Examples with Frequency org.apache.commons.math3.stat.Frequency used on opensource projects

Example 6 with Frequency

use of org.apache.commons.math3.stat.Frequency in project narchy by automenta.

the class RouletteTest method testDecideRouletteFlat.

@Test
public void testDecideRouletteFlat() {
    XorShift128PlusRandom rng = new XorShift128PlusRandom(1);
    int uniques = 4;
    int samples = 100;
    Frequency f = new Frequency();
    for (int i = 0; i < samples; i++) f.addValue(Roulette.decideRoulette(uniques, (k) -> 0.5f, rng));
    // System.out.println(f);
    assertEquals(f.getUniqueCount(), uniques);
    float total = f.getSumFreq();
    for (int i = 0; i < uniques; i++) assertEquals(f.getCount(i) / total, 1f / uniques, 1f / (4 * uniques));
}

Example 7 with Frequency

use of org.apache.commons.math3.stat.Frequency in project narchy by automenta.

the class BaggieTest method testSampling.

@Test
public void testSampling() {
    int cap = 8;
    Baggie<String> s = new Baggie(cap);
    for (int i = 0; i < cap; i++) {
        s.put("x" + i, i / ((float) cap));
    }
    String t = Joiner.on(",").join(s.toList());
    assertEquals("x7=0.87498856,x6=0.7500076,x5=0.6249962,x4=0.50001526,x3=0.3750038,x2=0.24999237,x1=0.12501144,x0=0.0", t);
    Random rng = new XorShift128PlusRandom(1);
    Frequency f = new Frequency();
    final int[] num = { cap * 100 };
    s.sample(rng, (x) -> {
        f.addValue(x.get());
        return num[0]-- > 0;
    });
    System.out.println(f);
    assertTrue(f.getCount("x" + (cap - 1)) > f.getCount("x0"));
    {
        // change all to a new value (0.5)
        final int[] resetNum = { cap * 100 };
        // TODO use s.commit()
        s.sample(rng, (x) -> {
            x.set(0.5f);
            return resetNum[0]-- > 0;
        });
        s.forEach((x, p) -> {
            assertEquals(0.5f, p, 0.001f);
            return true;
        });
        // effectively cleared
        assertEquals(cap, s.size());
        assertEquals(0.5f, s.priMax(), 0.001f);
        assertEquals(0.5f, s.priMin(), 0.001f);
    }
    {
        // remove everything
        final int[] remNum = { 0 };
        s.sample(rng, (x) -> {
            // delete it
            x.set(Float.NaN);
            remNum[0]++;
            return true;
        });
        // all removed during sampling
        assertEquals(cap, remNum[0]);
        // effectively cleared
        assertEquals(0, s.size());
        assertEquals(Float.NaN, s.priMax(), 0.001f);
        assertEquals(Float.NaN, s.priMin(), 0.001f);
    }
}

Example 8 with Frequency

use of org.apache.commons.math3.stat.Frequency in project GDSC-SMLM by aherbert.

the class PCPALMMolecules method calculateAveragePrecision.

