Implementing Skeletonisation Without Using bwmorph (or other in-built functions)

Hello,

I am currently trying to implement sketelonization in matlab without using any of the in-built functions. I think my code is close to being correct, albeit messy, but when I run it the image I get is the exact same as the original (i.e. the skeletonisation procedure doesn't seem to be changing the image). My Matlab skills are not great so any help in how to get my code sucessfully working would be much appreciated :)

im = im2double(imread('mapleleaf.tif'));
%figure(1);
%imshow(im);

[rows, cols] = size(im);
I = imbinarize(im); %gives binary of image
b = bwboundaries(I);
flag = 0;
T = 0;

 for x = 2 : rows - 1 
    for y = 2 : cols - 1
                p1 = I(x,y);
                p2 = I(x-1,y);
                p3 = I(x+1,y-1);
                p4 = I(x,y+1);
                p5 = I(x+1,y+1);
                p6 = I(x,y+1);
                p7 = I(x-1,y+1);
                p8 = I(x,y-1);
                p9 = I(x-1,y-1);
                N = p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9;
                if ((p2 == 0) && (p3 == 1))
                             T = T + 1;
                end
                if ((p3 == 0) && (p4 == 1))
                            T = T + 1;
                end
                if ((p4 == 0) && (p5 == 1))
                            T = T + 1;
                end
                if ((p5 == 0) && (p6 == 1))
                            T = T + 1;
                end
                if ((p6 == 0) && (p7 == 1))
                            T = T + 1;
                end
                if ((p7 == 0) && (p8 == 1))
                            T = T + 1;
                end
                if ((p8 == 0) && (p9 == 1))
                            T = T + 1;
                end
                if ((p9 == 0) && (p2 == 1))
                            T = T + 1;
                end
                if ((2 <= N) && (N <= 6) && (T == 1) && (p2*p4*p6 == 0) && (p4*p6*p8 == 0))
                    flag = p1;   
                    I(x,y) = flag;
                else  
                    I(x,y) = p1;
                end
                if ((2 <= N) && (N <= 6) && (T == 1) && (p2*p4*p8 == 0) && (p2*p6*p8 == 0))
                    flag = p1;   
                    I(x,y) = flag;
                else  
                    I(x,y) = p1;
                end 
                T = 0;
                flag = 0;
    end
 end
 
figure,
imshow(I);