Creating approximation line between objects.

Hello, I have image with a few objects I measured centroids of each one, now I want to create approximation line using centroids. Do you have any ideas how could I do that? Thank you in advance.

Answer 1

[Image Analyst]

Compute the centroids with regionprops(). Then pass those into polyfit(). Then use polyval() to get coordinates along the line.

[Marcin Heba]

Thank you for yor answer. I wrote a code but results are not so good. Could you look at this and give me some advice?

Here's my code:

clear all
close all

obraz_org = imread('image1.png'); 
obraz_bw = im2bw(obraz_org);
obraz_label = bwlabel(obraz_bw, 8);
bb  = regionprops(obraz_label,'Centroid');
centroids = cat(1, bb.Centroid);
imshow(obraz_bw);
axis on;
hold on

[Y,I]=sort(centroids(:,2));
B=centroids(I,:);

x = B(:,1)
y = B(:,2)

plot(x, y, 'r+')
[p,~,mu] = polyfit(x, y, 1);
f = polyval(p,x,[],mu);
plot(x,f)
hold off

Final image:

Orginal image:

[John D'Errico]

Note that polyfit is NOT the right tool for this fit. You need a code that can fit a line with errors in BOTH variables. If you choose to use the wrong tool (i.e., polyfit) then you WILL get a biased line. The slope will be wrong. Always.

My comment above should be a hint as to why polyfit gave the wrong slope. Again, polyfit is the WRONG tool here.

Look on the file exchange. There are lots of such tools. I would start with the keyword "orthogonal regression".

Be careful though, because not all orthogonal regressions were done at all well. (I just looked, and I found a fair amount of crap.) You need to use a tool that has SVD at its core. This one should suffice:

http://www.mathworks.com/matlabcentral/fileexchange/16800-orthogonal-linear-regression

[Image Analyst]

Marcin: you got confused when you did the fit as to which coordinate was the independent variable and which was the dependent variable. Fixed code is below:

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 = 20;

%===============================================================================
% Read in a gray scale demo image.
folder = pwd;
baseFileName = 'image1.png';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
grayImage = imread(fullFileName);
% Get the dimensions of the image.  
% numberOfColorBands should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage);
if numberOfColorChannels > 1
  % It's not really gray scale like we expected - it's color.
  % Convert it to gray scale by taking only the green channel,
  % which in a typical snapshot will be the least noisy channel.
  % grayImage = grayImage(:, :, 2); % Take green channel.
end
% Display the image.
% subplot(2, 2, 1);
imshow(grayImage, []);
axis on;
axis image;
title('Original Grayscale Image', 'FontSize', fontSize, 'Interpreter', 'None');

% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Get rid of tool bar and pulldown menus that are along top of figure.
set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off') 

binaryImage = im2bw(grayImage);
labeledImage = bwlabel(binaryImage, 8);
props  = regionprops(labeledImage, 'Centroid');
centroids = [props.Centroid];
xCenters = centroids(1:2:end);
yCenters = centroids(2:2:end);
hold on;
plot(xCenters, yCenters, 'r+', 'LineWidth', 2, 'MarkerSize', 20);
% Fit to a polynomial
coefficients = polyfit(yCenters, xCenters, 1);
% Get fit over all y (row) values.
rowFit = 1 : rows;
% Get an x value (columns value) for each row.
colFit = polyval(coefficients, rowFit);
% Plot it over the image.
plot(colFit, rowFit, 'm-', 'LineWidth', 2);
hold off

[Marcin Heba]

Thank you very much for your help