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ImageJ is an open source Java image processing program inspired by NIH Image for the Macintosh.

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package ij.process;
import ij.*;
import ij.gui.*;
import ij.measure.*;
import ij.plugin.filter.Analyzer;
import java.awt.*;

/** Statistics, including the histogram, of a stack. */
public class StackStatistics extends ImageStatistics {
	
	/** Creates a StackStatistics object from a stack, using 256 
		histogram bins and the entire stack pixel value range. */
	public StackStatistics(ImagePlus imp) {
		this(imp, 256, 0.0, imp.getBitDepth()==8||imp.getBitDepth()==24?256.0:0.0);
	}

	/** Creates a StackStatistics object from a stack, using the specified 
		histogram bin count and x-axis range (pixel value tange). */
	public StackStatistics(ImagePlus imp, int nBins, double xMin, double xMax) {
		int bits = imp.getBitDepth();
		stackStatistics = true;
		if ((bits==8||bits==24) && nBins==256 && xMin==0.0 && xMax==256.0)
			sum8BitHistograms(imp);
		else if (bits==16 && nBins==256 && xMin==0.0 && xMax==0.0 && !imp.getCalibration().calibrated())
			sum16BitHistograms(imp);
		else
			doCalculations(imp, nBins, xMin, xMax);
	}

    void doCalculations(ImagePlus imp,  int bins, double histogramMin, double histogramMax) {
       ImageProcessor ip = imp.getProcessor();
		boolean limitToThreshold = (Analyzer.getMeasurements()&LIMIT)!=0;
		double minThreshold = -Float.MAX_VALUE;
		double maxThreshold = Float.MAX_VALUE;
        Calibration cal = imp.getCalibration();
		if (limitToThreshold && ip.getMinThreshold()!=ImageProcessor.NO_THRESHOLD) {
			minThreshold=cal.getCValue(ip.getMinThreshold());
			maxThreshold=cal.getCValue(ip.getMaxThreshold());
		}
    	nBins = bins;
    	histMin = histogramMin;
    	histMax = histogramMax;
        ImageStack stack = imp.getStack();
        int size = stack.size();
        ip.setRoi(imp.getRoi());
        byte[] mask = ip.getMaskArray();
        float[] cTable = imp.getCalibration().getCTable();
        longHistogram = new long[nBins];
        double v;
        double sum = 0;
        double sum2 = 0;
        int width, height;
        int rx, ry, rw, rh;
        double pw, ph;
        
        width = ip.getWidth();
        height = ip.getHeight();
        Rectangle roi = ip.getRoi();
        if (roi != null) {
            rx = roi.x;
            ry = roi.y;
            rw = roi.width;
            rh = roi.height;
        } else {
            rx = 0;
            ry = 0;
            rw = width;
            rh = height;
        }
        
        pw = 1.0;
        ph = 1.0;
        roiX = rx*pw;
        roiY = ry*ph;
        roiWidth = rw*pw;
        roiHeight = rh*ph;
        boolean fixedRange = histMin!=0 || histMax!=0.0;
        
        // calculate min and max
		double roiMin = Double.MAX_VALUE;
		double roiMax = -Double.MAX_VALUE;
		for (int slice=1; slice<=size; slice++) {
			IJ.showStatus("Calculating stack histogram...");
			IJ.showProgress(slice/2, size);
			ip = stack.getProcessor(slice);
			//ip.setCalibrationTable(cTable);
			for (int y=ry, my=0; y<(ry+rh); y++, my++) {
				int i = y * width + rx;
				int mi = my * rw;
				for (int x=rx; x<(rx+rw); x++) {
					if (mask==null || mask[mi++]!=0) {
						v = ip.getPixelValue(x,y);
						if (v>=minThreshold && v<=maxThreshold) {
							if (vroiMax)
								roiMax = v;
						}
					}
					i++;
				}
			}
		 }
		min = roiMin;
		max = roiMax;
		if (fixedRange) {
			if (minhistMax) max = histMax;
		} else {
			histMin = min; 
			histMax =  max;
		}
       