/**
	 * Calculate the average precision by fitting a skewed Gaussian to the histogram of the precision distribution.
	 * <p>
	 * A simple mean and SD of the histogram is computed. If the mean of the Skewed Gaussian does not fit within 3 SDs
	 * of the simple mean then the simple mean is returned.
	 * 
	 * @param molecules
	 * @param title
	 *            the plot title (null if no plot should be displayed)
	 * @param histogramBins
	 * @param logFitParameters
	 *            Record the fit parameters to the ImageJ log
	 * @param removeOutliers
	 *            The distribution is created using all values within 1.5x the inter-quartile range (IQR) of the data
	 * @return The average precision
	 */
public double calculateAveragePrecision(ArrayList<Molecule> molecules, String title, int histogramBins, boolean logFitParameters, boolean removeOutliers) {
    // Plot histogram of the precision
    float[] data = new float[molecules.size()];
    DescriptiveStatistics stats = new DescriptiveStatistics();
    double yMin = Double.NEGATIVE_INFINITY, yMax = 0;
    for (int i = 0; i < data.length; i++) {
        data[i] = (float) molecules.get(i).precision;
        stats.addValue(data[i]);
    }
    // Set the min and max y-values using 1.5 x IQR 
    if (removeOutliers) {
        double lower = stats.getPercentile(25);
        double upper = stats.getPercentile(75);
        if (Double.isNaN(lower) || Double.isNaN(upper)) {
            if (logFitParameters)
                Utils.log("Error computing IQR: %f - %f", lower, upper);
        } else {
            double iqr = upper - lower;
            yMin = FastMath.max(lower - iqr, stats.getMin());
            yMax = FastMath.min(upper + iqr, stats.getMax());
            if (logFitParameters)
                Utils.log("  Data range: %f - %f. Plotting 1.5x IQR: %f - %f", stats.getMin(), stats.getMax(), yMin, yMax);
        }
    }
    if (yMin == Double.NEGATIVE_INFINITY) {
        yMin = stats.getMin();
        yMax = stats.getMax();
        if (logFitParameters)
            Utils.log("  Data range: %f - %f", yMin, yMax);
    }
    float[][] hist = Utils.calcHistogram(data, yMin, yMax, histogramBins);
    Plot2 plot = null;
    if (title != null) {
        plot = new Plot2(title, "Precision", "Frequency");
        float[] xValues = hist[0];
        float[] yValues = hist[1];
        if (xValues.length > 0) {
            double xPadding = 0.05 * (xValues[xValues.length - 1] - xValues[0]);
            plot.setLimits(xValues[0] - xPadding, xValues[xValues.length - 1] + xPadding, 0, Maths.max(yValues) * 1.05);
        }
        plot.addPoints(xValues, yValues, Plot2.BAR);
        Utils.display(title, plot);
    }
    // Extract non-zero data
