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Unformatted text preview: Camera Calibration What is Camera Calibration? Primarily, finding the quantities internal to the camera that affect the imaging process Position of image center in the image It is typically not at (width/2, height/2) of image Focal length Different scaling factors for row pixels and column pixels Skew factor Lens distortion (pincushion effect) Motivation Good calibration is important when we need to Reconstruct a world model: Virtual L.A. project Interact with the world Robot, handeye coordination Image plane We see a square of known size Evaluation of position of a square for 2 focal lengths (red and blue projection geometry) Scaling of Rows and Columns in Image Camera pixels are not necessarily square Camera output may be analog (NTSC) Image may be obtained by digitizing card A/D converter samples NTSC signal Camera NTSC signal Digitizing Monitor display CCD/ CMOS Compound Lens Imaging Inexpensive single lens systems distort image at its periphery Compound lenses may be used to reduce chromatic effects and pincushion effects C Camera Image plane Image plane for equivalent pinhole camera is not camera image plane Principal planes Center of Projection Nodal Point f f Variety of Techniques VERY large literature on the subject Work of Roger Tsai influential Linear algebra method described here Can be used as initialization for iterative non linear methods. Some interesting methods use vanishing points Camera and Calibration Target Calibration Procedure Calibration target: 2 planes at right angle with checkerboard patterns (Tsai grid) We know positions of pattern corners only with respect to a coordinate system of the target We position camera in front of target and find images of corners We obtain equations that describe imaging and contain internal parameters of camera As a side benefit, we find position and orientation of camera with respect to target (camera pose ) Image Processing of Image of Target Canny edge detection Straight line fitting to detected linked edges Intersecting the lines to obtain the image corners Matching image corners and 3D target checkerboard corners By counting if whole target is visible in image We get pairs (image point)(world point) ) , , ( ) , ( i i i i i Z Y X y x Central Projection s s i s s i z y f y z x f x = = Scene point (x s , y s , z s ) Image point (x i , y i , f) x z C f y center of projection Image plane = 1 1 s s s z y x f f w v u w v y w u x i i / , / = = If world and image points are represented by homogeneous vectors, central projection is a linear transformation: Transformation From Lengths to Pixels...
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This note was uploaded on 01/12/2012 for the course CMSC 733 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff

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