Date of Award


Document Type

Campus Access Thesis

Degree Name

Master of Science (MS)


Computer Science

First Advisor

Dan A. Simovici

Second Advisor

Wei Ding

Third Advisor

Nurit Haspel


In this thesis, the problem of finding complex regions in 2-dimensional image domains is addressed. The targeted complexity corresponds to the presence of variation and randomness of the histogram of pixel values in various and possibly progressively smaller areas of an image. An algorithm for identifying high complexity regions is introduced. Two different methods for mining are considered. The first method performs an information theoretic analysis based on the Shannon entropy to find diverse areas. The second method applies a variation of the concept of box-counting dimension related to fractal geometry. The algorithm uses a quadtree for image segmentation. Complex regions are represented by leaves of the quadtree with high feature value at the highest level on the tree, where the feature is based on either entropy or box-counting dimension. Nodes corresponding to sub-domains are split when the level of the analyzed feature exceeds a chosen threshold. The efficiency of both methods is demonstrated on test images. The relationship between the threshold and the number of pixels located in areas with high feature value at the highest level on the resultant quadtree for both methods suggest that the choice of the threshold should take into account certain characteristics of the images such as the amount of texture or noise and the presence of natural scenes or man-made objects. Finally, a comparison between the results generated by both methods for test images shows a significant similarity regarding the final quadtrees.


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