Adaptive sampling by histogram equalization: theory, algorithms, and applications, 2007

Atlanta University and Clark Atlanta University Theses and Dissertations
Adaptive sampling by histogram equalization: theory, algorithms, and applications, 2007
Fadiran, Oladipo O.
Date of Original:
Degrees, Academic
Dissertations, Academic
United States, Georgia, Fulton County, Atlanta, 33.749, -84.38798
Degree Type: dissertation
Degree Name: Doctor of Philosophy (PhD)
Date of Degree: 2007
Granting Institution: Clark Atlanta University
Department/ School: Department of Engineering, System Science Program
We present the investigation of a novel, progressive, adaptive sampling scheme. This scheme is based on the distribution of already obtained samples. Even spaced sampling of a function with varying slopes or degrees of complexity yields relatively fewer samples from the regions of higher slopes. Hence, a distribution of these samples will exhibit a relatively lower representation of the function values from regions of higher complexity. When compared to even spaced sampling, a scheme that attempts to progressively equalize the histogram of the function values results in a higher concentration of samples in regions of higher complexity. This is a more efficient distri-bution of sample points, hence the term adaptive sampling. This conjecture is confirmed by numerous examples. Compared to existing adaptive sampling schemes, our approach has the unique ability to efficiently obtain expensive samples from a space with no prior knowledge of the relative levels of variation or complexity in the sampled function. This is a requirement in numerous scientific computing applications. Three models are employed to achieve the equalization in the distribution of sampled function values: (1) an active-walker model, containing elements of the random walk theory, and the motion of Brownian particles, (2) an ant model, based on the simulation of the behavior of ants in search of resources, and (3) an evolutionary algorithm model. Their performances are compared on objective basis such as entropy measure of information, and the Nyquist-Shannon minimum sampling rate for band-limited signals. The development of this adaptive sampling scheme was informed by a need to effi-ciently synthesize hyperspectral images used in place of real images. The performance of the adaptive sampling scheme as an aid to the image synthesis process is evaluated. The synthesized images are used in the development of a measure of clutter in hyperspectral images. This process is described, and the results are presented.
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Clark Atlanta University
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