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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 9, Iss. 5 — Apr. 29, 2014

Evaluating logarithmic kernel for spectral reflectance estimation—effects on model parametrization, training set size, and number of sensor spectral channels

Timo Eckhard, Eva M. Valero, Javier Hernández-Andrés, and Ville Heikkinen  »View Author Affiliations

JOSA A, Vol. 31, Issue 3, pp. 541-549 (2014)

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In this work, we evaluate the conditionally positive definite logarithmic kernel in kernel-based estimation of reflectance spectra. Reflectance spectra are estimated from responses of a 12-channel multispectral imaging system. We demonstrate the performance of the logarithmic kernel in comparison with the linear and Gaussian kernel using simulated and measured camera responses for the Pantone and HKS color charts. Especially, we focus on the estimation model evaluations in case the selection of model parameters is optimized using a cross-validation technique. In experiments, it was found that the Gaussian and logarithmic kernel outperformed the linear kernel in almost all evaluation cases (training set size, response channel number) for both sets. Furthermore, the spectral and color estimation accuracies of the Gaussian and logarithmic kernel were found to be similar in several evaluation cases for real and simulated responses. However, results suggest that for a relatively small training set size, the accuracy of the logarithmic kernel can be markedly lower when compared to the Gaussian kernel. Further it was found from our data that the parameter of the logarithmic kernel could be fixed, which simplified the use of this kernel when compared with the Gaussian kernel.

© 2014 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(150.0150) Machine vision : Machine vision
(330.1710) Vision, color, and visual optics : Color, measurement
(110.4234) Imaging systems : Multispectral and hyperspectral imaging

ToC Category:
Image Processing

Original Manuscript: July 2, 2013
Revised Manuscript: December 12, 2013
Manuscript Accepted: December 25, 2013
Published: February 13, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Timo Eckhard, Eva M. Valero, Javier Hernández-Andrés, and Ville Heikkinen, "Evaluating logarithmic kernel for spectral reflectance estimation—effects on model parametrization, training set size, and number of sensor spectral channels," J. Opt. Soc. Am. A 31, 541-549 (2014)

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