Color in Computer Vision by Theo Gevers & Arjan Gijsenij & Joost van de Weijer & Jan-Mark Geusebroek

Author:Theo Gevers & Arjan Gijsenij & Joost van de Weijer & Jan-Mark Geusebroek
Language: eng
Format: epub
Publisher: John Wiley & Sons
Published: 2012-08-07T04:00:00+00:00

From previous work, it is known that the angular error is not normally distributed [196]. To test whether the perceptual Euclidean distance is normally distributed, a similar experiment as in Reference 14 is conducted. In Figure 12.4, the errors for the white-patch algorithm on the 11,000 images from the RGB images data set [201] are plotted, from which it is clear that both the angular error and the perceptual Euclidean distance are not normally distributed. The distributions of both metrics have a high peak at lower error rates, and a fairly long tail. For such distributions, it is known that the mean is a poor summary statistic, and hence, previously, it was proposed to use the median to describe the central tendency [196]. Alternatively, to provide more insight into the complete distribution of errors, one can calculate boxplots or compute the trimean instead of the median. Boxplots are used to visualize the underlying distributions of the error metric of a given color constancy method, as an addition to a summarizing statistic. This summarizing statistic can be the median, as proposed by Hordley and Finlayson [196], or it can be the trimean, a statistic that is robust to outliers (the main advantage of the median over a statistic such as the root mean square), but still has attention to the extreme values in the distribution [229, 230]. The trimean can be calculated as the weighted average of the first, second, and third quantile Q1, Q2 and Q3, respectively:

12.9

The second quantile Q2 is the median of the distribution, and the first and third quantiles Q1 and Q3 are called hinges. In other words, the trimean can be described as the average of the median and the midhinge.

Figure 12.4 Distribution of estimated illuminant errors for the white-patch algorithm, obtained for a set of over 11,000 images.

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