# MIT 6 801 - Camera calibration and radiometry (50 pages)

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## Camera calibration and radiometry

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Lecture Notes

- Pages:
- 50
- School:
- Massachusetts Institute of Technology
- Course:
- 6 801 - Machine Vision

**Unformatted text preview: **

Camera calibration radiometry Reading Chapter 2 and section 5 4 Forsyth Ponce Chapter 10 Horn Optional reading Chapter 4 Forsyth Ponce Sept 17 2002 MIT 6 801 6 866 Profs Freeman and Darrell Camera calibration Geometric how positions in the image relate to 3 d positions in the world Photometric how the intensities in the image relate surface and lighting properties in the world Calibration target http www kinetic bc ca CompVision opti CAL html From last lecture camera calibration pixel coordinates world coordinates r 1 r p MP z m u 1 v m 1 z m T 1 T 2 T 3 Wx W y Wz 1 z is in the camera coordinate rsystem but we can solve for that since 1 m3 P leading to z r m1 P r u m3 Pr m2 P r v m3 P Camera calibration r m P u 1 r m3 Pr Because of these relations m2 P r v m3 P For each feature point i we have r m1 ui m3 Pi 0 r m2 vi m3 Pi 0 Camera calibration P1x P1 y 0 0 0 P Pny nx 0 0 0 P1z 1 0 0 0 0 u1 P1x u1 P1 y u1 P1z P1z 1 v1 P1x v1 P1 y L L L 1 0 0 0 0 un Pnx un Pny v1 P1z Pnz 1 vn Pnx vn Pnz 0 P1x Pnz 0 Pnx P1 y Pny P vn Pny un Pnz m11 m 12 m 13 m u1 14 0 m21 0 v1 m 22 M un m23 0 vn m24 0 m31 m 32 m33 m 34 m 0 We want to solve for the unit vector m the stacked one that minimizes Pm 2 The eigenvector corresponding to the minimum eigenvalue of the matrix PTP gives us that see Forsyth Ponce 3 1 What makes a valid M matrix rT a1 r rT M A b a2 ar T 3 r b defined only up to a scale rT rT normalize M so that a3 r3 1 M is a perspective projection matrix iff Det A 0 Camera calibration Geometric how positions in the image relate to 3 d positions in the world Photometric how the intensities in the image relate surface and lighting properties in the world light Irradiance E surface Light power per unit area watts per square meter incident on a surface light Radiance L surface Amount of light radiated from a surface into a given solid angle per unit area watts per square meter per steradian Note the area is the foreshortened area as seen from the direction that the light is being

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