Examples with StoredDataStatistics uk.ac.sussex.gdsc.core.utils.StoredDataStatistics used on opensource projects

Example 21 with StoredDataStatistics

use of uk.ac.sussex.gdsc.core.utils.StoredDataStatistics in project GDSC-SMLM by aherbert.

the class BenchmarkFit method runFit.

private void runFit() {
    // Initialise the answer.
    answer[Gaussian2DFunction.BACKGROUND] = benchmarkParameters.getBackground();
    answer[Gaussian2DFunction.SIGNAL] = benchmarkParameters.getSignal();
    answer[Gaussian2DFunction.X_POSITION] = benchmarkParameters.x;
    answer[Gaussian2DFunction.Y_POSITION] = benchmarkParameters.y;
    answer[Gaussian2DFunction.Z_POSITION] = benchmarkParameters.z;
    answer[Gaussian2DFunction.X_SD] = benchmarkParameters.sd / benchmarkParameters.pixelPitch;
    answer[Gaussian2DFunction.Y_SD] = benchmarkParameters.sd / benchmarkParameters.pixelPitch;
    // Set up the fit region. Always round down since 0.5 is the centre of the pixel.
    final int x = (int) benchmarkParameters.x;
    final int y = (int) benchmarkParameters.y;
    region = new Rectangle(x - regionSize, y - regionSize, 2 * regionSize + 1, 2 * regionSize + 1);
    if (!new Rectangle(0, 0, imp.getWidth(), imp.getHeight()).contains(region)) {
        // Check if it is incorrect by only 1 pixel
        if (region.width <= imp.getWidth() + 1 && region.height <= imp.getHeight() + 1) {
            ImageJUtils.log("Adjusting region %s to fit within image bounds (%dx%d)", region.toString(), imp.getWidth(), imp.getHeight());
            region = new Rectangle(0, 0, imp.getWidth(), imp.getHeight());
        } else {
            IJ.error(TITLE, "Fit region does not fit within the image");
            return;
        }
    }
    // Adjust the centre & account for 0.5 pixel offset during fitting
    answer[Gaussian2DFunction.X_POSITION] -= (region.x + 0.5);
    answer[Gaussian2DFunction.Y_POSITION] -= (region.y + 0.5);
    // Configure for fitting
    fitConfig.setBackgroundFitting(backgroundFitting);
    fitConfig.setNotSignalFitting(!signalFitting);
    fitConfig.setComputeDeviations(false);
    // Create the camera model
    CameraModel cameraModel = fitConfig.getCameraModel();
    // Crop for speed. Reset origin first so the region is within the model
    cameraModel.setOrigin(0, 0);
    cameraModel = cameraModel.crop(region, false);
    final ImageStack stack = imp.getImageStack();
    final int totalFrames = benchmarkParameters.frames;
    // Create a pool of workers
    final int nThreads = Prefs.getThreads();
    final BlockingQueue<Integer> jobs = new ArrayBlockingQueue<>(nThreads * 2);
    final List<Worker> workers = new LinkedList<>();
    final List<Thread> threads = new LinkedList<>();
    final Ticker ticker = ImageJUtils.createTicker(totalFrames, nThreads, "Fitting frames ...");
    for (int i = 0; i < nThreads; i++) {
        final Worker worker = new Worker(jobs, stack, region, fitConfig, cameraModel, ticker);
        final Thread t = new Thread(worker);
        workers.add(worker);
        threads.add(t);
        t.start();
    }
    // Store all the fitting results
    results = new double[totalFrames * startPoints.length][];
    resultsTime = new long[results.length];
    // Fit the frames
    for (int i = 0; i < totalFrames; i++) {
        // Only fit if there were simulated photons
        if (benchmarkParameters.framePhotons[i] > 0) {
            put(jobs, i);
        }
    }
    // Finish all the worker threads by passing in a null job
    for (int i = 0; i < threads.size(); i++) {
        put(jobs, -1);
    }
    // Wait for all to finish
    for (int i = 0; i < threads.size(); i++) {
        try {
            threads.get(i).join();
        } catch (final InterruptedException ex) {
            Thread.currentThread().interrupt();
            throw new ConcurrentRuntimeException(ex);
        }
    }
    threads.clear();
    if (hasOffsetXy()) {
        ImageJUtils.log(TITLE + ": CoM within start offset = %d / %d (%s%%)", comValid.intValue(), totalFrames, MathUtils.rounded((100.0 * comValid.intValue()) / totalFrames));
    }
    ImageJUtils.finished("Collecting results ...");
    // Collect the results
    Statistics[] stats = null;
    for (int i = 0; i < workers.size(); i++) {
        final Statistics[] next = workers.get(i).stats;
        if (stats == null) {
            stats = next;
            continue;
        }
        for (int j = 0; j < next.length; j++) {
            stats[j].add(next[j]);
        }
    }
    workers.clear();
    Objects.requireNonNull(stats, "No statistics were computed");
    // Show a table of the results
    summariseResults(stats, cameraModel);
    // Optionally show histograms
    if (showHistograms) {
        IJ.showStatus("Calculating histograms ...");
        final WindowOrganiser windowOrganiser = new WindowOrganiser();
        final double[] convert = getConversionFactors();
        final HistogramPlotBuilder builder = new HistogramPlotBuilder(TITLE).setNumberOfBins(histogramBins);
        for (int i = 0; i < NAMES.length; i++) {
            if (displayHistograms[i] && convert[i] != 0) {
                // We will have to convert the values...
                final double[] tmp = ((StoredDataStatistics) stats[i]).getValues();
                for (int j = 0; j < tmp.length; j++) {
                    tmp[j] *= convert[i];
                }
                final StoredDataStatistics tmpStats = StoredDataStatistics.create(tmp);
                builder.setData(tmpStats).setName(NAMES[i]).setPlotLabel(String.format("%s +/- %s", MathUtils.rounded(tmpStats.getMean()), MathUtils.rounded(tmpStats.getStandardDeviation()))).show(windowOrganiser);
            }
        }
        windowOrganiser.tile();
    }
    if (saveRawData) {
        final String dir = ImageJUtils.getDirectory("Data_directory", rawDataDirectory);
        if (dir != null) {
            saveData(stats, dir);
        }
    }
    IJ.showStatus("");
}

