Computer Vision Pattern Recognition

High Precision Camera Calibration by Tobias Hanning

By Tobias Hanning

A calibrated digital camera is the foremost to every optical size challenge. This paintings introduces digicam modelling and calibration in computing device imaginative and prescient. Tobias Hanning explains the vintage pinhole digicam version with distortion derived from 3rd order optics and indicates tips to receive an optimum resolution inside of this version. the restrictions of the vintage digital camera version in machine imaginative and prescient are defined and confirmed experimentally. to beat those obstacles substitute ways which increase the normal version are presented.

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The scale factor can be obtained simply by the fact that P˜33 = 1 holds for the image transformation. However, a Cholesky factorization requires that b∗ encodes a positive definite matrix. 32), one needs at least three observations of the pattern in general position (mutually not co-planar). However, the knowledge of a parameter (like α, β, u0 , v0 or αβ of the image transformation) yields to a system of linear equations with less unknowns (see [SM99] for more details). 8 we apply such adjustments for some known parameters in our experiments.

Note that the constraint b = 1 has no other justification than to avoid the trivial solution. g. b1 = 1 (since b1 should not be zero) can also be applied. From b∗ = λ(B11 , B12 , B22 , B13 , B23 , B33 )t Zhang ([Zha98]) derives b∗2 b∗4 − b∗1 b∗5 , b∗1 b∗3 − b∗2 2 b∗ 2 + v0 (b∗2 b∗4 − b∗1 b∗5 ) λ = b∗6 − 4 , b∗1 v0 = α= λ b∗1 , and β= λb∗1 , b∗1 b∗3 − b∗ 22 b∗2 α2 β , λ γv0 b∗4 α2 u0 = − . 33) are well defined, nor that α and β are positive. g. [HZ00]). For a positive definite symmetric matrix A the Cholesky factorization A = C t C ensures that the diagonal entries in the upper triangular matrix C are positive.

1 (undistortion, re-projection) ˜ D )−1 the un-distortion mapping. Furthermore, With the premises above we call (δ| we call the mapping ip → ip,B the re-projection of the camera mapping. For a simpler notation we identify ip,B with B −1 [{ip }]. 2 To keep a simple notation we omit the restriction of δ to the compact domain D in the following. Note that this is in fact a constraint for the observed points. For the pinhole assumption the closure of all sets B −1 [{ip }] (for ip ∈ I) intersect in the origin.

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