    float[] x = Arrays.copyOf(hist[0], hist[0].length);
    float[] y = hist[1];
    int count = 0;
    float dx = (x[1] - x[0]) * 0.5f;
    for (int i = 0; i < y.length; i++) if (y[i] > 0) {
        x[count] = x[i] + dx;
        y[count] = y[i];
        count++;
    }
    x = Arrays.copyOf(x, count);
    y = Arrays.copyOf(y, count);
    // Sense check to fitted data. Get mean and SD of histogram
    double[] stats2 = Utils.getHistogramStatistics(x, y);
    double mean = stats2[0];
    if (logFitParameters)
        log("  Initial Statistics: %f +/- %f", stats2[0], stats2[1]);
    // Standard Gaussian fit
    double[] parameters = fitGaussian(x, y);
    if (parameters == null) {
        log("  Failed to fit initial Gaussian");
        return mean;
    }
    double newMean = parameters[1];
    double error = Math.abs(stats2[0] - newMean) / stats2[1];
    if (error > 3) {
        log("  Failed to fit Gaussian: %f standard deviations from histogram mean", error);
        return mean;
    }
    if (newMean < yMin || newMean > yMax) {
        log("  Failed to fit Gaussian: %f outside data range %f - %f", newMean, yMin, yMax);
        return mean;
    }
    mean = newMean;
    if (logFitParameters)
        log("  Initial Gaussian: %f @ %f +/- %f", parameters[0], parameters[1], parameters[2]);
    double[] initialSolution = new double[] { parameters[0], parameters[1], parameters[2], -1 };
    // Fit to a skewed Gaussian (or appropriate function)
    double[] skewParameters = fitSkewGaussian(x, y, initialSolution);
    if (skewParameters == null) {
        log("  Failed to fit Skewed Gaussian");
        return mean;
    }
    SkewNormalFunction sn = new SkewNormalFunction(skewParameters);
    if (logFitParameters)
        log("  Skewed Gaussian: %f @ %f +/- %f (a = %f) => %f +/- %f", skewParameters[0], skewParameters[1], skewParameters[2], skewParameters[3], sn.getMean(), Math.sqrt(sn.getVariance()));
    newMean = sn.getMean();
    error = Math.abs(stats2[0] - newMean) / stats2[1];
    if (error > 3) {
        log("  Failed to fit Skewed Gaussian: %f standard deviations from histogram mean", error);
        return mean;
    }
    if (newMean < yMin || newMean > yMax) {
        log("  Failed to fit Skewed Gaussian: %f outside data range %f - %f", newMean, yMin, yMax);
        return mean;
    }
    // Use original histogram x-axis to maintain all the bins
    if (plot != null) {
        x = hist[0];
        for (int i = 0; i < y.length; i++) x[i] += dx;
        plot.setColor(Color.red);
        addToPlot(plot, x, skewParameters, Plot2.LINE);
        plot.setColor(Color.black);
        Utils.display(title, plot);
    }
    // Return the average precision from the fitted curve
    return newMean;
}