Example 22 with StoredDataStatistics

use of uk.ac.sussex.gdsc.core.utils.StoredDataStatistics in project GDSC-SMLM by aherbert.

the class CreateData method createPhotonDistribution.

/**
 * Creates the photon distribution.
 *
 * @return A photon distribution loaded from a file of floating-point values with the specified
 *         population mean.
 */
private RealDistribution createPhotonDistribution() {
    if (PHOTON_DISTRIBUTION[PHOTON_CUSTOM].equals(settings.getPhotonDistribution())) {
        // Get the distribution file
        final String filename = ImageJUtils.getFilename("Photon_distribution", settings.getPhotonDistributionFile());
        if (filename != null) {
            settings.setPhotonDistributionFile(filename);
            try (BufferedReader in = new BufferedReader(new UnicodeReader(new FileInputStream(new File(settings.getPhotonDistributionFile())), null))) {
                final StoredDataStatistics stats = new StoredDataStatistics();
                String str = in.readLine();
                double val = 0.0d;
                while (str != null) {
                    val = Double.parseDouble(str);
                    stats.add(val);
                    str = in.readLine();
                }
                if (stats.getSum() > 0) {
                    // Update the statistics to the desired mean.
                    final double scale = settings.getPhotonsPerSecond() / stats.getMean();
                    final double[] values = stats.getValues();
                    for (int i = 0; i < values.length; i++) {
                        values[i] *= scale;
                    }
                    // TODO - Investigate the limits of this distribution.
                    // How far above and below the input data will values be generated.
                    // Create the distribution using the recommended number of bins
                    final int binCount = stats.getN() / 10;
                    final EmpiricalDistribution dist = new EmpiricalDistribution(binCount, new RandomGeneratorAdapter(createRandomGenerator()));
                    dist.load(values);
                    return dist;
                }
            } catch (final IOException | NullArgumentException | NumberFormatException ex) {
            // Ignore
            }
        }
        ImageJUtils.log("Failed to load custom photon distribution from file: %s. Default to fixed.", settings.getPhotonDistributionFile());
    } else if (PHOTON_DISTRIBUTION[PHOTON_UNIFORM].equals(settings.getPhotonDistribution())) {
        if (settings.getPhotonsPerSecond() < settings.getPhotonsPerSecondMaximum()) {
            return new UniformRealDistribution(new RandomGeneratorAdapter(createRandomGenerator()), settings.getPhotonsPerSecond(), settings.getPhotonsPerSecondMaximum());
        }
    } else if (PHOTON_DISTRIBUTION[PHOTON_GAMMA].equals(settings.getPhotonDistribution())) {
        final double scaleParameter = settings.getPhotonsPerSecond() / settings.getPhotonShape();
        return new GammaDistribution(new RandomGeneratorAdapter(createRandomGenerator()), settings.getPhotonShape(), scaleParameter, ExponentialDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    } else if (PHOTON_DISTRIBUTION[PHOTON_CORRELATED].equals(settings.getPhotonDistribution())) {
        // No distribution required
        return null;
    }
    settings.setPhotonDistribution(PHOTON_DISTRIBUTION[PHOTON_FIXED]);
    return null;
}

