Method fitCircle

ij/src/main/java/ij/plugin/Selection.java:147–263

(ImagePlus imp)

	Authors: Nikolai Chernov, Michael Doube, Ved Sharma
	*/
	void fitCircle(ImagePlus imp) {
		if (!imp.okToDeleteRoi()) return;
		Roi roi = imp.getRoi();
		if (roi==null) {
			noRoi("Fit Circle");
			return;
		}
		
		if (roi.isArea()) {	  //create circle with the same area and centroid
			Undo.setup(Undo.ROI, imp);
			ImageProcessor ip = imp.getProcessor();
			ip.setRoi(roi);
			ImageStatistics stats = ImageStatistics.getStatistics(ip, Measurements.AREA+Measurements.CENTROID, null);
			double r = Math.sqrt(stats.pixelCount/Math.PI);
			imp.deleteRoi();
			int d = (int)Math.round(2.0*r);
			Roi roi2 = new OvalRoi((int)Math.round(stats.xCentroid-r), (int)Math.round(stats.yCentroid-r), d, d);
			transferProperties(roi, roi2);
			imp.setRoi(roi2);
			return;
		}
		
		Polygon poly = roi.getPolygon();
		int n=poly.npoints;
		int[] x = poly.xpoints;
		int[] y = poly.ypoints;
		if (n<3) {
			IJ.error("Fit Circle", "At least 3 points are required to fit a circle.");
			return;
		}
		
		// calculate point centroid
		double sumx = 0, sumy = 0;
		for (int i=0; i<n; i++) {
			sumx = sumx + poly.xpoints[i];
			sumy = sumy + poly.ypoints[i];
		}
		double meanx = sumx/n;
		double meany = sumy/n;
		
		// calculate moments
		double[] X = new double[n], Y = new double[n];
		double Mxx=0, Myy=0, Mxy=0, Mxz=0, Myz=0, Mzz=0;
		for (int i=0; i<n; i++) {
			X[i] = x[i] - meanx;
			Y[i] = y[i] - meany;
			double Zi = X[i]*X[i] + Y[i]*Y[i];
			Mxy = Mxy + X[i]*Y[i];
			Mxx = Mxx + X[i]*X[i];
			Myy = Myy + Y[i]*Y[i];
			Mxz = Mxz + X[i]*Zi;
			Myz = Myz + Y[i]*Zi;
			Mzz = Mzz + Zi*Zi;
		}
		Mxx = Mxx/n;
		Myy = Myy/n;
		Mxy = Mxy/n;
		Mxz = Mxz/n;