The Princess Theatre in the Melbourne CBD is rumoured to be haunted by the ghost of Frederick Federici, an opera singer who died of a heart attack during a performance of Faust in $1888.$ Even today, a seat is always saved and left empty for Federici's ghost on each opening night of a new production. An image featuring the Princess Theatre has been provided for this question as 'princess.jpeg'. Do the following:

Use imread to read the image from the file 'princess.jpeg' and store it as a matrix named Princess.

In Figure $1,$ display the image Princess using imagesc. Turn off the axis labels and make sure the pixels are square. Add a title 'Princess'.

Convert the $3-$channel colour image Princess to grayscale using the mean function. Store this as a new matrix named GrayPrincess.

Create an A x A averaging filter named f$.$

Use the conv$2$ function to apply the averaging filter f to the image GrayPrincess. Use the 'same' parameter during convolution, and store the result as a new matrix named BlurPrincess.

Create a new matrix EdgePrincess that contains the edges of the Princess Theatre image, by defining EdgePrincess as the absolute value $($you may use the abs function$)$ of the difference between GrayPrincess and BlurPrincess.

In Figure $2,$ display the image EdgePrincess using imagesc. Turn off the axis labels, make the colormap gray, and make sure the pixels are square. Add a title 'Edgy Princess'.

Create a horizontal edge detector named h$,$ with the values given in B$.$

Create a vertical edge detector named v$,$ with the values given in C$.$

Use the conv$2$ function to apply the horizontal edge detector h to the image GrayPrincess. Use the 'same' parameter during convolution, and store the result as a new matrix named HPrincess.

Use the conv$2$ function to apply the vertical edge detector v to the image GrayPrincess. Use the 'same' parameter during convolution, and store the result as a new matrix named VPrincess.

Combine the horizontal and vertical edges, and store the result as a new matrix named CombPrincess.

Use the rescale function to rescale the pixel intensities in CombPrincess to between $0$ and $1,$ and store the result as a new matrix named ResPrincess.

Create a new matrix NewPrincess that contains a version of the image ResPrincess in the colour specified by D$.$ That is$,$ set ResPrincess as the appropriate two colour channels of a new $3$D matrix named NewPrincess, and set all intensities in the remaining colour channel to zero $($hint: recall that Red $+$ Green $=$ Yellow, Red $+$ Blue $=$ Magenta, and Blue $+$ Green $=$ Cyan$).$

In Figure $3,$ display the image NewPrincess using imagesc. Turn off the axis labels and make sure the pixels are square. Add a title 'Colourful Princess'.

Note:

Use semicolons $($;$)$ to suppress code output, or answers may not compute properly as the image matrices are large.

You must use the variable names specified in the question $($case is important$).$

DO NOT use any clear, clc$,$ or close all commands in your script.