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 ... ttmethod
Code: Select all
function Par = CircleFitByPratt(XY)
%
%
% Circle fit by Pratt
% V. Pratt, "Direct leastsquares fitting of algebraic surfaces",
% Computer Graphics, Vol. 21, pages 145152 (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 builtin 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=1e12;
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('NewtonPratt goes wrong direction: ynew > yold');
xnew = 0;
break;
end
Dy = A1 + xnew*(A22 + 16*xnew*xnew);
xold = xnew;
xnew = xold  ynew/Dy;
if (abs((xnewxold)/xnew) < epsilon), break, end
if (iter >= IterMax)
disp('NewtonPratt will not converge');
xnew = 0;
end
if (xnew<0.)
fprintf(1,'NewtonPratt negative root: x=%f\n',xnew);
xnew = 0;
end
end
% computing the circle parameters
DET = xnew*xnew  xnew*Mz + Cov_xy;
Center = [Mxz*(Myyxnew)Myz*Mxy , Myz*(Mxxxnew)Mxz*Mxy]/DET/2;
Par = [Center+centroid , sqrt(Center*Center'+Mz+2*xnew)];
end % CircleFitByPratt
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,
