Selection to fit points + refine

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bluecd
Posts: 3
Joined: Sat Mar 24, 2018 1:36 pm

Selection to fit points + refine

Postby bluecd » Sat Mar 24, 2018 4:23 pm

Hello!
Ive been starting with scripting so forgive my saying possible nonsense ))
I need to automate extraction of circular object from the +/- consistent background.
Just thought about fitting circular selection to sth like this: https://www.mathworks.com/matlabcentral ... tt-method-

Code: Select all

function Par = CircleFitByPratt(XY)

%--------------------------------------------------------------------------
%
% Circle fit by Pratt
% V. Pratt, "Direct least-squares fitting of algebraic surfaces",
% Computer Graphics, Vol. 21, pages 145-152 (1987)
%
% Input: XY(n,2) is the array of coordinates of n points x(i)=XY(i,1), y(i)=XY(i,2)
%
% Output: Par = [a b R] is the fitting circle:
% center (a,b) and radius R
%
% Note: this fit does not use built-in matrix functions (except "mean"),
% so it can be easily programmed in any programming language
%
%--------------------------------------------------------------------------

n = size(XY,1); % number of data points

centroid = mean(XY); % the centroid of the data set

% computing moments (note: all moments will be normed, i.e. divided by n)

Mxx=0; Myy=0; Mxy=0; Mxz=0; Myz=0; Mzz=0;

for i=1:n
Xi = XY(i,1) - centroid(1); % centering data
Yi = XY(i,2) - centroid(2); % centering data
Zi = Xi*Xi + Yi*Yi;
Mxy = Mxy + Xi*Yi;
Mxx = Mxx + Xi*Xi;
Myy = Myy + Yi*Yi;
Mxz = Mxz + Xi*Zi;
Myz = Myz + Yi*Zi;
Mzz = Mzz + Zi*Zi;
end

Mxx = Mxx/n;
Myy = Myy/n;
Mxy = Mxy/n;
Mxz = Mxz/n;
Myz = Myz/n;
Mzz = Mzz/n;

% computing the coefficients of the characteristic polynomial

Mz = Mxx + Myy;
Cov_xy = Mxx*Myy - Mxy*Mxy;
Mxz2 = Mxz*Mxz;
Myz2 = Myz*Myz;

A2 = 4*Cov_xy - 3*Mz*Mz - Mzz;
A1 = Mzz*Mz + 4*Cov_xy*Mz - Mxz2 - Myz2 - Mz*Mz*Mz;
A0 = Mxz2*Myy + Myz2*Mxx - Mzz*Cov_xy - 2*Mxz*Myz*Mxy + Mz*Mz*Cov_xy;
A22 = A2 + A2;

epsilon=1e-12;
ynew=1e+20;
IterMax=20;
xnew = 0;

% Newton's method starting at x=0

for iter=1:IterMax
yold = ynew;
ynew = A0 + xnew*(A1 + xnew*(A2 + 4.*xnew*xnew));
if (abs(ynew)>abs(yold))
disp('Newton-Pratt goes wrong direction: |ynew| > |yold|');
xnew = 0;
break;
end
Dy = A1 + xnew*(A22 + 16*xnew*xnew);
xold = xnew;
xnew = xold - ynew/Dy;
if (abs((xnew-xold)/xnew) < epsilon), break, end
if (iter >= IterMax)
disp('Newton-Pratt will not converge');
xnew = 0;
end
if (xnew<0.)
fprintf(1,'Newton-Pratt negative root: x=%f\n',xnew);
xnew = 0;
end
end

% computing the circle parameters

DET = xnew*xnew - xnew*Mz + Cov_xy;
Center = [Mxz*(Myy-xnew)-Myz*Mxy , Myz*(Mxx-xnew)-Mxz*Mxy]/DET/2;

Par = [Center+centroid , sqrt(Center*Center'+Mz+2*xnew)];

end % CircleFitByPratt
1. then refining with preview possibility and manual adjustments /typical PS set of adjustments to a selection/
2. masking the background on the same layer as the objects are

Point no 1 I do manually, no 2 - have action set for it.

Assuming good quality and ca.consistent background /to be achieved/ I can automate whole process with quite good success percentage (+75%)
Would anybody help just to advice to start proper approach to such problem. How about shape recognition using JS? How about /semi/automatic selection refine?

cheers,
-

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