$1.$ Create a new matlab script $$harrisCorner$.$m$$

$2.$ Read in the Penguins.jpg image from the Windows sample pictures folder using the imread command $($store it in $$myImage$)$

$3.$ Convert the image to grayscale using the rgb$2$gray command.

$4.$ Cast your variable to a double and reassign it to itself.

myImage $=$ double$($myImage$)$

$5.$ Create the x and y derivative filters

dxFilter $=[-10-1$; $-101$; $-101]$;

dyFilter $=$ dxFilter';

$6.$ Create an X derivative image and a Y derivative image by convolving the appropriate filters with the grayscale penguin image. Use the following names for your new images:

myImageDerivativeX

myImageDerivativeY

$7.$ Now that we have the derivatives, we can calculate A$,$ B$,$ C from the book.

A $=$ myImageDerivativeX $.^2$

B $=$ myImageDerivativeY $.^2$

C $=$ myImageDerivativeX $.*$ myImageDerivativeY

$8.$ After you calculate the above you want to apply Gaussian smoothing $($using a Gaussian Filter$)$

using the conv$2$ command. Store each of the smoothed derivatives in: smoothedA, smoothedB,

smoothedC. You can use the following command to create your Gaussian filter:

gaussianFilter $=$ fspecial$(\text{'}$gaussian$\text{'})$;

$9.$ In order to compute the Corner Response Function, we use the following formula $($define alpha$=0\mathrm{.}04)$:

cornerResponseFunction $=$ A $.*$ B $$ C$2-$ alpha $*($A $+$ B$)2$

$**$Note: Please be sure to use the smoothed versions of A$,$ B & C for the above formula

$10.$ Next we need to create our isLocalMax function. The Corner Response function usually will have several $$corners$$ all that appear in the same area. This function will help us to determine which is the best corner for our program to use. Use the following code for $$isLocalMax$$:

function $[$myBool$]=$ isLocalMax$($harrisMatrix$,$ u$,$ v$)$

height $=$ size$($harrisMatrix$,1)$;

width $=$ size$($harrisMatrix$,2)$;

if$($u $<=1||$ u $>=$ height $||$ v$<=1||$ v$>=$width$)$

myBool $=$ false;

else

pix $=$ reshape$($harrisMatrix$,$ height$*$width$,1)$; $\%$return the image as

a $1$ dimensional array $($like the book does$)$

i$0=($v$-1)*$height$+$u;

i$1=$ v$*$height$+$u;

i$2=($v$+1)*$height$+$u;

cp $=$ pix$($i$1)$;

myBool $=($cp $>$ pix$($i$0-1)$ && cp $>$ pix$($i$0)$ && cp $>$ pix$($i$0+1)$ && cp $>$

pix$($i$1-1)$ && cp $>$ pix$($i$1+1)$ && cp $>$ pix$($i$2-1)$ && cp $>$ pix$($i$2)$ && cp $>$

pix$($i$2+1))$;

end

end

$11.$ We use this function to help us determine the best corners to use. We do this by stepping

through our cornerResponseFunction matrix and check to see if it$$s value is greater than a

certain threshold and it is a local maximum $($this is checked by calling the isLocalMax function

you just created$)$

$12.$ Implement the pseudo code listed below in order to perform the above task:

Initialize totalCorners to zero

For each u:

For each v:

If $($cornerResponseFunction $($u$,$ v$)>$ threshold && islocalMax$($cornerResponseFunction$,$ u$,$ v$)$

Increment totalCorners by $1.$

Add the corner to our list $($each corner contains u$,$ v$,$ q$)$

cornerList$($totalCorners$).$x $=$ u;

cornerList$($totalCorners$).$y $=$ v;

cornerList$($totalCorners$).$q $=$ q;

Output the total number of corners that passed the threshold and isLocalMax

$*$NOTE: Use an initial threshold of $200000($threshold $=200000)$

$13.$ Sort the corners by their respective q value in descending order

$14.$ Create a new variable goodCorners and initialize it to an empty array:

goodCorners $=[]$;

$15.$ Our corner response function may return a lot of corners that can be quite close to each other.

What we$$d like to do next is define a minimum distance that we want these features $($corners$)$ to

be from each other. We$$ll then want to step through each of our corners and remove the ones

that are close too close to each other. We do this by starting with the strongest corner that we

found $($the first one in the list because it$$s sorted$)$ and remove other corners that are within the

minimum distance to this point.

$16.$ First thing we will want to do is initialize our minimum distance:

minDistance $=10$;

$17.$ Copy and paste the following code into your program and complete the code

while$($size$($cornerList$,2)>0)$

c$1=$ cornerList$(1)$;

cornerList $=$ cornerList$(2$:end$)$; $\%$remove the first one

goodCorners $=[$goodCorners c$1]$;

cornersToRemove $=[]$;

for i$=2$:size$($cornerList$,2)$

if$(<<>>>)$

cornersToRemove $=[$cornersToRemove i$]$;

end

end

cornerList$($cornersToRemove$)=[]$; $\%$remove the corners that we found

that are too close

end

$18.$ Step through the goodCorners list and mark each of the corners in the image with a green cross that is $3$ pixels in width and height.

$19.$ Display the image to the user