Introduction to homography

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 ∞

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)

2D Homography ,[object Object],[object Object]

DLT Algorithm (2) ,[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]

Introduction to homography

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Introduction to homography