Differential Equations Solutions 52

Differential Equations Solutions 52 - 62 Chapter 11....

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Unformatted text preview: 62 Chapter 11. Solutions: Case Study: Classified Information Figure 11.3. The images resulting from minimizing D. is very dependent on the initial guess, but the rather unlikely choice that we made (all zeros in the green coordinate) gave some of the best results. Our first evaluation criterion should be how the image looks, sometimes called the “eyeball norm”. In the results for minimizing D, it is harder to differentiate the dog from the background. For minimizing R with k = 3, his white fur is rendered as green and the image quality is much worse than for minimizing D or using k -means. For k = 4 or k = 5, though, minimizing R yields a good reconstruction, with good shading in the fur and good rendering of the table legs in the background, and the results look better than those for minimizing D. (Note that the table legs were not part of the sample that determined the cluster centers.) We can measure the quantitative change in the images, too. Each pixel value xi in the original or the clustered image is a vector with q dimensions, and we can measure the relative change in the image as n i=1 ||xoriginal − xclustered ||2 i i n i=1 ||xoriginal ||2 i 1/ 2 . This measure is usually smaller when minimizing R rather than D: .363 vs .271 for k = 3, .190 vs .212 for k = 4, and .161 vs .271 for k = 5. The optimization program sometimes stops with negative coordinates for a cluster center or no points in the ...
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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