$2$ Matched filtering $($correlation$)$

Create or download an image that contains several lines of text, $f(xy).$ Don't make the text too

small, and make the text lighter than the background. Extract one character from the text

image and create a small image from it $c(x,y).$ Perform the correlation between the two images

with the result $r(x,y)$ the same size as the larger image.

$($a$)$ Indicate the position$($s$)$ of the maxima in $r(x,y).$ Are the in the positions of the characters

in the text image?

$($b$)$ Determine the ratio of the correlation peak corresponding to a letter and the next

highest peak that is not a letter in $r(x,y).$

$($c$)$ Normalize the correlation result by dividing $r(x,y)$ by the sum of all pixel values used in

the correlation operation. The easiest way to do this is to filter $($convolution$)$ the original

image with a window of all $1^{\text{'}}$ s$,$ that is the same size as $c(x,y),a(x,y)=f(x,y)**$ ones $(x,y).$

Then form the ratio: $r\frac{x,y}{a}(x,y).$

$($d$)$ What is the new ratio of the correlation peak corresponding to a letter and the next

highest peak in $r(x,y)?$