Example 23 with StoredDataStatistics

use of uk.ac.sussex.gdsc.core.utils.StoredDataStatistics in project GDSC-SMLM by aherbert.

the class BaseFunctionSolverTest method canFitSingleGaussianBetter.

void canFitSingleGaussianBetter(RandomSeed seed, FunctionSolver solver, boolean applyBounds, FunctionSolver solver2, boolean applyBounds2, String name, String name2, NoiseModel noiseModel) {
    final double[] noise = getNoise(seed, noiseModel);
    if (solver.isWeighted()) {
        solver.setWeights(getWeights(seed, noiseModel));
    }
    final int loops = 5;
    final UniformRandomProvider rg = RngUtils.create(seed.getSeed());
    final StoredDataStatistics[] stats = new StoredDataStatistics[6];
    final String[] statName = { "Signal", "X", "Y" };
    final int[] betterPrecision = new int[3];
    final int[] totalPrecision = new int[3];
    final int[] betterAccuracy = new int[3];
    final int[] totalAccuracy = new int[3];
    final String msg = "%s vs %s : %.1f (%s) %s %f +/- %f vs %f +/- %f  (N=%d) %b %s";
    int i1 = 0;
    int i2 = 0;
    for (final double s : signal) {
        final double[] expected = createParams(1, s, 0, 0, 1);
        double[] lower = null;
        double[] upper = null;
        if (applyBounds || applyBounds2) {
            lower = createParams(0, s * 0.5, -0.3, -0.3, 0.8);
            upper = createParams(3, s * 2, 0.3, 0.3, 1.2);
        }
        if (applyBounds) {
            solver.setBounds(lower, upper);
        }
        if (applyBounds2) {
            solver2.setBounds(lower, upper);
        }
        for (int loop = loops; loop-- > 0; ) {
            final double[] data = drawGaussian(expected, noise, noiseModel, rg);
            for (int i = 0; i < stats.length; i++) {
                stats[i] = new StoredDataStatistics();
            }
            for (final double db : base) {
                for (final double dx : shift) {
                    for (final double dy : shift) {
                        for (final double dsx : factor) {
                            final double[] p = createParams(db, s, dx, dy, dsx);
                            final double[] fp = fitGaussian(solver, data, p, expected);
                            i1 += solver.getEvaluations();
                            final double[] fp2 = fitGaussian(solver2, data, p, expected);
                            i2 += solver2.getEvaluations();
                            // Get the mean and sd (the fit precision)
                            compare(fp, expected, fp2, expected, Gaussian2DFunction.SIGNAL, stats[0], stats[1]);
                            compare(fp, expected, fp2, expected, Gaussian2DFunction.X_POSITION, stats[2], stats[3]);
                            compare(fp, expected, fp2, expected, Gaussian2DFunction.Y_POSITION, stats[4], stats[5]);
                        // Use the distance
                        // stats[2].add(distance(fp, expected));
                        // stats[3].add(distance(fp2, expected2));
                        }
                    }
                }
            }
            // two sided
            final double alpha = 0.05;
            for (int i = 0; i < stats.length; i += 2) {
                double u1 = stats[i].getMean();
                double u2 = stats[i + 1].getMean();
                final double sd1 = stats[i].getStandardDeviation();
                final double sd2 = stats[i + 1].getStandardDeviation();
                final TTest tt = new TTest();
                final boolean diff = tt.tTest(stats[i].getValues(), stats[i + 1].getValues(), alpha);
                final int index = i / 2;
                final Object[] args = new Object[] { name2, name, s, noiseModel, statName[index], u2, sd2, u1, sd1, stats[i].getN(), diff, "" };
                if (diff) {
                    // Different means. Check they are roughly the same
                    if (DoubleEquality.almostEqualRelativeOrAbsolute(u1, u2, 0.1, 0)) {
                        // Basically the same. Check which is more precise
                        if (!DoubleEquality.almostEqualRelativeOrAbsolute(sd1, sd2, 0.05, 0)) {
                            if (sd2 < sd1) {
                                betterPrecision[index]++;
                                args[args.length - 1] = "P*";
                                logger.log(TestLogUtils.getRecord(Level.FINE, msg, args));
                            } else {
                                args[args.length - 1] = "P";
                                logger.log(TestLogUtils.getRecord(Level.FINE, msg, args));
                            }
                            totalPrecision[index]++;
                        }
                    } else {
                        // Check which is more accurate (closer to zero)
                        u1 = Math.abs(u1);
                        u2 = Math.abs(u2);
                        if (u2 < u1) {
                            betterAccuracy[index]++;
                            args[args.length - 1] = "A*";
                            logger.log(TestLogUtils.getRecord(Level.FINE, msg, args));
                        } else {
                            args[args.length - 1] = "A";
                            logger.log(TestLogUtils.getRecord(Level.FINE, msg, args));
                        }
                        totalAccuracy[index]++;
                    }
                // The same means. Check that it is more precise
                } else if (!DoubleEquality.almostEqualRelativeOrAbsolute(sd1, sd2, 0.05, 0)) {
                    if (sd2 < sd1) {
                        betterPrecision[index]++;
                        args[args.length - 1] = "P*";
                        logger.log(TestLogUtils.getRecord(Level.FINE, msg, args));
                    } else {
                        args[args.length - 1] = "P";
                        logger.log(TestLogUtils.getRecord(Level.FINE, msg, args));
                    }
                    totalPrecision[index]++;
                }
            }
        }
    }
    int better = 0;
    int total = 0;
    for (int index = 0; index < statName.length; index++) {
        better += betterPrecision[index] + betterAccuracy[index];
        total += totalPrecision[index] + totalAccuracy[index];
        test(name2, name, statName[index] + " P", betterPrecision[index], totalPrecision[index], Level.FINE);
        test(name2, name, statName[index] + " A", betterAccuracy[index], totalAccuracy[index], Level.FINE);
    }
    test(name2, name, String.format("All (eval [%d] [%d]) : ", i1, i2), better, total, Level.INFO);
}