        // Generate histogram
        double scale = nBins/( histMax-histMin);
        pixelCount = 0;
        int index;
        boolean first = true;
        for (int slice=1; slice<=size; slice++) {
            IJ.showProgress(size/2+slice/2, size);
            ip = stack.getProcessor(slice);
            ip.setCalibrationTable(cTable);
            for (int y=ry, my=0; y<(ry+rh); y++, my++) {
                int i = y * width + rx;
                int mi = my * rw;
                for (int x=rx; x<(rx+rw); x++) {
                    if (mask==null || mask[mi++]!=0) {
                        v = ip.getPixelValue(x,y);
						if (v>=minThreshold && v<=maxThreshold && v>=histMin && v<=histMax) {
							longPixelCount++;
							sum += v;
							sum2 += v*v;
							index = (int)(scale*(v-histMin));
							if (index>=nBins)
								index = nBins-1;
							longHistogram[index]++;
						}
                    }
                    i++;
                }
            }
        }
        pixelCount = (int)longPixelCount;
        area = longPixelCount*pw*ph;
        mean = sum/longPixelCount;
        calculateStdDev(longPixelCount, sum, sum2);
        histMin = cal.getRawValue(histMin); 
        histMax =  cal.getRawValue(histMax);
        binSize = (histMax-histMin)/nBins;
        int bits = imp.getBitDepth();
        if (histMin==0.0 && histMax==256.0 && (bits==8||bits==24))
        	histMax = 255.0;
        dmode = getMode(cal);
		copyHistogram(nBins);
		median = getMedian(longHistogram, (int)minThreshold, (int)maxThreshold, cal);
        IJ.showStatus("");
        IJ.showProgress(1.0);
    }
    
	void sum8BitHistograms(ImagePlus imp) {
		Calibration cal = imp.getCalibration();
		boolean limitToThreshold = (Analyzer.getMeasurements()&LIMIT)!=0;
		int minThreshold = 0;
		int maxThreshold = 255;
		ImageProcessor ip = imp.getProcessor();
		if (limitToThreshold && ip.getMinThreshold()!=ImageProcessor.NO_THRESHOLD) {
			minThreshold = (int)ip.getMinThreshold();
			maxThreshold = (int)ip.getMaxThreshold();
		}
		ImageStack stack = imp.getStack();
		Roi roi = imp.getRoi();
		longHistogram = new long[256];
		int n = stack.size();
		for (int slice=1; slice<=n; slice++) {
			IJ.showProgress(slice, n);
			ip = stack.getProcessor(slice);
			if (roi!=null) ip.setRoi(roi);
			int[] hist = ip.getHistogram();
			for (int i=0; i<256; i++)
				longHistogram[i] += hist[i];
		}
		pw=1.0; ph=1.0;
		getRawStatistics(longHistogram, minThreshold, maxThreshold);
		getRawMinAndMax(longHistogram, minThreshold, maxThreshold);
		copyHistogram(256);
		median = getMedian(longHistogram, minThreshold, maxThreshold, cal);
		IJ.showStatus("");
		IJ.showProgress(1.0);
	}
	
	private void copyHistogram(int nbins) {
		histogram = new int[nbins];
		for (int i=0; ilongMaxCount) {
				longMaxCount = count;
				mode = i;
			}
		}
		maxCount = (int)longMaxCount;
		pixelCount = (int)longPixelCount;
		area = longPixelCount*pw*ph;
		mean = sum/longPixelCount;
		umean = mean;
		dmode = mode;
		calculateStdDev(longPixelCount, sum, sum2);
		histMin = 0.0;
		histMax = 255.0;
	}

	void getRawMinAndMax(long[] histogram, int minThreshold, int maxThreshold) {
		int min = minThreshold;
		while ((histogram[min]==0L) && (min<255))
			min++;
		this.min = min;
		int max = maxThreshold;
		while ((histogram[max]==0L) && (max>0))
			max--;
		this.max = max;
	}

