This code of matlab run a project of Segmentation by fourier and transform inverse Z $,$ i want to explain in handwritting ALL the code with maths equations, Just explain every step of the code i want maths expression explain $,$ To run just download any image of net like tomografy in dark scales and rename example$1.$jpg or jpg

I dont want machine answers only math handwritting $\%$ List of images

imageFiles $=\{\text{'}$EXAMPLE$.$jpg$\text{'}\}$;

numImages $=$ length$($imageFiles$)$;

$\%$ Parameters

sizeIm $=100$;

dt $=0\mathrm{.}425$;

eps $=1$E$-7$;

Nx $=$ sizeIm;

Ny $=$ sizeIm;

Lx $=100$;

Ly $=100$;

$\%$ Process each image

for idx $=1$:numImages

$\%$ Load and process the image

A $=$ imread$($imageFiles$\{$idx$\})$;

Im $=$ imresize$($A$,[$sizeIm$,$ sizeIm$])$;

$\%$ Convert to grayscale if not already

if size$($Im$,3)==3$

B $=$ rgb$2$gray$($Im$)$;

else

B $=$ Im;

end

C $=$ double$($B$($:$))$;

$\%$ Grid dx$=$dy in mesh

x $=$ linspace$(0,$ Lx$,$ Nx$)$;

y $=$ linspace$(0,$ Ly$,$ Ny$)$;

dx $=$ x$(2)-$ x$(1)$;

r $=($eps$)/(($dx$)^2)$;

$\%$ Array initialization

unk $=$ Nx $*$ Ny; $\%$ number of unknowns

M $=$ zeros$($unk$,$ unk$)$;

$\%$ Interior nodes

for ii $=2$:Nx$-1$

for jj $=2$:Ny$-1$

n $=$ ii $+($jj$-1)*$ Nx; $\%$ convert point ij to mesh point

M$($n$,$ n$)=-4*$ r $+((1)/$ dt$)$; $\%$ main diagonal

M$($n$,$ n$-1)=$ r; $\%$ left of diagonal

M$($n$,$ n$+1)=$ r; $\%$ right of diagonal

M$($n$,$ n$-$Nx$)=$ r; $\%$ left far diagonal

M$($n$,$ n$+$Nx$)=$ r; $\%$ far right diagonal

end

end

$\%$ Boundary conditions

$\%$ Left border

ii $=1$;

for jj $=2$:Ny$-1$

n $=$ ii $+($jj$-1)*$Nx;

M$($n$,$ n$)=-4*$r $+(1/$ dt$)$;

M$($n$,$ n$+1)=2*$r;

M$($n$,$ n$+$Nx$)=$ r;

M$($n$,$ n$-$Nx$)=$ r;

end

$\%$ Right border

ii $=$ Nx;

for jj $=2$:Ny$-1$

n $=$ ii $+($jj$-1)*$Nx;

M$($n$,$ n$)=-4*$r $+(1/$ dt$)$;

M$($n$,$ n$-1)=2*$r;

M$($n$,$ n$+$Nx$)=$ r;

M$($n$,$ n$-$Nx$)=$ r;

end

$\%$ Lower border

jj $=1$;

for ii $=2$:Nx$-1$

n $=$ ii $+($jj$-1)*$Nx;

M$($n$,$ n$)=-4*$r $+(1/$ dt$)$;

M$($n$,$ n$-1)=$ r;

M$($n$,$ n$+1)=$ r;

M$($n$,$ n$+$Nx$)=2*$r;

end

$\%$ Upper border

jj $=$ Ny;

for ii $=2$:Nx$-1$

n $=$ ii $+($jj$-1)*$Nx;

M$($n$,$ n$)=-4*$r $+(1/$ dt$)$;

M$($n$,$ n$-1)=$ r;

M$($n$,$ n$+1)=$ r;

M$($n$,$ n$-$Nx$)=2*$r;

end

$\%$ Upper left corner

jj $=$ Ny;

ii $=1$;

for ii $=1$:Nx$-($Nx$-1)$

n $=$ ii $+($jj$-1)*$Nx;

M$($n$,$ n$)=-4*$r $+(1/$ dt$)$;

M$($n$,$ n$+1)=2*$r;

M$($n$,$ n$-$Nx$)=2*$r;

end

$\%$ Right upper corner

jj $=$ Ny;

ii $=$ Nx;

for ii $=$ Nx: Nx

n $=$ ii $+($jj$-1)*$Nx;

M$($n$,$ n$)=-4*$r $+(1/$ dt$)$;

M$($n$,$ n$-1)=2*$r;

M$($n$,$ n$-$Nx$)=2*$r;

end

$\%$ Lower right corner

jj $=1$;

ii $=$ Nx;

for ii $=$ Nx: Nx

n $=$ ii $+($jj$-1)*$Nx;

M$($n$,$ n$)=-4*$r $+(1/$ dt$)$;

M$($n$,$ n$-1)=2*$r;

M$($n$,$ n$+$Nx$)=2*$r;

end

$\%$ Bottom left corner

jj $=1$;

ii $=1$;

for ii $=1$:Nx$-($Nx$-1)$

n $=$ ii $+($jj$-1)*$Nx;

M$($n$,$ n$)=-4*$r $+(1/$ dt$)$;

M$($n$,$ n$+1)=2*$r;

M$($n$,$ n$+$Nx$)=2*$r;

end

$\%$ Solve the system

Uvec $=$ M$\backslash$C;

Upix $=$ round$($Uvec$)$;

UM $=$ reshape$($Upix$($:$),$ sizeIm, $[])$;

$\%$ Display of the processed image

figure;

imagesc$($UM$)$;

colormap$($gray$)$;

title$([\text{'}$Rescaling in Gray Tones $-$ Image $\text{'},$ num$2$str$($idx$)])$;

$\%$ Discrete Fourier Transform $($DFT$)$

X $=$ fft$2($double$($B$))$;

$\%$ Display of the Discrete Fourier Transform

figure;

imshow$($log$($abs$($fftshift$($X$))+1),[])$;

colormap$($jet$)$;

colorbar;

title$([\text{'}$Discrete Fourier Transform $($DFT$)-$ Image $\text{'},$ num$2$str$($idx$)])$;

$\%$ Inverse Z Transform using IFFT

Y $=$ ifft$2($X$)$;

$\%$ Display of the Inverse Z Transform

figure;

imshow$($abs$($Y$),[])$;

title$([\text{'}$Inverse Z Transform $-$ Image $\text{'},$ num$2$str$($idx$)])$;

$\%$ Segmentation by light intensity with custom colormap

level $=$ graythresh$($B$)$;

binaryImage $=$ imbinarize$($B$,$ level$)$;

$\%$ Custom Colormap $($parula in this case$)$

colormap$($parula$)$;

$\%$ Shows the image segmented with the colormap

figure;

imagesc$($binaryImage$)$;

axis equal;

axis off;

title$([\text{'}$Light Intensity Segmentation $($Custom Colormap$)-$ Image $\text{'},$ num$2$str$($idx$)])$;

colorbar;

end