CSE527-l10a

# CSE527-l10a - Overview Page 1 of 1 Next Imaging Geometry Up...

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Next: Imaging Geometry Up: No Title Previous: No Title Overview The main points covered in this lecture are: z A perspective (central) projection camera is represented by a matrix. z The most general perspective transformation transformation between two planes (a world plane and the image plane, or two image planes induced by a world plane) is a plane projective transformation. This can be computed from the correspondence of four (or more) points. z The epipolar geometry between two views is represented by the fundamental matrix. This can be computed from the correspondence of seven (or more) points. Both geometric and algebraic descriptions are given. Bob Fisher Wed Apr 16 00:58:54 BST 1997 Page 1 of 1 Overview 2/26/2004 http://www.dai.ed.ac.uk/CVonline/LOCAL_COPIES/EPSRC_SSAZ/node1.html

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Next: 3x4 Projection Matrix Up: No Title Previous: Overview Imaging Geometry Central Projection Vector notation: where and are 3-vectors, with . Here central projection is represented in the coordinate frame attached to the camera. Generally, there is not direct access to this camera coordinate frame. Instead, we need to determine the mapping from a world coordinate frame to an image coordinate system (see next slide). Bob Fisher Wed Apr 16 00:58:54 BST 1997 Page 1 of 1 Imaging Geometry 2/26/2004 http://www.dai.ed.ac.uk/CVonline/LOCAL_COPIES/EPSRC_SSAZ/node2.html
Next: Summary and Properties Up: No Title Previous: Imaging Geometry 3x4 Projection Matrix There are three coordinate systems involved --- camera, image and world. 1. Camera : perspective projection. This can be written as a linear mapping between homogeneous coordinates (the equation is only up to a scale factor): where a projection matrix represents a map from 3D to 2D. 2. Image : (intrinsic/internal camera parameters) is a upper triangular matrix, called the camera calibration matrix : Page 1 of 3 3x4 Projection Matrix 2/26/2004 http://www.dai.ed.ac.uk/CVonline/LOCAL_COPIES/EPSRC_SSAZ/node3.html

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where , . { provides the transformation between an image point and a ray in Euclidean 3-space. { There are four parameters: 1. The scaling in the image x and y directions, and . 2. The principal point , which is the point where the optic axis intersects the image plane. The aspect ratio is . { Once is known the camera is termed calibrated . { A calibrated camera is a direction sensor , able to measure the direction of rays --- like a 2D protractor. 3. World : (extrinsic/external camera parameters) The Euclidean transformation between the camera and world coordinates is : Finally, concatenating the three matrices, which defines the projection matrix from Euclidean 3-space to an image: Page 2 of 3 3x4 Projection Matrix 2/26/2004 http://www.dai.ed.ac.uk/CVonline/LOCAL_COPIES/EPSRC_SSAZ/node3.html
Bob Fisher Wed Apr 16 00:58:54 BST 1997 Page 3 of 3 3x4 Projection Matrix 2/26/2004 http://www.dai.ed.ac.uk/CVonline/LOCAL_COPIES/EPSRC_SSAZ/node3.html

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Next: Camera Calibration Up: No Title Previous: 3x4 Projection Matrix
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## This note was uploaded on 11/06/2010 for the course CSE 527 taught by Professor Ab during the Fall '09 term at Cornell.

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CSE527-l10a - Overview Page 1 of 1 Next Imaging Geometry Up...

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