## Calibrating color cameras using metameric blacks

JOSA A, Vol. 24, Issue 1, pp. 11-17 (2007)

http://dx.doi.org/10.1364/JOSAA.24.000011

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### Abstract

Spectral calibration of digital cameras based on the spectral data of commercially available calibration charts is an ill-conditioned problem that has an infinite number of solutions. We introduce a method to estimate the sensor's spectral sensitivity function based on metamers. For a given patch on the calibration chart we construct numerical metamers by computing convex linear combinations of spectra from calibration chips with lower and higher sensor response values. The difference between the measured reflectance spectrum and the numerical metamer lies in the null space of the sensor. For each measured spectrum we use this procedure to compute a collection of color signals that lie in the null space of the sensor. For a collection of such spaces we compute the robust principal components, and we obtain an estimate of the sensor by computing the common null space spanned by these vectors. Our approach has a number of advantages over standard techniques: It is robust to outliers and is not dominated by larger response values, and it offers the ability to evaluate the goodness of the solution where it is possible to show that the solution is optimal, given the data, if the calculated range is one dimensional.

© 2006 Optical Society of America

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(110.2990) Imaging systems : Image formation theory

(330.1690) Vision, color, and visual optics : Color

(330.1710) Vision, color, and visual optics : Color, measurement

**ToC Category:**

Vision, Color, and Visual Optics

**History**

Original Manuscript: February 21, 2006

Revised Manuscript: May 30, 2006

Manuscript Accepted: June 30, 2006

**Virtual Issues**

Vol. 2, Iss. 2 *Virtual Journal for Biomedical Optics*

**Citation**

Ali Alsam and Reiner Lenz, "Calibrating color cameras using metameric blacks," J. Opt. Soc. Am. A **24**, 11-17 (2007)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-1-11

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