Rectification (Affine, Metric) with Vanishing Point

Woo Yeong CHO·2021년 11월 20일
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Affine rectification


i) Taking two parallel lines and find the vanishing line.
ii) Taking a vanishing line that is in a finite space into a line at infinity (0,0,1)(0,0,1)

iii) Doing Homography : Two line that do have not Parrellel relationship are retificated.

Metric retification

i Pairs of line that were originally vertical in the image. Finding constraint ss in this equation:

(l1m1,l1m2+l2m1,l2m2)s=0(l_1m_1, l_1m_2 + l_2m_1, l_2m_2)s = 0

Based on the example, we do SVD to solve the linear equations of AS=0AS = 0, and the last column of vector is used as the solution.

Using Equation, we can obtain CDCP, linear with AS = 0

If you put sqrt on the diagonal component in U,D,VT=svd(S)U, D, V^T = svd(S) on the result of svd SS
H=[K,0;0,1]H = [K,0;0,1] corresponding to the affine matrix can be obtained. Affine as Inv(H)Inv(H)
If you do homography on the rectified image, the metric rectified image is comes out.

Five pairs of straight lines can be given for CDCP with dof of 5 in the following way,
This is the process of finding the solution of the linear equation, and CDCP can be obtained. After that the above process repeat.

if  lm, then  lTCimagem=0.if \ \ l \bot m,\ then \ \ l^{'T}C^*_{image}m'=0.

CimageC^*_{image} can be obtained by using five pairs of orthogonal lines.

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2022년 9월 28일

안녕하세요. 해당 수식을 표현한 코드가 따로 있나요? 링크라도 남겨주시면 감사하겠습니다.

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