Example 24 with StoredDataStatistics

use of uk.ac.sussex.gdsc.core.utils.StoredDataStatistics in project GDSC-SMLM by aherbert.

the class BoundedFunctionSolverTest method fitSingleGaussianWithoutBias.

private void fitSingleGaussianWithoutBias(RandomSeed seed, boolean applyBounds, int clamping) {
    final double bias = 100;
    final NonLinearFit solver = getLvm((applyBounds) ? 2 : 1, clamping, false);
    final NonLinearFit solver2 = getLvm((applyBounds) ? 2 : 1, clamping, false);
    final String name = getLvmName(applyBounds, clamping, false);
    final int loops = 5;
    final UniformRandomProvider rg = RngUtils.create(seed.getSeed());
    final StoredDataStatistics[] stats = new StoredDataStatistics[6];
    for (final double s : signal) {
        final double[] expected = createParams(1, s, 0, 0, 1);
        double[] lower = null;
        double[] upper = null;
        if (applyBounds) {
            lower = createParams(0, s * 0.5, -0.2, -0.2, 0.8);
            upper = createParams(3, s * 2, 0.2, 0.2, 1.2);
            solver.setBounds(lower, upper);
        }
        final double[] expected2 = addBiasToParams(expected, bias);
        if (applyBounds) {
            final double[] lower2 = addBiasToParams(lower, bias);
            final double[] upper2 = addBiasToParams(upper, bias);
            solver2.setBounds(lower2, upper2);
        }
        for (int loop = loops; loop-- > 0; ) {
            final double[] data = drawGaussian(expected, rg);
            final double[] data2 = data.clone();
            for (int i = 0; i < data.length; i++) {
                data2[i] += bias;
            }
            for (int i = 0; i < stats.length; i++) {
                stats[i] = new StoredDataStatistics();
            }
            for (final double db : base) {
                for (final double dx : shift) {
                    for (final double dy : shift) {
                        for (final double dsx : factor) {
                            final double[] p = createParams(db, s, dx, dy, dsx);
                            final double[] p2 = addBiasToParams(p, bias);
                            final double[] fp = fitGaussian(solver, data, p, expected);
                            final double[] fp2 = fitGaussian(solver2, data2, p2, expected2);
                            // The result should be the same without a bias
                            Assertions.assertEquals(solver.getEvaluations(), solver2.getEvaluations(), () -> name + " Iterations");
                            fp2[0] -= bias;
                            Assertions.assertArrayEquals(fp, fp2, 1e-6, () -> name + " Solution");
                        }
                    }
                }
            }
        }
    }
}

