Essential Matrix: Difference between revisions

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We now consider two cameras:

Camera 1 is at the origin of world space (or it's object space) <math>P = (I | 0)</math>.

Camera 2 is displaced with some rotation <math>R</math> and translation <math>R</math>, <math>P' = (R | -RT)</math>.<br>

Camera 2 is displaced with some rotation <math>R</math> and translation <math>-RT</math>, <math>P' = (R | -RT)</math>.<br>

Any point <math>\mathbf{u} = (u,v,w)^T</math> in camera 1 is represented by an epipolar line in camera 2.<br>

Under camera 2, the position of camera 1 is <math>-RT</math> and <math>P' (u,v,w,0)^T = R\mathbf{u}</math> is somewhere on this epipolar line.

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For planar images, only one of these 4 options is feasible.

You can determine which one is feasibly using triangulation with one of your points.

~~In the implausible 3 possibilities, <math>P'\mathbf{u}</math> will be out of bounds or negative~~

==3D points==

See [[Wikipedia: Essential_matrix]]

==Fundamental Matrix==

The fundamental matrix is a generalization of the essential matrix which also takes into account the calibration of the camera.

==Resources==

* [[Wikipedia: Essential_matrix]]

* [http://robotics.stanford.edu/~birch/projective/node20.html stanford essential and fundamental matricies]

* [https://github.com/darknight1900/books/blob/master/Multiple%20View%20Geometry%20in%20Computer%20Vision%20(Second%20Edition).pdf Multiple View Geometry in Computer Vision by Hartley and Zisserman]

==References==

@@ Line 15: / Line 15: @@
 We now consider two cameras:
 Camera 1 is at the origin of world space (or it's object space) <math>P = (I | 0)</math>.
-Camera 2 is displaced with some rotation <math>R</math> and translation <math>R</math>, <math>P' = (R | -RT)</math>.<br>
+Camera 2 is displaced with some rotation <math>R</math> and translation <math>-RT</math>, <math>P' = (R | -RT)</math>.<br>
 Any point <math>\mathbf{u} = (u,v,w)^T</math> in camera 1 is represented by an epipolar line in camera 2.<br>
 Under camera 2, the position of camera 1 is <math>-RT</math> and <math>P' (u,v,w,0)^T = R\mathbf{u}</math> is somewhere on this epipolar line.
@@ Line 141: / Line 141: @@
 For planar images, only one of these 4 options is feasible.
 You can determine which one is feasibly using triangulation with one of your points.
-In the implausible 3 possibilities, <math>P'\mathbf{u}</math> will be out of bounds or negative
 ==3D points==
 See [[Wikipedia: Essential_matrix]]
+==Fundamental Matrix==
+The fundamental matrix is a generalization of the essential matrix which also takes into account the calibration of the camera.
 ==Resources==
 * [[Wikipedia: Essential_matrix]]
 * [http://robotics.stanford.edu/~birch/projective/node20.html stanford essential and fundamental matricies]
+* [https://github.com/darknight1900/books/blob/master/Multiple%20View%20Geometry%20in%20Computer%20Vision%20(Second%20Edition).pdf Multiple View Geometry in Computer Vision by Hartley and Zisserman]
 ==References==