$1$ Correlation and convolution$2$ 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: $f\frac{x,y}{a}(x,y).$

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

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

Consider two images. One image should be relatively large, like $512512$ pixels that contains

all zeros with several sparsely populated points with magnitude $255.$ The other image should be

small, something like, $1515$ pixels and contains an asymmetric object like,

with the

object white and the background black.

with the

Perform both the correlation, and convolution of the two images separately and correctly label

each result. Make the resulting image the same size as the larger input image.