
Orthocenter Theorem:Let T be the triangle on the image plane defined by the three vanishing points of three mutually orthogonal sets of parallel lines in space. Then, (ox, oy) is the orthocenter of T.