Example 25 with StoredDataStatistics

use of uk.ac.sussex.gdsc.core.utils.StoredDataStatistics in project GDSC-SMLM by aherbert.

the class Fire method runQEstimation.

@SuppressWarnings("null")
private void runQEstimation() {
    IJ.showStatus(pluginTitle + " ...");
    if (!showQEstimationInputDialog()) {
        return;
    }
    MemoryPeakResults inputResults = ResultsManager.loadInputResults(settings.inputOption, false, null, null);
    if (MemoryPeakResults.isEmpty(inputResults)) {
        IJ.error(pluginTitle, "No results could be loaded");
        return;
    }
    if (inputResults.getCalibration() == null) {
        IJ.error(pluginTitle, "The results are not calibrated");
        return;
    }
    inputResults = cropToRoi(inputResults);
    if (inputResults.size() < 2) {
        IJ.error(pluginTitle, "No results within the crop region");
        return;
    }
    initialise(inputResults, null);
    // We need localisation precision.
    // Build a histogram of the localisation precision.
    // Get the initial mean and SD and plot as a Gaussian.
    final PrecisionHistogram histogram = calculatePrecisionHistogram();
    if (histogram == null) {
        IJ.error(pluginTitle, "No localisation precision available.\n \nPlease choose " + PrecisionMethod.FIXED + " and enter a precision mean and SD.");
        return;
    }
    final StoredDataStatistics precision = histogram.precision;
    final double fourierImageScale = Settings.scaleValues[settings.imageScaleIndex];
    final int imageSize = Settings.imageSizeValues[settings.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 ...");
    final 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");
    final Frc frc = new Frc();
    frc.setTrackProgress(progress);
    frc.setFourierMethod(fourierMethod);
    frc.setSamplingMethod(samplingMethod);
    frc.setPerimeterSamplingFactor(settings.perimeterSamplingFactor);
    final FrcCurve frcCurve = frc.calculateFrcCurve(images.ip1, images.ip2, images.nmPerPixel);
    if (frcCurve == null) {
        IJ.error(pluginTitle, "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
    final double qNorm = (1 / frcCurve.mean1 + 1 / frcCurve.mean2);
    final double[] frcnum = new double[frcCurve.getSize()];
    for (int i = 0; i < frcnum.length; i++) {
        final FrcCurveResult r = frcCurve.get(i);
        frcnum[i] = qNorm * r.getNumerator() / r.getNumberOfSamples();
    }
    // Compute the spatial frequency and the region for curve fitting
    final double[] q = Frc.computeQ(frcCurve, false);
    int low = 0;
    int high = q.length;
    while (high > 0 && q[high - 1] > settings.maxQ) {
        high--;
    }
    while (low < q.length && q[low] < settings.minQ) {
        low++;
    }
    // Require we fit at least 10% of the curve
    if (high - low < q.length * 0.1) {
        IJ.error(pluginTitle, "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
    final boolean sampleDecay = precision != null && settings.sampleDecay;
    double[] expDecay;
    if (sampleDecay) {
        // Random sample of precision values from the distribution is used to
        // construct the decay curve
        final int[] sample = RandomUtils.sample(10000, precision.getN(), UniformRandomProviders.create());
        final double four_pi2 = 4 * Math.PI * Math.PI;
        final 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;
        final 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] += StdMath.exp(pre[i] * s2);
            }
        }
        for (int i = 1; i < q.length; i++) {
            hq[i] /= n;
        }
        expDecay = new double[q.length];
        expDecay[0] = 1;
        for (int i = 1; i < q.length; i++) {
            final double sinc_q = sinc(Math.PI * q[i]);
            expDecay[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
        expDecay = computeExpDecay(histogram.mean / images.nmPerPixel, histogram.sigma / images.nmPerPixel, q);
    }
    // Smoothing
    double[] smooth;
    if (settings.loessSmoothing) {
        // Note: This computes the log then smooths it
        final double bandwidth = 0.1;
        final int robustness = 0;
