Assignments

Revision as of 12:43, 12 June 2013

Let \(A=\begin{pmatrix}1&2&3\\4&5&6\\7&8&10\end{pmatrix}\). Find a matrix X such that \(X\cdot A=\begin{pmatrix}7&8&10\\4&5&6\\1&2&3\end{pmatrix}\). What do you get if you compute \(A\cdot X\)?
Find a 4x4 orthogonal matrix with at least 5 non-zero entries.
Can you find a 3x3 orthogonal matrix with no zeroes? Notebook
Find the vertical edges of a grayscale image (of your choice). Hint: For horizontal edges this is done in Notebook 031.
Pick a small grayscale image (your choice) and use matrix transposition and multiplication with suitable matrices to produce the following six images:
In Notebook 032 you have seen how to convert a color image to its YCbCr components. Recreate the original color image from its Y-, Cb- and Cr- components. (Check your result by computing the Peak Signal to Noise Ratio to the original image. Note that when computing the luminance/chrominance components, we round to the nearest integer. )
Problem 3.8
Problem 3.16
Problem 3.23
Problem 3.26
Problem 3.35
Problem 3.37
Problem 3.50
Problem 3.42

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 # Find the vertical edges of a grayscale image (of your choice).   Hint: For horizontal edges this is done in Notebook 031.
 # Pick a small grayscale image (your choice) and use matrix transposition and multiplication with suitable matrices to produce the following six images: [[image:FN.jpg|500px]]
+# In Notebook 032 you have seen how to convert a color image to its YCbCr components. Recreate the original color image from its Y-, Cb- and Cr- components. (Check your result by computing the Peak Signal to Noise Ratio to the original image. Note that when computing the luminance/chrominance components, we round to the nearest integer. )
 # Problem 3.8
 # Problem 3.16
+# Problem 3.23
+# Problem 3.26
+# Problem 3.35
+# Problem 3.37
+# Problem 3.50
+# Problem 3.42