fitting a curve on a binary image and interpolating to produce a continuous graph

This is first time I have ever used mathworks, so your help is greatly appreciated. I took a m-mode ultrasound image and imputed it into imagej in which I removed the noise and binarized the image. This resulted in a graph like image, but it is not as smooth as I want. I want to able to curve fit it and potentially use interpollation to give a filled in graph. linked below is my binarized image.

[Matt J]

Is the curve supposed to follow any particular model? Is it a pure sinusoid?

[EYAD SALEH]

this is the ultrasound image. I found the binirization of the image, and now I want to curve fit it. For some reason, I can't link the binirized image in the comment so here is the inital ultrasound image.

[Matt J]

Is the curve supposed to follow any particular model? Is it a pure sinusoid?

[EYAD SALEH]

@Matt J yes it is sinusoidal

Answer 1

[Image Analyst]

Try this:

% Demo by Image Analyst
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 22;
markerSize = 40;
%--------------------------------------------------------------------------------------------------------
%    READ IN IMAGE
folder = [];
baseFileName = 'sinusoid ultrasound.jpeg';
fullFileName = fullfile(folder, baseFileName);
% Check if file exists.
if ~exist(fullFileName, 'file')
    % The file doesn't exist -- didn't find it there in that folder.
    % Check the entire search path (other folders) for the file by stripping off the folder.
    fullFileNameOnSearchPath = baseFileName; % No path this time.
    if ~exist(fullFileNameOnSearchPath, 'file')
        % Still didn't find it.  Alert user.
        errorMessage = sprintf('Error: %s does not exist in the search path folders.', fullFileName);
        uiwait(warndlg(errorMessage));
        return;
    end
end
grayImage = imread(fullFileName);
% Get the dimensions of the image.
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage)
%--------------------------------------------------------------------------------------------------------
% Display the image.
subplot(2, 2, 1);
imshow(grayImage);
impixelinfo;
axis('on', 'image');
title('Original Image', 'FontSize', fontSize, 'Interpreter', 'None');
if numberOfColorChannels > 1
    % It's not really gray scale like we expected - it's color.
    fprintf('It is not really gray scale like we expected - it is color\n');
    % Extract the blue channel.
    grayImage = grayImage(:, :, 3);
end
% Update the dimensions of the image.
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage)
% Maximize window.
g = gcf;
g.WindowState = 'maximized';
drawnow;
%--------------------------------------------------------------------------------------------------------
% Display the histogram.
subplot(2, 2, 2);
histogram(grayImage(grayImage>0), 256);
grid on;
title('Histogram of Image Gray Levels', 'FontSize', fontSize, 'Interpreter', 'None');
% Threshold the image to get the dark stuff.
% https://www.mathworks.com/matlabcentral/fileexchange/29372-thresholding-an-image?s_tid=srchtitle
lowThreshold = 64;
highThreshold = 255;
% [lowThreshold, highThreshold, lastThresholdedBand] = threshold(lowThreshold, highThreshold, grayImage)
mask = grayImage >= lowThreshold & grayImage <= highThreshold;
% Take 5 largest blobs
mask = bwareafilt(mask, [10, inf]);
% Fill in the bubble so that it will have only 3 sides.
mask = imfill(mask, 'holes');
subplot(2, 2, 3);
imshow(mask)
title('Mask Image', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
impixelinfo
% Sum the first 30 rows
horizontalProfile = sum(grayImage(1:30, :));
% Display summed lines.
subplot(2, 2, 4);
hold on;
plot(horizontalProfile, 'b-', 'LineWidth',2);
grid on;
title('Horizontal Profile with Peaks Shown', 'FontSize', fontSize, 'Interpreter', 'None');
% Threshold at 3000 to find peaks
horizontalProfile(horizontalProfile<3000) = 0; % Suppress small peaks
[peakValues, indexesOfPeaks] = findpeaks(horizontalProfile)
hold on
plot(indexesOfPeaks, peakValues, 'rv', 'LineWidth', 2);
% Find the average peak to peak wavelength
meanPeriod = mean(diff(indexesOfPeaks))
% Show sine wave over image
hfig = figure;
imshow(grayImage, []);
title('Image With Sine Wave', 'FontSize', fontSize, 'Interpreter', 'None');
axis('on', 'image');
impixelinfo
hold on
amplitude = rows/2;
x = 1 : columns;
phasex = mean([x(indexesOfPeaks(1)), x(indexesOfPeaks(2))])
y = amplitude * sin(2 * pi * (x - phasex/2) / meanPeriod) + rows/2;
plot(x, y, 'r-', 'LineWidth', 3);
hfig.WindowState = 'maximized'