eces523project

# eces523project - ECE-S523 Detection and Estimate Theory...

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ECE-S523 Detection and Estimate Theory Project Introduction The final project assigned in ECE-S523 supplies us with data files that represent an image. In each image, there may be at most 2 classes (object and background), with the object having some mass. We are tasked to come up with an algorithm that separates each image into object (if the object exists) and background, showing the estimated object boundary. The estimated parameters and probability distribution functions that describe the data should be found as well. The main non-parametric testing that was used was the Kolmogorov-Smirnov test (KS-test) which tries to determine if two datasets differ significantly or not. Scope of the Data Given the data files, a MATLAB script was written in an attempt to learn some things about the distributions of the files before testing. First the data files were plotted in an attempt to see differences in distributions. It is already known that at most two classes exist in each image and

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that the object has a mass. As seen in Figure 1, data1, data2, data3 and data5 all have a visible color difference indicating more than one distribution exists in the data file, and provides a good idea of where the object may lie. The plot showing data4 is the only one of the five plots that were not easily visibly distinguished which supplies reason to believe that data4 may only have one distribution. But this can’t be proven without further analysis. Next a histogram was plotted of each of the five data files. Visually judging this output, it appears that each of the entire data files’ distributions follows a standard normal distribution except for that of data5 which appears to follow an exponential distribution. Using the dfittool in MATLAB also verified that an exponential distribution looks likely in this file. Again, these observations need to be tested for accuracy but the visual relationship helps support the analysis of the data files. These histograms can be shown in Figure 2.
CDF other than that of data5. These CDFs can be found in Figure 3. The code used to plot these three figures can be found in Appendix A. Figure : Empirical CDFs of data files

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## This document was uploaded on 10/26/2011 for the course ECES 523 at Drexel.

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eces523project - ECE-S523 Detection and Estimate Theory...

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