Example 9 with Frequency

use of org.apache.commons.math3.stat.Frequency in project GDSC-SMLM by aherbert.

the class FIRE method runQEstimation.

private void runQEstimation() {
    IJ.showStatus(TITLE + " ...");
    if (!showQEstimationInputDialog())
        return;
    MemoryPeakResults results = ResultsManager.loadInputResults(inputOption, false);
    if (results == null || results.size() == 0) {
        IJ.error(TITLE, "No results could be loaded");
        return;
    }
    if (results.getCalibration() == null) {
        IJ.error(TITLE, "The results are not calibrated");
        return;
    }
    results = cropToRoi(results);
    if (results.size() < 2) {
        IJ.error(TITLE, "No results within the crop region");
        return;
    }
    initialise(results, null);
    // We need localisation precision.
    // Build a histogram of the localisation precision.
    // Get the initial mean and SD and plot as a Gaussian.
    PrecisionHistogram histogram = calculatePrecisionHistogram();
    if (histogram == null) {
        IJ.error(TITLE, "No localisation precision available.\n \nPlease choose " + PrecisionMethod.FIXED + " and enter a precision mean and SD.");
        return;
    }
    StoredDataStatistics precision = histogram.precision;
    //String name = results.getName();
    double fourierImageScale = SCALE_VALUES[imageScaleIndex];
    int imageSize = IMAGE_SIZE_VALUES[imageSizeIndex];
    // Create the image and compute the numerator of FRC. 
    // Do not use the signal so results.size() is the number of localisations.
    IJ.showStatus("Computing FRC curve ...");
    FireImages images = createImages(fourierImageScale, imageSize, false);
    // DEBUGGING - Save the two images to disk. Load the images into the Matlab 
    // code that calculates the Q-estimation and make this plugin match the functionality.
    //IJ.save(new ImagePlus("i1", images.ip1), "/scratch/i1.tif");
    //IJ.save(new ImagePlus("i2", images.ip2), "/scratch/i2.tif");
    FRC frc = new FRC();
    frc.progress = progress;
    frc.setFourierMethod(fourierMethod);
    frc.setSamplingMethod(samplingMethod);
    frc.setPerimeterSamplingFactor(perimeterSamplingFactor);
    FRCCurve frcCurve = frc.calculateFrcCurve(images.ip1, images.ip2, images.nmPerPixel);
    if (frcCurve == null) {
        IJ.error(TITLE, "Failed to compute FRC curve");
        return;
    }
    IJ.showStatus("Running Q-estimation ...");
    // Note:
    // The method implemented here is based on Matlab code provided by Bernd Rieger.
    // The idea is to compute the spurious correlation component of the FRC Numerator
    // using an initial estimate of distribution of the localisation precision (assumed 
    // to be Gaussian). This component is the contribution of repeat localisations of 
    // the same molecule to the numerator and is modelled as an exponential decay
    // (exp_decay). The component is scaled by the Q-value which
    // is the average number of times a molecule is seen in addition to the first time.
    // At large spatial frequencies the scaled component should match the numerator,
    // i.e. at high resolution (low FIRE number) the numerator is made up of repeat 
    // localisations of the same molecule and not actual structure in the image.
    // The best fit is where the numerator equals the scaled component, i.e. num / (q*exp_decay) == 1.
    // The FRC Numerator is plotted and Q can be determined by
    // adjusting Q and the precision mean and SD to maximise the cost function.
    // This can be done interactively by the user with the effect on the FRC curve
    // dynamically updated and displayed.
    // Compute the scaled FRC numerator
    double qNorm = (1 / frcCurve.mean1 + 1 / frcCurve.mean2);
    double[] frcnum = new double[frcCurve.getSize()];
    for (int i = 0; i < frcnum.length; i++) {
        FRCCurveResult r = frcCurve.get(i);
        frcnum[i] = qNorm * r.getNumerator() / r.getNumberOfSamples();
    }
    // Compute the spatial frequency and the region for curve fitting
    double[] q = FRC.computeQ(frcCurve, false);
    int low = 0, high = q.length;
    while (high > 0 && q[high - 1] > maxQ) high--;
    while (low < q.length && q[low] < minQ) low++;
    // Require we fit at least 10% of the curve
