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Out of the Depths: Image Statistics of Space, Water, and the Minuscule World
Nimit S. Dhulekar
Dartmouth TR2011-678

Abstract: In images of natural scenes, a consistent relationship exists between spectral power and spatial frequency. The power spectrum falls off with a form 1/f^p as spatial frequency f increases, with values of p approximately equal to 2. To quantify the extent to which this statistical characteristic is exhibited by other classes of images, we examined astronomical, underwater, and microscale images. It was found that this property holds for all three categories of images, although the value of p varies in the range 1.76 to 2.37. The second statistical characteristic computed was the angular spread of the power spectrum. This metric is a means to verify whether the image categories investigated tend to display more power in the horizontal and vertical orientations, akin to natural images. It was found that these image categories have primarily isotropic spectral signatures with a much reduced anisotropy as compared to natural images. Along similar lines, we introduce a new measure called the anisotropy index which compares the power in the horizontal and vertical orientations with power in oblique orientations. The statistics thus presented are for the ensemble power spectrum. We also construct 4 classifiers to distinguish between natural images and astronomical, microscale, and underwater images. The k-nearest neighbor classifier with Mahalanobis distance had the best accuracy of 70.5% on the training set and 66.9% on the test set, for correctly identifying natural images. From these classifiers, we can not only view the confusion in classification among the investigated image categories, but also the difference in statistics as compared to natural images. These classifiers also make it possible to verify that the images in a particular class display statistics similar to that of the ensemble image.

Note: M.S. Thesis. Advisor: Richard H. Granger.


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   Nimit S. Dhulekar, "Out of the Depths: Image Statistics of Space, Water, and the Minuscule World." Dartmouth Computer Science Technical Report TR2011-678, September 2010.

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