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

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Next: Camera Calibration Up: No Title Previous: 3x4 Projection Matrix
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 46

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online