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Introduction to homography

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Shih-Hsiang Lin
Shih-Hsiang Lin
EducaciónTecnología
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Introduction to Homography 2010.01.19
Coordinate System view coordinate system object coordinate system x y z world coordinate system
History P->G: 以 E 為眼點從平面 G 到平面 W 的 透視對應
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Homo. representation (1) ,[object Object],[object Object],representative
Homo. representation (2) ,[object Object],Homo. representation
Degree of freedom (DoF) ,[object Object],[object Object]
[object Object],[object Object],Intersection of lines (1)
Intersection of lines (2) ,[object Object],y = 1 x = 1
Line joining points ,[object Object],[object Object]
Line at infinity (1) ,[object Object],[object Object]
Line at infinity (2) ,[object Object],[object Object],Homogeneous coordinates (x, y, 0) T do not correspond to any finite point in R 2
Line at infinity (3) ,[object Object],The point at infinity in the direction of the y-axis
Line at infinity (4) ,[object Object],[object Object],[object Object]
Concept of points at infinity ,[object Object],[object Object],[object Object],[object Object]
A model for the projective plane Points and Lines of P 2 are represented by Rays and Planes , respectively, through the origin in R 3 Lines lying in the x 1 x 2 -plane represent ideal points , and the x 1 x 2 -plane represents l ∞
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Mapping between planes
Definition (1) ,[object Object],[object Object],[object Object],[object Object]
Definition (2) ,[object Object],[object Object]
Definition (3) ,[object Object]
A hierarchy of transformations (1)
A hierarchy of transformations (2)
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Document Distortion
Correction
2D Homography ,[object Object],[object Object]
DLT Algorithm (1)
DLT Algorithm (2) ,[object Object],[object Object]
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
OpenCV Implementation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Homography Estimation Projective Transform
Reference ,[object Object],[object Object]

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Introduction to homography