How does the matlab's contourf work

So I am able to get the contour matrix from contourf.Now when I try to plot the points on the figure shown below,I end up getting pretty good results.

However,when I manipulate the matrix returned from contourf ,and then try plotting the points,the results are not accurate.Infact the points get shifted.

So,I am thinking that somehow the way I am plotting the matrix and the way Matlab's contourf plots it is different.

Any ideas on what can be done here to get accurate results.

Enclosed is the code block used to get the contour plots as well as the edge points obtained from the below link

Accurate subpixel edge location - File Exchange - MATLAB Central (mathworks.com)

Code block for generatnig contours using contourf

I=imread('V.jpg');
I=I(:,:,1);
figure(2)
level=[160,160];
[M,h]=contourf(I,level);
clabel(M,h);
set(gca, 'YDir','reverse')

Code block used to manipulate the Matrix M(more specifically we want to ignore the columns which show us how many points are there for a particular level set).

level_set=load('updated_level_ptsV160.mat');
M=level_set.M;
%idx=find(M(1,:)==110);
%M(:,1)=missing;
%M(:,93)=missing;
%M(:,idx)=(missing);
%M(:,108:110)=missing;
%M(:,112:114)=missing;
plot(M(1,:),M(2,:));
set(gca, 'YDir','reverse')
%save('updated_level_ptsV110.mat','M');

*Please note that these manipulations are specific to contour level 110.I am enclosing the updated file after removing the values as mentinoned earlier.As well as the plot of what happens if I directly plot the contour matrix M.

And finally the result of plotting the points on the contour.

The mat-files for inspection are enclosed

For those interested in why I am plotting the points on the contour the goal is to find a solution to the below question posted by me

DLTR: Want to know why the plot from contourf and my plot are showing different results.Is it because of how matlab's contourf is designed?

Why does plot(X,Y,'or') and plot(X,Y) give different results - MATLAB Answers - MATLAB Central (mathworks.com)

[Sparsh Garg]

it seems that i was working on 2 different images of the same letter,so that's why there was the issue.