How to count how many different objects

So I have this image:

There are 36 objects in total and roughly 10 different ones.

Is there a method to calculate how many different objects there are?

Answer 1

[Akira Agata]

How about the following way?

% Load the image
BW = imread('bARgija.png');

% Remove small area (< 10 pixel)
BW2 = bwareaopen(BW,10);

% Obtain area and bounding box for each area
s = regionprops('table',BW2,{'Area','BoundingBox'});

% Set allowable area torelance (e.g 5 pixel)
tolPixel = 5;

% Assume same object has same area (with 5 pixel torelance)
r = tolPixel/max(s.Area);
[~,~,group] = uniquetol(s.Area,r);

% Show the result
color = jet(max(group));
figure
imshow(BW)
hold on
for kk = 1:height(s)
rectangle(...
  'Position',   s.BoundingBox(kk,:),...
  'EdgeColor',  color(group(kk),:),...
  'LineWidth',  2);
end

The number of different objects can be obtained by max(group).

>> max(group)
ans =
  12

[Image Analyst]

Very nice - clever. I was going to use some kind of machine learning method to figure out how many area clusters there are. I didn't know about uniquetol(). It looks like a nice function - perfect for using here.

I also learned about height() and width() from your code. However, I'm disappointed that the Mathworks chose to create a built-in functions with those names, instead of tableheight() and tablewidth() because I've often used variables with those names (height and width). I guess I'll have to change now.

[João Oliveira]

Thank you for the answer. Really apreciated.

[Paolo Piazza]

This is really interesting, I'd have another question: is it possible to calculate how simillar/dissimilar the objects are in an image? for instance, if all objects were saws (or more less have the same shape).

[Image Analyst]

What I'd probably do is to align the objects, like with imregister() or imrotate() or something, then compute the Dice Sorensen Coefficient. It's been talked about here before so look it up. Also run my attached demo on it.