## 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

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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