Learn multiple with me view geometry multi-View geometry (1)

This series of blog continues to update, with you to Exchange learning, if the reader found that there are errors or questions, please leave a message.

Preface:

　　a few days ago Bo Master bought this multiple View Geometry second Edition, has been looking at this book, have to say before the internet to find a lot of theories are from this book, so in order to facilitate their learning more profound and communicate with you, I have read the chapters of the understanding and ideas will be written down, Also ask you to correct the great God, I feel professional vocabulary or English better, translated into Chinese for themselves and everyone's English literature reading ability and there is no good influence.

2016.07.02
Part Ii:two-view Geometry
Chapter 9
The whole Part II is about two view geometry, two different view images can be obtained from both cameras at the same time, or it can be obtained from a camera, without distinction, Each view corresponds to a camera matrix p and P ', such as a space point coordinate x, the pixel coordinates of the two images are X and X ', then for the left we have x=px, right: X ' =p ' x, this part we will revolve around three questions unfold:
1,correspondence geometry, given a point x on the left, how to determine its position constraint on the right graph corresponding to X '.
2,camera Geometry (motion), given the left and right graphs a series of corresponding points {xi↔x? i}, i = 1, ..., n, how do we determine p and P '.
3,scene geometry (structure), given a series of corresponding points in the left and right graphs {xi↔x? i}, i = 1, ..., N, and P and P ', how do we determine the position of x in space.
What we're going to learn today. Chapter 9 mainly speaks of the two view of Epipolar geometry, which directly answers the first question above, that a point x on the left side of the graph will determine the right side of an X ' must go through the line epipolar line,epipolar The geometry is only related to the camera itself (relative position and the respective internal reference), regardless of the scene structure. We use a 3x3 fundamental matrix:f to represent epipolar geometry, and then we will analyze the matrix and how to find the matrix F from P and P ', as well as the method of P and p from F.

9.1 epipolar Geometry
The second view of the epipolar geometry is actually two image plane and a cluster of lines through the base line (two camera lens center line) of the intersection relationship, the following figure A:x,x and X ' three points coplanar in Π,epipolar plane,c and C ' is two lens center.
　　

Now we have the answer to the first question, Figure B: We know the Left X, the back projection after the X should be in line C and X lines above, it is easy to find this line in the right projection is a straight line L ', so the question is the answer is x must fall on the right figure of l ', we call this line for Epipolar, So later we have to find X in the right side of the matching point does not need full image to find, just need to search on this line OK.

Epipole: Connects the base line of the two lens centers to the intersection of the images (two).
Epipolar plane: A cluster plane through base line
Epipolar line:epipolar plane with two lines of image plane (two).

The examples in this section will be given in sections 9.3 and 9.4, so remember to pay attention to them.