# hw-01 - Homework I 1(Camera models For a camera the image x...

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Homework I 1. (Camera models) For a camera, the image x of a point X in space is given by: PX x , with x and X homogeneous 3 and 4- vectors respectively. (a) If 0 PC , where C a homogeneous 4-vector, show that C is the camera center. (b) The camera projection matrix P can be written as : ] | [ ~ C I KR P , where K is the calibration matrix, R the rotation between the camera and world coordinate frames, and the camera center C is expressed as ~ ) 1 , ( C C . Show that the calibration matrix can be obtained from a RQ decomposition of the first 3X3 sub matrix of the camera matrix P. (c) In some application we obtained the following camera matrix: 1837 22 . 1 7 . 0 4 . 1 6325250 2 . 919 6 . 46 207 2898920 4 . 555 2 . 679 707 P . Find the camera center and the calibration parameters. 2. (Affine and metric rectification) Consider the image posted in the class web page. Read the image into matlab and use matlab to perform the calculations necessary for the following questions: (a) Calculate two vanishing points.

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