In this exercise, you will implement the Canny edge detector $($without hysteresis thresholding$).$ You are

required to write each of the functions. You may not use any of the in$-$built MATLAB edge detection

functions.

Task $1$: Implement Gaussian blur

Write a program that performs Gaussian blur on an input image using the following $55$ kernel, where $B$ is

the blurred version of input image A$.$ Show your result on the screen. $($Hint: Use imfilter$)$

$B=\frac{1}{159}\left[\begin{array}{ccccc}2& 4& 5& 4& 2\\ 4& 9& 12& 9& 4\\ 5& 12& 15& 12& 5\\ 4& 9& 12& 9& 4\\ 2& 4& 5& 4& 2\end{array}\right]*A$

Task $2$: Calculate image gradients

Write a program that does the following in order. You should reuse your Task $1$ code.

Load an imsge.

Convert it into a grayscale $($single channel$)$ image.

Blur the image using a $55$ Gaussion filter

Calculate the gradient of the blurred image in the $x$ and $y$ directions using a $33$ Sobel filter $($Tlint: Recoll

that SobelX and SobelY kermels from your Lecture and do the same thing as Task $1,$ but with the Sobel filters

insteadj

Check the $x$ and $y$ gradient values $($i$.$e$.G,$ and $G,)$ to make sure ther are correct $($Hint: After you hove

apalied the Sobel kernels, you would have gorten the grodients, just plor them using inshow$)$

Task $3$: Calculate gradient magnitude

Extend your program to calculate the gradient magnitude. Gradient magritude $G$ is a function of the

gradients in the $x$ and $y$ directions $(G,$ Gy$).$ Show the gradient magnitude on the screen as a grayscale image

$G=\sqrt[\phantom{2}]{G_x^2+G_y^2}$

Task $4$: Calculate gradient orientation

totend your proeram to cokculate the grasent oriereation as folom:

$=$arctas$(\frac{{}_z}{G_x})$

You may find the finction oton? useful for this purpose. &Get atand wil return the ongle in radions, If yoy

At this point, you will here $4$ arres that should hare coactly the same number ef rows and columen. Your

image arrar holds oripinal image $($and the cfore should have $3$ dimeroions mhich are rowh, columes, and

colourl. Then there is a Eapcale wersion of the oribinel imuge $12$ dmeroioral. Then wou have a thets and a $G$

Task $5$: Non$-$maxima Suppression and thresholding

Finally eatend your code to perform nan$-$masima superesion in order to "bin" the edees along the gradiem

orietation. A detaled summery bo provided bere. The idee a wo cere any pisel that is eot greader in terms of

$($tent: the beir way to go aboor this is ro ereate on arroy sher holds the ongles mar pou cas monually

calculate in the $8$ compass direcniens. Jo hrlp you, you moy ase Dhe informanion below and seme strep$-$by$-$step.

instrucnions

Fiow the sbove image is is olesr thor pi and pi both point to the West. If nou get $0,$ that poists to the Gast if

Fov get p$/2,$ that points so the Nerth. $1$ you get $-$pi$/2,$ that poirs to the Soath

To make ble casc, ivat push them iste the round the frection down, romer than tuke the average.

anglen $=|-Q,-3^4\frac{p}{4},-\frac{p}{2},-\frac{p}{4},Q,\frac{p}{4},p\frac{V}{2},3^{\text{'}}pV4,pl$ : Nelrections in radars

what the ancles mes

If you want to take the "closest", which is more accurate you will need to further divide the angles to be

between $N-NW,$ and then compare theta to decide which to push it to$.$

Step $1$: Your loop will run from the pixel in row $2$ until $($total rows $-1),$ and from column $2$ until $($total columns

$-1).$ This means you need two for$-$loops. Use the nested for loops to run through all elements in theta.. If the

current pixel is not a local maximum, suppress it $($set it to zero$).$

For example, the code below checks the theta for north and west, and we only keep the element which has

the maximum gradient magnitude in the given gradient orientation. You will need to write the code for the

other $6$ composs directionsfor $\backslash \backslash 21$sire$($theta$,1)-1$ currentMaq $-$ G$(1,\backslash )$ ; fourrent elenent $11$f this $10$ the case, you are facing North elseif $($theta$(1,2)>--$p$165$ thetap$1/4)$ brest elseif tthe reat of your code goes here $4$ We otarted with $0,$ so WM$5$ wi$11$ be changed to G if it is the naximum VourrentKag $>=$ nesghbouri,end endStep $2$: Test your code against your test images and visualise them using imshow:

Step $3$: Threshold your NMS results by using imhist to get a histogram that will help you to set it$.$ You can get

the top $10$ of this by using the function prctile

Step $4$: Show the thresholded result using inshow.