void createEllipse(ImagePlus imp) {
IJ.showStatus("Fitting ellipse");
Roi roi = imp.getRoi();
if (roi == null) {
noRoi("Fit Ellipse");
return;
}
if (roi.isLine()) {
IJ.error("Fit Ellipse", "\"Fit Ellipse\" does not work with line selections");
return;
}
ImageProcessor ip = imp.getProcessor();
ip.setRoi(roi);
int options = Measurements.CENTROID + Measurements.ELLIPSE;
ImageStatistics stats = ImageStatistics.getStatistics(ip, options, null);
double dx = stats.major * Math.cos(stats.angle / 180.0 * Math.PI) / 2.0;
double dy = -stats.major * Math.sin(stats.angle / 180.0 * Math.PI) / 2.0;
double x1 = stats.xCentroid - dx;
double x2 = stats.xCentroid + dx;
double y1 = stats.yCentroid - dy;
double y2 = stats.yCentroid + dy;
double aspectRatio = stats.minor / stats.major;
imp.killRoi();
imp.setRoi(new EllipseRoi(x1, y1, x2, y2, aspectRatio));
}
/*
if selection is closed shape, create a circle with the same area and centroid, otherwise use<br>
the Pratt method to fit a circle to the points that define the line or multi-point selection.<br>
Reference: Pratt V., Direct least-squares fitting of algebraic surfaces", Computer Graphics, Vol. 21, pages 145-152 (1987).<br>
Original code: Nikolai Chernov's MATLAB script for Newton-based Pratt fit.<br>
(http://www.math.uab.edu/~chernov/cl/MATLABcircle.html)<br>
Java version: https://github.com/mdoube/BoneJ/blob/master/src/org/doube/geometry/FitCircle.java<br>
@authors Nikolai Chernov, Michael Doube, Ved Sharma
*/
void fitCircle(ImagePlus imp) {
Roi roi = imp.getRoi();
if (roi == null) {
noRoi("Fit Circle");
return;
}
if (roi.isArea()) { // create circle with the same area and centroid
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.killRoi();
int d = (int) Math.round(2.0 * r);
IJ.makeOval(
(int) Math.round(stats.xCentroid - r), (int) Math.round(stats.yCentroid - r), d, d);
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;
Myz = Myz / n;
Mzz = Mzz / n;
// calculate the coefficients of the characteristic polynomial
double Mz = Mxx + Myy;
double Cov_xy = Mxx * Myy - Mxy * Mxy;
double Mxz2 = Mxz * Mxz;
double Myz2 = Myz * Myz;
double A2 = 4 * Cov_xy - 3 * Mz * Mz - Mzz;
double A1 = Mzz * Mz + 4 * Cov_xy * Mz - Mxz2 - Myz2 - Mz * Mz * Mz;
double A0 = Mxz2 * Myy + Myz2 * Mxx - Mzz * Cov_xy - 2 * Mxz * Myz * Mxy + Mz * Mz * Cov_xy;
double A22 = A2 + A2;
double epsilon = 1e-12;
double ynew = 1e+20;
int IterMax = 20;
double xnew = 0;
int iterations = 0;
// Newton's method starting at x=0
for (int iter = 1; iter <= IterMax; iter++) {
iterations = iter;
double yold = ynew;
ynew = A0 + xnew * (A1 + xnew * (A2 + 4. * xnew * xnew));
if (Math.abs(ynew) > Math.abs(yold)) {
if (IJ.debugMode) IJ.log("Fit Circle: wrong direction: |ynew| > |yold|");
xnew = 0;
break;
}
double Dy = A1 + xnew * (A22 + 16 * xnew * xnew);
double xold = xnew;
xnew = xold - ynew / Dy;
if (Math.abs((xnew - xold) / xnew) < epsilon) break;
if (iter >= IterMax) {
if (IJ.debugMode) IJ.log("Fit Circle: will not converge");
xnew = 0;
}
if (xnew < 0) {
if (IJ.debugMode) IJ.log("Fit Circle: negative root: x = " + xnew);
xnew = 0;
}
}
if (IJ.debugMode)
IJ.log("Fit Circle: n=" + n + ", xnew=" + IJ.d2s(xnew, 2) + ", iterations=" + iterations);
// calculate the circle parameters
double DET = xnew * xnew - xnew * Mz + Cov_xy;
double CenterX = (Mxz * (Myy - xnew) - Myz * Mxy) / (2 * DET);
double CenterY = (Myz * (Mxx - xnew) - Mxz * Mxy) / (2 * DET);
double radius = Math.sqrt(CenterX * CenterX + CenterY * CenterY + Mz + 2 * xnew);
if (Double.isNaN(radius)) {
IJ.error("Fit Circle", "Points are collinear.");
return;
}
CenterX = CenterX + meanx;
CenterY = CenterY + meany;
imp.killRoi();
IJ.makeOval(
(int) Math.round(CenterX - radius),
(int) Math.round(CenterY - radius),
(int) Math.round(2 * radius),
(int) Math.round(2 * radius));
}