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Obtain Number of Pixels in Area Around Binary Image Object

Asked by Andrew Poissant on 5 Jul 2018
Latest activity Edited by Anton Semechko on 6 Jul 2018
I have a binary image and use matlab's 'regionprops' function to fit ellipses to the image (see attached photo). I want to obtain the total number of pixels of the black area within each ellipse. I use the 'Area' property of regionprops to get the total number of pixels of the white area within the fitted ellipses, but I want the total number of pixels of the black area within each fitted ellipse. How would I get this?

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1 Answer

Answer by Anton Semechko on 5 Jul 2018
 Accepted Answer

To distinguish between points/pixels inside the ellipse vs. those outside, you need to know parameters of the ellipse. Here is an example:
% Ellipse parameters
ab=sort(3*rand(1,2)+1,'descend'); % lengths of the principal semi-axes
r=pi*rand(1); % orientation of the ellipse; relative to the x-axis
R=[cos(r) -sin(r);sin(r) cos(r)]; % directions of the principal axes (along columns)
C=10*randn(2,1); % center of the ellipse
% Visualize ellipse
t=linspace(0,2*pi,1E3);
X=[cos(t);sin(t)];
Y=bsxfun(@plus,R*diag(ab)*X,C);
figure('color','w')
plot(Y(1,:),Y(2,:),'-b','LineWidth',2)
axis equal
hold on
% Generate a random set of points around the ellipse
N=1E3;
P=2*rand(2,N)-1;
P=bsxfun(@plus,2*R*diag(ab)*P,C); % random point cloud
% Classify points depending on whether they are inside (and on the boundary)
% or outside the ellipse; to do this we need to know parameters of the ellipse
dP=bsxfun(@minus,P,C); % center the points
dP=R'*dP; % change basis
dP=diag(1./ab)*dP; % normalize length of principal axes to 1
id_in=sum(dP.^2,1)<=1; % point P(:,i) is inside the ellipse if norm(dP(:,i))<1 and on its boundary if norm(dP(:,i))=1
% Visualize points
P_in=P(:,id_in);
P_out=P(:,~id_in);
plot(P_in(1,:),P_in(2,:),'.g','MarkerSize',10,'LineWidth',2)
plot(P_out(1,:),P_out(2,:),'xr','MarkerSize',5,'LineWidth',2)
xlabel('x','FontSize',25)
ylabel('y','FontSize',25)

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Binary image is composed on pixels --> pixels have (x,y) coordinates
Let's say bw is your binary image. To get (x,y) coordinates of all black pixels, use command:
[y,x]=find(~bw);
Ah yes, great point. Thanks for the help! Very easy to understand.
You are welcome, Andrew. Let me know if run into any problems when classifying pixels as inside or outside ellipse boundary.

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