    if (high - low < q.length * 0.1) {
        IJ.error(TITLE, "Not enough points for Q estimation");
        return;
    }
    // Obtain initial estimate of Q plateau height and decay.
    // This can be done by fitting the precision histogram and then fixing the mean and sigma.
    // Or it can be done by allowing the precision to be sampled and the mean and sigma
    // become parameters for fitting.
    // Check if we can sample precision values
    boolean sampleDecay = precision != null && FIRE.sampleDecay;
    double[] exp_decay;
    if (sampleDecay) {
        // Random sample of precision values from the distribution is used to 
        // construct the decay curve
        int[] sample = Random.sample(10000, precision.getN(), new Well19937c());
        final double four_pi2 = 4 * Math.PI * Math.PI;
        double[] pre = new double[q.length];
        for (int i = 1; i < q.length; i++) pre[i] = -four_pi2 * q[i] * q[i];
        // Sample
        final int n = sample.length;
        double[] hq = new double[n];
        for (int j = 0; j < n; j++) {
            // Scale to SR pixels
            double s2 = precision.getValue(sample[j]) / images.nmPerPixel;
            s2 *= s2;
            for (int i = 1; i < q.length; i++) hq[i] += FastMath.exp(pre[i] * s2);
        }
        for (int i = 1; i < q.length; i++) hq[i] /= n;
        exp_decay = new double[q.length];
        exp_decay[0] = 1;
        for (int i = 1; i < q.length; i++) {
            double sinc_q = sinc(Math.PI * q[i]);
            exp_decay[i] = sinc_q * sinc_q * hq[i];
        }
    } else {
        // Note: The sigma mean and std should be in the units of super-resolution 
        // pixels so scale to SR pixels
        exp_decay = computeExpDecay(histogram.mean / images.nmPerPixel, histogram.sigma / images.nmPerPixel, q);
    }
    // Smoothing
    double[] smooth;
    if (loessSmoothing) {
        // Note: This computes the log then smooths it 
        double bandwidth = 0.1;
        int robustness = 0;
        double[] l = new double[exp_decay.length];
        for (int i = 0; i < l.length; i++) {
            // Original Matlab code computes the log for each array.
            // This is equivalent to a single log on the fraction of the two.
            // Perhaps the two log method is more numerically stable.
            //l[i] = Math.log(Math.abs(frcnum[i])) - Math.log(exp_decay[i]);
            l[i] = Math.log(Math.abs(frcnum[i] / exp_decay[i]));
        }
        try {
            LoessInterpolator loess = new LoessInterpolator(bandwidth, robustness);
            smooth = loess.smooth(q, l);
        } catch (Exception e) {
            IJ.error(TITLE, "LOESS smoothing failed");
            return;
        }
    } else {
        // Note: This smooths the curve before computing the log 
        double[] norm = new double[exp_decay.length];
        for (int i = 0; i < norm.length; i++) {
            norm[i] = frcnum[i] / exp_decay[i];
        }
        // Median window of 5 == radius of 2
        MedianWindow mw = new MedianWindow(norm, 2);
        smooth = new double[exp_decay.length];
        for (int i = 0; i < norm.length; i++) {
            smooth[i] = Math.log(Math.abs(mw.getMedian()));
            mw.increment();
        }
    }
    // Fit with quadratic to find the initial guess.
    // Note: example Matlab code frc_Qcorrection7.m identifies regions of the 
    // smoothed log curve with low derivative and only fits those. The fit is 
    // used for the final estimate. Fitting a subset with low derivative is not 
    // implemented here since the initial estimate is subsequently optimised 
    // to maximise a cost function. 
    Quadratic curve = new Quadratic();
    SimpleCurveFitter fit = SimpleCurveFitter.create(curve, new double[2]);
    WeightedObservedPoints points = new WeightedObservedPoints();
    for (int i = low; i < high; i++) points.add(q[i], smooth[i]);
    double[] estimate = fit.fit(points.toList());
    double qValue = FastMath.exp(estimate[0]);
    //System.out.printf("Initial q-estimate = %s => %.3f\n", Arrays.toString(estimate), qValue);
    // This could be made an option. Just use for debugging
    boolean debug = false;
    if (debug) {
        // Plot the initial fit and the fit curve
