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The Gough Map is a late medieval map of the island of Great Britain, which has been receiving a lot of research attention and many studies have been conducted to analyze the map. With the hyperspectral image (HSI) of the Gough Map collected, we are allowed to further analysis the map in a different angle. Our goal is to semi-automatically identify and separate iron-gall and carbon black inks written on the Gough map. Unlike traditional target detection problems, there are unique characteristics in our data: Firstly, the targets are not sparsely distributed and their statistical contributions to the background estimation cannot be ignored. Secondly, the spectral differences between the targets are subtle. Lastly, the variances of the background data are so low that the distinction between it and noise is challenging. To address these issues, we made the following modification to the traditional adaptive coherence estimator (ACE): First, manually select the background data instead of using the whole data to estimate the background. Moreover, the pixels with strong spectral features of other pigments are removed and only the black ink candidates are feed into the detector. Thirdly, the number of eigenvectors were limited in the calculation of whitening operator so that the impact of noise can be controlled. It is clear that the trailing eigenvectors are usually dominated by the noise, so the majority of the information of background data can be effectively compressed only with the top-ranked eigenvectors. This is critical because whitening the noise means increasing the variance of the noise based on the fact that our background has super low variances. The whitening matrix needs to be used for whitening target candidates which have subtle spectral differences, and whitening the noise will cause the spectral features to disappear in the whitening sub-space. In conclusion, the whitening operator used in ACE should whiten the useful information of background data and reduce the effect caused by the noise as much as possible so that the subtle spectral differences of targets will not be buried in the whitening sub-space. Our results show that the modified target detection algorithm can both separate the targets from the background and each other.
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