        final double[] l = new double[expDecay.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] / expDecay[i]));
        }
        try {
            final LoessInterpolator loess = new LoessInterpolator(bandwidth, robustness);
            smooth = loess.smooth(q, l);
        } catch (final Exception ex) {
            IJ.error(pluginTitle, "LOESS smoothing failed");
            return;
        }
    } else {
        // Note: This smooths the curve before computing the log
        final double[] norm = new double[expDecay.length];
        for (int i = 0; i < norm.length; i++) {
            norm[i] = frcnum[i] / expDecay[i];
        }
        // Median window of 5 == radius of 2
        final DoubleMedianWindow mw = DoubleMedianWindow.wrap(norm, 2);
        smooth = new double[expDecay.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.
    final Quadratic curve = new Quadratic();
    final SimpleCurveFitter fit = SimpleCurveFitter.create(curve, new double[2]);
    final WeightedObservedPoints points = new WeightedObservedPoints();
    for (int i = low; i < high; i++) {
        points.add(q[i], smooth[i]);
    }
    final double[] estimate = fit.fit(points.toList());
    double qvalue = StdMath.exp(estimate[0]);
    // This could be made an option. Just use for debugging
    final boolean debug = false;
    if (debug) {
        // Plot the initial fit and the fit curve
        final double[] qScaled = Frc.computeQ(frcCurve, true);
        final double[] line = new double[q.length];
        for (int i = 0; i < q.length; i++) {
            line[i] = curve.value(q[i], estimate);
        }
        final String title = pluginTitle + " Initial fit";
        final Plot plot = new Plot(title, "Spatial Frequency (nm^-1)", "FRC Numerator");
        final 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);
        ImageJUtils.display(title, plot, ImageJUtils.NO_TO_FRONT);
    }
    if (settings.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
            final 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 ...
        final SimplexOptimizer opt = new SimplexOptimizer(1e-6, 1e-10);
        PointValuePair pair = null;
        final MultiPlateauness f = new MultiPlateauness(frcnum, q, low, high);
        final double[] initial = new double[] { histogram.mean / images.nmPerPixel, histogram.sigma / images.nmPerPixel, qvalue };
        pair = findMin(pair, opt, f, scale(initial, 0.1));
        pair = findMin(pair, opt, f, scale(initial, 0.5));
        pair = findMin(pair, opt, f, initial);
        pair = findMin(pair, opt, f, scale(initial, 2));
        pair = findMin(pair, opt, f, scale(initial, 10));
        if (pair != null) {
            final double[] point = pair.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
                final double meanSumOfSquares = (precision.getSumOfSquares() / (images.nmPerPixel * images.nmPerPixel)) / precision.getN();
                histogram.mean = images.nmPerPixel * Math.sqrt(meanSumOfSquares - estimate[1] / (4 * Math.PI * Math.PI));
            }
            expDecay = 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.
        final UnivariateOptimizer o = new BrentOptimizer(1e-3, 1e-6);
        final Plateauness f = new Plateauness(frcnum, expDecay, low, high);
        UnivariatePointValuePair result = null;
        result = findMin(result, o, f, qvalue, 0.1);
        result = findMin(result, o, f, qvalue, 0.2);
        result = findMin(result, o, f, qvalue, 0.333);
        result = findMin(result, o, f, qvalue, 0.5);
        // Do some Simplex repeats as well
        final SimplexOptimizer opt = new SimplexOptimizer(1e-6, 1e-10);
        result = findMin(result, opt, f, qvalue * 0.1);
        result = findMin(result, opt, f, qvalue * 0.5);
        result = findMin(result, opt, f, qvalue);
        result = findMin(result, opt, f, qvalue * 2);
        result = findMin(result, opt, f, qvalue * 10);
        if (result != null) {
            qvalue = result.getPoint();
        }
    }
    final 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, images.nmPerPixel);
    IJ.showStatus(pluginTitle + " complete");
}