        double[] qScaled = FRC.computeQ(frcCurve, true);
        double[] line = new double[q.length];
        for (int i = 0; i < q.length; i++) line[i] = curve.value(q[i], estimate);
        String title = TITLE + " Initial fit";
        Plot2 plot = new Plot2(title, "Spatial Frequency (nm^-1)", "FRC Numerator");
        String label = String.format("Q = %.3f", qValue);
        plot.addPoints(qScaled, smooth, Plot.LINE);
        plot.setColor(Color.red);
        plot.addPoints(qScaled, line, Plot.LINE);
        plot.setColor(Color.black);
        plot.addLabel(0, 0, label);
        Utils.display(title, plot, Utils.NO_TO_FRONT);
    }
    if (fitPrecision) {
        // Q - Should this be optional?
        if (sampleDecay) {
            // If a sample of the precision was used to construct the data for the initial fit 
            // then update the estimate using the fit result since it will be a better start point. 
            histogram.sigma = precision.getStandardDeviation();
            // Normalise sum-of-squares to the SR pixel size
            double meanSumOfSquares = (precision.getSumOfSquares() / (images.nmPerPixel * images.nmPerPixel)) / precision.getN();
            histogram.mean = images.nmPerPixel * Math.sqrt(meanSumOfSquares - estimate[1] / (4 * Math.PI * Math.PI));
        }
        // Do a multivariate fit ...
        SimplexOptimizer opt = new SimplexOptimizer(1e-6, 1e-10);
        PointValuePair p = null;
        MultiPlateauness f = new MultiPlateauness(frcnum, q, low, high);
        double[] initial = new double[] { histogram.mean / images.nmPerPixel, histogram.sigma / images.nmPerPixel, qValue };
        p = findMin(p, opt, f, scale(initial, 0.1));
        p = findMin(p, opt, f, scale(initial, 0.5));
        p = findMin(p, opt, f, initial);
        p = findMin(p, opt, f, scale(initial, 2));
        p = findMin(p, opt, f, scale(initial, 10));
        if (p != null) {
            double[] point = p.getPointRef();
            histogram.mean = point[0] * images.nmPerPixel;
            histogram.sigma = point[1] * images.nmPerPixel;
            qValue = point[2];
        }
    } else {
        // If so then this should be optional.
        if (sampleDecay) {
            if (precisionMethod != PrecisionMethod.FIXED) {
                histogram.sigma = precision.getStandardDeviation();
                // Normalise sum-of-squares to the SR pixel size
                double meanSumOfSquares = (precision.getSumOfSquares() / (images.nmPerPixel * images.nmPerPixel)) / precision.getN();
                histogram.mean = images.nmPerPixel * Math.sqrt(meanSumOfSquares - estimate[1] / (4 * Math.PI * Math.PI));
            }
            exp_decay = computeExpDecay(histogram.mean / images.nmPerPixel, histogram.sigma / images.nmPerPixel, q);
        }
        // Estimate spurious component by promoting plateauness.
        // The Matlab code used random initial points for a Simplex optimiser.
        // A Brent line search should be pretty deterministic so do simple repeats.
        // However it will proceed downhill so if the initial point is wrong then 
        // it will find a sub-optimal result.
        UnivariateOptimizer o = new BrentOptimizer(1e-3, 1e-6);
        Plateauness f = new Plateauness(frcnum, exp_decay, low, high);
        UnivariatePointValuePair p = null;
        p = findMin(p, o, f, qValue, 0.1);
        p = findMin(p, o, f, qValue, 0.2);
        p = findMin(p, o, f, qValue, 0.333);
        p = findMin(p, o, f, qValue, 0.5);
        // Do some Simplex repeats as well
        SimplexOptimizer opt = new SimplexOptimizer(1e-6, 1e-10);
        p = findMin(p, opt, f, qValue * 0.1);
        p = findMin(p, opt, f, qValue * 0.5);
        p = findMin(p, opt, f, qValue);
        p = findMin(p, opt, f, qValue * 2);
        p = findMin(p, opt, f, qValue * 10);
        if (p != null)
            qValue = p.getPoint();
    }
    QPlot qplot = new QPlot(frcCurve, qValue, low, high);
    // Interactive dialog to estimate Q (blinking events per flourophore) using 
    // sliders for the mean and standard deviation of the localisation precision.
    showQEstimationDialog(histogram, qplot, frcCurve, images.nmPerPixel);
    IJ.showStatus(TITLE + " complete");
}