	void sum16BitHistograms(ImagePlus imp) {
		Calibration cal = imp.getCalibration();
		boolean limitToThreshold = (Analyzer.getMeasurements()&LIMIT)!=0;
		int minThreshold = 0;
		int maxThreshold = 65535;
		ImageProcessor ip = imp.getProcessor();
		if (limitToThreshold && ip.getMinThreshold()!=ImageProcessor.NO_THRESHOLD) {
			minThreshold = (int)ip.getMinThreshold();
			maxThreshold = (int)ip.getMaxThreshold();
		}
		ImageStack stack = imp.getStack();
		Roi roi = imp.getRoi();
		long[] hist16 = new long[65536];
		int n = stack.size();
		for (int slice=1; slice<=n; slice++) {
			IJ.showProgress(slice, n);
			IJ.showStatus(slice+"/"+n);
			ip = stack.getProcessor(slice);
			if (roi!=null) ip.setRoi(roi);
			int[] hist = ip.getHistogram();
			for (int i=0; i<65536; i++)
				hist16[i] += hist[i];
		}
		pw=1.0; ph=1.0;
		getRaw16BitMinAndMax(hist16, minThreshold, maxThreshold);
		get16BitStatistics(hist16, (int)min, (int)max);
		median = getMedian(hist16, minThreshold, maxThreshold, cal);
		histogram16 = new int[65536];
		for (int i=0; i<65536; i++) {
			long count = hist16[i];
			if (count<=Integer.MAX_VALUE)
				histogram16[i] = (int)count;
			else
				histogram16[i] = Integer.MAX_VALUE;
		}
		IJ.showStatus("");
		IJ.showProgress(1.0);
	}
	
	void getRaw16BitMinAndMax(long[] hist, int minThreshold, int maxThreshold) {
		int min = minThreshold;
		while ((hist[min]==0) && (min<65535))
			min++;
		this.min = min;
		int max = maxThreshold;
		while ((hist[max]==0) && (max>0))
			max--;
		this.max = max;
	}

	void get16BitStatistics(long[] hist, int min, int max) {
		long count;
		double value;
		double sum = 0.0;
		double sum2 = 0.0;
		nBins = 256;
		histMin = min; 
		histMax = max;
		binSize = (histMax-histMin)/nBins;
		double scale = 1.0/binSize;
		int hMin = (int)histMin;
		longHistogram = new long[nBins]; // 256 bin histogram
		int index;
        maxCount = 0;
		for (int i=min; i<=max; i++) {
			count = hist[i];
			longPixelCount += count;
			value = i;
			sum += value*count;
			sum2 += (value*value)*count;
			index = (int)(scale*(i-hMin));
			if (index>=nBins)
				index = nBins-1;
			longHistogram[index] += count;
		}
		copyHistogram(nBins);
		pixelCount = (int)longPixelCount;
		area = longPixelCount*pw*ph;
		mean = sum/longPixelCount;
		umean = mean;
		dmode = getMode(null);
		calculateStdDev(longPixelCount, sum, sum2);
	}

   double getMode(Calibration cal) {
        long count;
        long longMaxCount = 0L;
        for (int i=0; ilongMaxCount) {
                longMaxCount = count;
                mode = i;
            }
        }
		if (longMaxCount<=Integer.MAX_VALUE)
			maxCount = (int)longMaxCount;
		else
			maxCount = Integer.MAX_VALUE;
        double tmode = histMin+mode*binSize;
        if (cal!=null) tmode = cal.getCValue(tmode);
        return tmode;
    }
    
    double getMedian(long[] hist, int first, int last, Calibration cal) {
		//ij.IJ.log("getMedian: "+first+"  "+last+"  "+hist.length+"  "+pixelCount);
		if (pixelCount==0 || first<0 || last>hist.length)
			return Double.NaN;
		double sum = 0;
		int i = first-1;
		double halfCount = pixelCount/2.0;
		do {
			sum += hist[++i];
		} while (sum<=halfCount && i




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