How can I recognize shapes of simple geometrical objects using optimization tools

Here is the sample code to recognize a circle, looks like I need to create different functions to define a square, rectangle and a triangle first if I want recognize them. Can someone help me with it? Thanks.

clc
clear
M0=zeros(1024,1024); % Background of zeros
x=1:1024; 
y=1:1024;
[X,Y]=meshgrid(x,y); % grid of pixel positions
for in=11
    A=double(imread([num2str(in,'%4.3d'),'.jpg']))/255; % Load image and scale to 1
    M=@(p) M0+double((X-p(1)).^2+(Y-p(2)).^2<(p(3))^2); % define your teplate 
                                                        % You may need a separate funtion file
    
    fun=@(p) sum(sum(abs(A-M(p)).^2)); % The objective funtion to minimize
     
    % find the avergae center position and ditribution of the nonzero
    % pixels in image
    pos=find(A>0);
    x0=mean(X(pos));
    y0=mean(Y(pos));
    d=(range(X(pos))+range(Y(pos)))/2;
    
    trl=[x0 y0 d/2]; % The trial solution % number of parameters depend on the shape
    
    lb=[0 0 0];% lower bounds of the prameters
    ub=[1024 1024 512];% upper bounds of the prameters
    
    
    % Optimization process
    %You dont have to change the below lines
    opts=optimoptions('ga'); 
    opts.InitialPopulationMatrix=trl;
    opts.Display='iter';     
    [sol,fval]=ga(fun,length(trl),[],[],[],[],lb,ub,[],opts);
    
    if fval<100 
        'circle'
    else
        'unknown'
    end
    
    figure(1)
    clf
    surf(M(sol),'linestyle','none')
    view(2)
    daspect([1 1 1])
    

    figure(2)
    clf
    surf(A,'linestyle','none')
    view(2)
    daspect([1 1 1])     
end

[Walter Roberson]

Are the objects to be recognized the only things in the image? Are they outlines or filled ? Are they dark on light or light on dark or bright color or dark color ? I take it that part of the challenge is that they might be rotated.

[TOKEN]

They are the only things in the image, they are white in the image with the black background. Yes, the rotation should be easy. I just dont know how to define a rectangle for now

Answer 1

[Image Analyst]

Attach an image. In the meantime, see my attached shape recognition demo.