Example 10 with Frequency

use of org.apache.commons.math3.stat.Frequency in project GDSC-SMLM by aherbert.

the class BenchmarkSpotFit method showDoubleHistogram.

private double[] showDoubleHistogram(StoredDataStatistics[][] stats, final int i, WindowOrganiser wo, double[][] matchScores, double nPredicted) {
    String xLabel = filterCriteria[i].name;
    LowerLimit lower = filterCriteria[i].lower;
    UpperLimit upper = filterCriteria[i].upper;
    double[] j = null;
    double[] metric = null;
    double maxJ = 0;
    if (i <= FILTER_PRECISION && (showFilterScoreHistograms || upper.requiresJaccard || lower.requiresJaccard)) {
        // Jaccard score verses the range of the metric
        Arrays.sort(matchScores, new Comparator<double[]>() {

            public int compare(double[] o1, double[] o2) {
                if (o1[i] < o2[i])
                    return -1;
                if (o1[i] > o2[i])
                    return 1;
                return 0;
            }
        });
        final int scoreIndex = FILTER_PRECISION + 1;
        int n = results.size();
        double tp = 0;
        double fp = 0;
        j = new double[matchScores.length + 1];
        metric = new double[j.length];
        for (int k = 0; k < matchScores.length; k++) {
            final double score = matchScores[k][scoreIndex];
            tp += score;
            fp += (1 - score);
            j[k + 1] = tp / (fp + n);
            metric[k + 1] = matchScores[k][i];
        }
        metric[0] = metric[1];
        maxJ = Maths.max(j);
        if (showFilterScoreHistograms) {
            String title = TITLE + " Jaccard " + xLabel;
            Plot plot = new Plot(title, xLabel, "Jaccard", metric, j);
            // Remove outliers
            double[] limitsx = Maths.limits(metric);
            Percentile p = new Percentile();
            double l = p.evaluate(metric, 25);
            double u = p.evaluate(metric, 75);
            double iqr = 1.5 * (u - l);
            limitsx[1] = Math.min(limitsx[1], u + iqr);
            plot.setLimits(limitsx[0], limitsx[1], 0, Maths.max(j));
            PlotWindow pw = Utils.display(title, plot);
            if (Utils.isNewWindow())
                wo.add(pw);
        }
    }
    // [0] is all
    // [1] is matches
    // [2] is no match
    StoredDataStatistics s1 = stats[0][i];
    StoredDataStatistics s2 = stats[1][i];
    StoredDataStatistics s3 = stats[2][i];
    if (s1.getN() == 0)
        return new double[4];
    DescriptiveStatistics d = s1.getStatistics();
    double median = 0;
    Plot2 plot = null;
    String title = null;
    if (showFilterScoreHistograms) {
        median = d.getPercentile(50);
        String label = String.format("n = %d. Median = %s nm", s1.getN(), Utils.rounded(median));
        int id = Utils.showHistogram(TITLE, s1, xLabel, filterCriteria[i].minBinWidth, (filterCriteria[i].restrictRange) ? 1 : 0, 0, label);
        if (id == 0) {
            IJ.log("Failed to show the histogram: " + xLabel);
            return new double[4];
        }
        if (Utils.isNewWindow())
            wo.add(id);
        title = WindowManager.getImage(id).getTitle();
        // Reverse engineer the histogram settings
        plot = Utils.plot;
        double[] xValues = Utils.xValues;
        int bins = xValues.length;
        double yMin = xValues[0];
        double binSize = xValues[1] - xValues[0];
        double yMax = xValues[0] + (bins - 1) * binSize;
        if (s2.getN() > 0) {
            double[] values = s2.getValues();
            double[][] hist = Utils.calcHistogram(values, yMin, yMax, bins);
            if (hist[0].length > 0) {
                plot.setColor(Color.red);
                plot.addPoints(hist[0], hist[1], Plot2.BAR);
                Utils.display(title, plot);
            }
        }
        if (s3.getN() > 0) {
            double[] values = s3.getValues();
            double[][] hist = Utils.calcHistogram(values, yMin, yMax, bins);
            if (hist[0].length > 0) {
                plot.setColor(Color.blue);
                plot.addPoints(hist[0], hist[1], Plot2.BAR);
                Utils.display(title, plot);
            }
        }
    }
    // Do cumulative histogram
    double[][] h1 = Maths.cumulativeHistogram(s1.getValues(), true);
    double[][] h2 = Maths.cumulativeHistogram(s2.getValues(), true);
    double[][] h3 = Maths.cumulativeHistogram(s3.getValues(), true);
    if (showFilterScoreHistograms) {
        title = TITLE + " Cumul " + xLabel;
        plot = new Plot2(title, xLabel, "Frequency");
        // Find limits
