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Differential Equations Solutions 49

# Differential Equations Solutions 49 - Chapter 11 Solutions...

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Chapter 11 Solutions: Case Study: Classified Information: The Data Clustering Problem (coauthored by Nargess Memarsadeghi) CHALLENGE 11.1. The original image takes mpb bits, while the clustered image takes kb bits to store the cluster centers and mp log 2 k bits to store the cluster indices for all mp pixels. For jpeg images with RGB (red, green, blue) values ranging between 0 and 255, we need 8 bits for each of the q = 3 values (red, green, and blue). Therefore, an RGB image with 250,000 pixels takes 24 250 , 000 = 6 , 000 , 000 bits, while the clustered image takes about 250 , 000 log 2 4 = 500 , 000 bits if we have 3 or 4 clusters and 250,000 bits if we have 2 clusters. These numbers can be further reduced by compression techniques such as run-length encoding. CHALLENGE 11.2. (a) Neither D nor R is convex everywhere. Figure 11.2 plots these functions for a
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