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lec4 4pp

# lec4 4pp - Lecture 4 Sept 1 10 Course Enrollment HW1 to be...

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USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 1 Lecture 4: Sept 1, 10 Course Enrollment HW1 to be posted later today, Due Sept 13 Make up class today: 5-6:20PM, OHE 120 Last Class Intrinsic and extrinsic parameters Affine cameras Today’s objective Camera calibration – Photometry Color perception USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 2 Homogeneous Coords in 3-D Point X: normal coords (x,y,z); homogeneous (x, y, z,1) T Plane Π : ax + by + cz + d =0 is defined by (a, b, c, d) T Point X is on plane iff Π T X = 0 3 points define a plane ( X 1 T , X 2 T , X 3 T ) T Π = 0 Note: this equation is correct, the outer transpose is simply intended to indicate that the components X 1 T , X 2 T and X 3 T are arranged in a column, not a row. 3 planes define a point ( Π 1 T , Π 2 T , Π 3 T ) T X = 0 USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 3 Affine Cameras In many cases, perspective projection can be approximated by simpler camera models Typically when the objects are far from the camera relative to their size Projection matrix can be simplified by having only two rows: affine transformation M becomes a 2 x 4 (3-D point expressed as homogeneous, 2-D as non- homogeneous): examples to come Smaller number of parameters makes it easier to estimate them. Images of affine cameras have simpler properties, e.g. parallelism may be preserved under certain models Some specific affine cameras Orthographic camera Weak perspective camera Para-perspective camera USC CS574: Computer Vision, Fall 2010 Copyright 2010, by R. Nevatia 4 Weak Perspective All points at nearly same distance, but not necessarily very far

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