Smoothing the edges of my contour

Hello :)

Would you mind helping me to reduce the zigzags in my contour boundaries?

My code and contour image is attached.

Thanks a lot in advance!

My whole code for an image processing:

close all;
clear all; 
clc;

tic;
%{
 n is the number of images processed for the desirable result which depends
 on the experiment. In other words, each experiment has its own n.
%}
n = 601;

% Here is the preallocation section.
%==========================================================================
Peaks = zeros(1,360);
Degrees = (1:360);

x = cell(n,1);
fname = zeros(1,19);
fname1 = zeros(1,13);
angle0 = zeros(360,n);
angle1 = zeros(360,n);
st0 = zeros(360,n);
st1 = zeros(360,n);
x0 = zeros(1,n);
x1 = zeros(1,n);
y0 = zeros(1,n);
y1 = zeros(1,n);
%==========================================================================
for ii=1:n
    %Here the pictures will be read from their path.(line 27:40)
    fname = int2str(ii);
    
    if ii<10    
        fname1 = '10mm_exp01_000';           
    end
    
    if ii>=10 && ii<100
        fname1 = '10mm_exp01_00';            
    end
    
    if ii>=100 && ii<1000
        fname1 = '10mm_exp01_0';            
    end
    %{
    Here the name of the file is created in order to be read from the path
    and a proper size will be defined,some filters will be applied and at
    the end the images are turned into binary. The boundary function will
    find the boundaries of the image. (line 48:     
    %}
    
    fname = strcat(fname1,fname,'.tif');       
    im = imread(fname);                  
    im = im(20:770,70:820);             % Defining a proper frame size
    
    h = fspecial('gaussian',51,15);     % Filtering the image
    bim = imfilter(im,h,'replicate');   % Filtering the image
    bim = im2bw(bim);                   % Turning the images into binary
    bim = imfill(bim,'holes');          % Empty the center of the image 
    
    B0 = boundaries(bim);               % Finding the boundaries of the image
    d = cellfun('length',B0);
    [max_d,k] = max(d);
    b0 = B0{k};
    [M,N] = size(bim);                  % M=length and N=width of the image
    a1 = ones(1,5)/5;                   % 10 point averaging filter, Noncausal
    b0 = filtfilt(a1,1,b0);
    
    %{
     The x and y coordinates for the center of the image is manually added.
     x0 = 381 and y0 = 365 
    %}
    [st0(:,ii),angle0(:,ii),x0(ii),y0(ii)] = signature(b0,381,365);  
    
     
        for k=1:max(size(b0))
        
            b0(k,1) = b0(k,1) - x0(ii);
            b0(k,2) = b0(k,2) - y0(ii);
            
        end
     
    [st1(:,ii),angle1(:,ii),x1(ii),y1(ii)] = signature(b0); %st=radius 
   
end
%{
For each degree degrees we apply fft function.
%}
    for k=1:360
        
        x{k} = st1(k,:);
        Fs = 65;                        % Camera frequency which is added manually
        L = length(x);
        T_inc = 1/Fs;                   % Time increment for fft plot
        signal_FFT = fft(x{k})/L;       % MATLAB fft output
        amplitude = 2*abs(signal_FFT(2:L/2+2));
        frequency = Fs/2*linspace(0,1,L/2+1);
        Tf = T_inc*L;                   % Final time
        time=0:T_inc:Tf-T_inc;          % Time vector
        Peaks(k)= max(x{k});
        figure(k);
        fft_figure = figure(k);
        set(fft_figure, 'Visible', 'off');
        plot (frequency,amplitude,'red');
        title ('Signal-Sided Amplitude Spectrum')
        xlabel ('Frequency (Hz) ')
        ylabel ('Magnitude of Signal (units of signal)')
%         folder = 'C:\Users\umroot\Desktop\Debugging the MATLAB codes\8th Draft\FFT';
%         figFileName = sprintf('FFT for %d deg.tif',k);
%         fullFileName = fullfile(folder, figFileName);
%         saveas(gcf,fullFileName); 
        
        figure(k);              % Plotting the signals
        radius_figure = figure(k);
        set(radius_figure, 'Visible', 'off');
        plot(time(:),x{k,:});
        xlabel('Time (s)');
        ylabel('Radius');
        title('Simulated Signal of Radiuses');
%         folder = 'C:\Users\umroot\Desktop\Debugging the MATLAB codes\8th Draft\Radii';
%         figFileName = sprintf('Radii for image no %d .tif',k);
%         fullFileName = fullfile(folder, figFileName);
%         saveas(gcf,fullFileName); 
    end
X_Axis = linspace (-st1(180,1),st1(1,1),M);
Y_Axis = linspace (-st1(90,1),st1(270,1),N);

figure;
cont = contour (X_Axis,Y_Axis,flipud(bim),1,'red');
axis square;

toc;
 
 

The Original, edited pics and contour is below:

And with the the filters I have used in my code, the edges for the contour is like this:

Far being said, the reason to smooth the contour edges is to reduce the errors in fft function which I want to apply on my contour too.

Thanks again :)

Answer 1

[Image Analyst]

If the sort-of circular mask thing is a binary image, you can smooth the boundary by blurring it with conv2() or imfilter() and then thresholding.

[NIMA FARHANG]

Hello,

I am using the imfilter and my original image turnes to the binary, yet still the edges will not be smoothened,

Besides, could you please explain me how to threshold the image ?

[Image Analyst]

How much did you blur it by? Try a larger window.

[NIMA FARHANG]

I applied these filters :

h=fspecial('gaussian',51,15)
bim=imfilter(im,h,'replicate')

Besides, I have applied other imfilter filters too (circular and etc) and ther results yet again were not satisfactory; far being said , by increasing the radius of the blurness, there will be augmented margin which I will lose the exact shape of the boundaries of my image!

[Image Analyst]

You can control the size of the shape by what you threshold it at after you blur it.

bim = bim > 0.9; % Small size (fewer pixels are being selected by the threshold).

or

bim = bim > 0.1; % Large size (more pixels are being selected by the threshold).

But of course the boundaries of your exact original shape will change after you smooth it - what did you expect? It will be SMOOTHER, meaning the shape is not the same and you WILL "lose the exact shape of the boundaries". Why are you expecting anything different?

[NIMA FARHANG]

Thanks a lot!

As I have attached above (the last zoomed picture) there are zigzags in my boundaries. In large scale, it is fine; yet I want to apply fft on my image, which due to these zigzags, there are many signals amplitudes in my final fft plot that  interfere with my preferred result. All I want is something like 'feather' tool in photoshop which reduces the zigzag shape of the boundaries.

[Image Analyst]

NIMA:

As you can clearly see from the attached demo, as the window size gets larger, the image gets more blurry and thus the shape will be smoother. It it weren't so round already, you'd see it more clearly.

[NIMA FARHANG]

Cheifly thanks a lot for taking your time to answer my questions. I do really appreciate it! Unfortunately I get this error when running the attached code:

No appropriate method, property, or field Neighborhood for class strel.

(at this line: kernel = se.Neighborhood / sum(se.Neighborhood(:)); )

Far being said I am using 2012b version.

Again, thank you so much!