Chapter 10.4, Problem 60E

Digital Images A four-level gray scale is shown below.

1. (a) Use the gray scale to find a 6 × 6 matrix that digitally represents the image in the figure.

1. (b) Find a matrix that represents a darker version of the image in the figure.
2. (c) The negative of an image is obtained by reversing light and dark, as in the negative of a photograph. Find the matrix that represents the negative of the image in the figure. How do you change the elements of the matrix to create the negative?
3. (d) Increase the contrast of the image by changing each 1 to a 0 and each 2 to a 3 in the matrix you found in part (a). Draw the image represented by the resulting matrix. Does this clarify the image?
4. (e) Draw the image represented by the matrix I. Can you recognize what this is? If you don’t, try increasing the contrast.

$I=\left[\begin{array}{rrrrrr}\hfill 1& \hfill 2& \hfill 3& \hfill 3& \hfill 2& \hfill 0\\ \hfill 0& \hfill 3& \hfill 0& \hfill 1& \hfill 0& \hfill 1\\ \hfill 1& \hfill 3& \hfill 2& \hfill 3& \hfill 0& \hfill 0\\ \hfill 0& \hfill 3& \hfill 0& \hfill 1& \hfill 0& \hfill 1\\ \hfill 1& \hfill 3& \hfill 3& \hfill 2& \hfill 3& \hfill 0\\ \hfill 0& \hfill 1& \hfill 0& \hfill 1& \hfill 0& \hfill 1\end{array}\right]$