        double[] xlimit = Maths.limits(h1[0]);
        xlimit = Maths.limits(xlimit, h2[0]);
        xlimit = Maths.limits(xlimit, h3[0]);
        // Restrict using the inter-quartile range 
        if (filterCriteria[i].restrictRange) {
            double q1 = d.getPercentile(25);
            double q2 = d.getPercentile(75);
            double iqr = (q2 - q1) * 2.5;
            xlimit[0] = Maths.max(xlimit[0], median - iqr);
            xlimit[1] = Maths.min(xlimit[1], median + iqr);
        }
        plot.setLimits(xlimit[0], xlimit[1], 0, 1.05);
        plot.addPoints(h1[0], h1[1], Plot.LINE);
        plot.setColor(Color.red);
        plot.addPoints(h2[0], h2[1], Plot.LINE);
        plot.setColor(Color.blue);
        plot.addPoints(h3[0], h3[1], Plot.LINE);
    }
    // Determine the maximum difference between the TP and FP
    double maxx1 = 0;
    double maxx2 = 0;
    double max1 = 0;
    double max2 = 0;
    // We cannot compute the delta histogram, or use percentiles
    if (s2.getN() == 0) {
        upper = UpperLimit.ZERO;
        lower = LowerLimit.ZERO;
    }
    final boolean requireLabel = (showFilterScoreHistograms && filterCriteria[i].requireLabel);
    if (requireLabel || upper.requiresDeltaHistogram() || lower.requiresDeltaHistogram()) {
        if (s2.getN() != 0 && s3.getN() != 0) {
            LinearInterpolator li = new LinearInterpolator();
            PolynomialSplineFunction f1 = li.interpolate(h2[0], h2[1]);
            PolynomialSplineFunction f2 = li.interpolate(h3[0], h3[1]);
            for (double x : h1[0]) {
                if (x < h2[0][0] || x < h3[0][0])
                    continue;
                try {
                    double v1 = f1.value(x);
                    double v2 = f2.value(x);
                    double diff = v2 - v1;
                    if (diff > 0) {
                        if (max1 < diff) {
                            max1 = diff;
                            maxx1 = x;
                        }
                    } else {
                        if (max2 > diff) {
                            max2 = diff;
                            maxx2 = x;
                        }
                    }
                } catch (OutOfRangeException e) {
                    // Because we reached the end
                    break;
                }
            }
        } else {
            // Switch to percentiles if we have no delta histogram
            if (upper.requiresDeltaHistogram())
                upper = UpperLimit.NINETY_NINE_PERCENT;
            if (lower.requiresDeltaHistogram())
                lower = LowerLimit.ONE_PERCENT;
        }
    //			System.out.printf("Bounds %s : %s, pos %s, neg %s, %s\n", xLabel, Utils.rounded(getPercentile(h2, 0.01)),
    //					Utils.rounded(maxx1), Utils.rounded(maxx2), Utils.rounded(getPercentile(h1, 0.99)));
    }
    if (showFilterScoreHistograms) {
        // We use bins=1 on charts where we do not need a label
        if (requireLabel) {
            String label = String.format("Max+ %s @ %s, Max- %s @ %s", Utils.rounded(max1), Utils.rounded(maxx1), Utils.rounded(max2), Utils.rounded(maxx2));
            plot.setColor(Color.black);
            plot.addLabel(0, 0, label);
        }
        PlotWindow pw = Utils.display(title, plot);
        if (Utils.isNewWindow())
            wo.add(pw.getImagePlus().getID());
    }
    // Now compute the bounds using the desired limit
    double l, u;
    switch(lower) {
        case ONE_PERCENT:
            l = getPercentile(h2, 0.01);
            break;
        case MAX_NEGATIVE_CUMUL_DELTA:
            l = maxx2;
            break;
        case ZERO:
            l = 0;
            break;
        case HALF_MAX_JACCARD_VALUE:
            l = getValue(metric, j, maxJ * 0.5);
            break;
        default:
            throw new RuntimeException("Missing lower limit method");
    }
    switch(upper) {
        case MAX_POSITIVE_CUMUL_DELTA:
            u = maxx1;
            break;
        case NINETY_NINE_PERCENT:
            u = getPercentile(h2, 0.99);
            break;
        case NINETY_NINE_NINE_PERCENT:
            u = getPercentile(h2, 0.999);
            break;
        case ZERO:
            u = 0;
            break;
        case MAX_JACCARD2:
            u = getValue(metric, j, maxJ) * 2;
            //System.out.printf("MaxJ = %.4f @ %.3f\n", maxJ, u / 2);
            break;
        default:
            throw new RuntimeException("Missing upper limit method");
    }
    double min = getPercentile(h1, 0);
    double max = getPercentile(h1, 1);
    return new double[] { l, u, min, max };
}