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

Example 26 with StoredDataStatistics

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

the class EmGainAnalysis method pdfEmGain.

/**
 * Calculate the probability density function for EM-gain. The maximum count to evaluate is
 * calculated dynamically so that the cumulative probability does not change.
 *
 * <p>See Ulbrich & Isacoff (2007). Nature Methods 4, 319-321, SI equation 3.
 *
 * @param step the step between counts to evaluate
 * @param photons The average number of photons per pixel input to the EM-camera
 * @param gain The multiplication factor (gain)
 * @return The PDF
 */
private static double[] pdfEmGain(final double step, final double photons, final double gain) {
    final StoredDataStatistics stats = new StoredDataStatistics(100);
    stats.add(StdMath.exp(-photons));
    for (int c = 1; ; c++) {
        final double g = probabilityEmGain(c * step, photons, gain);
        stats.add(g);
        final double delta = g / stats.getSum();
        if (delta < 1e-5) {
            break;
        }
    }
    return stats.getValues();
}

Example 27 with StoredDataStatistics

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

the class PcPalmMolecules method runSimulation.

private void runSimulation(boolean resultsAvailable) {
    if (resultsAvailable && !showSimulationDialog()) {
        return;
    }
    startLog();
    log("Simulation parameters");
    if (settings.blinkingDistribution == 3) {
        log("  - Clusters = %d", settings.numberOfMolecules);
        log("  - Simulation size = %s um", MathUtils.rounded(settings.simulationSize, 4));
        log("  - Molecules/cluster = %s", MathUtils.rounded(settings.blinkingRate, 4));
        log("  - Blinking distribution = %s", Settings.BLINKING_DISTRIBUTION[settings.blinkingDistribution]);
        log("  - p-Value = %s", MathUtils.rounded(settings.pvalue, 4));
    } else {
        log("  - Molecules = %d", settings.numberOfMolecules);
        log("  - Simulation size = %s um", MathUtils.rounded(settings.simulationSize, 4));
        log("  - Blinking rate = %s", MathUtils.rounded(settings.blinkingRate, 4));
        log("  - Blinking distribution = %s", Settings.BLINKING_DISTRIBUTION[settings.blinkingDistribution]);
    }
    log("  - Average precision = %s nm", MathUtils.rounded(settings.sigmaS, 4));
    log("  - Clusters simulation = " + Settings.CLUSTER_SIMULATION[settings.clusterSimulation]);
    if (settings.clusterSimulation > 0) {
        log("  - Cluster number = %s +/- %s", MathUtils.rounded(settings.clusterNumber, 4), MathUtils.rounded(settings.clusterNumberStdDev, 4));
        log("  - Cluster radius = %s nm", MathUtils.rounded(settings.clusterRadius, 4));
    }
    final double nmPerPixel = 100;
    final double width = settings.simulationSize * 1000.0;
    final UniformRandomProvider rng = UniformRandomProviders.create();
    final UniformDistribution dist = new UniformDistribution(null, new double[] { width, width, 0 }, rng.nextInt());
    final NormalizedGaussianSampler gauss = SamplerUtils.createNormalizedGaussianSampler(rng);
    settings.molecules = new ArrayList<>(settings.numberOfMolecules);
    // Create some dummy results since the calibration is required for later analysis
    settings.results = new MemoryPeakResults(PsfHelper.create(PSFType.CUSTOM));
    settings.results.setCalibration(CalibrationHelper.create(nmPerPixel, 1, 100));
    settings.results.setSource(new NullSource("Molecule Simulation"));
    settings.results.begin();
    int count = 0;
    // Generate a sequence of coordinates
    final ArrayList<double[]> xyz = new ArrayList<>((int) (settings.numberOfMolecules * 1.1));
    final Statistics statsRadius = new Statistics();
    final Statistics statsSize = new Statistics();
    final String maskTitle = TITLE + " Cluster Mask";
    ByteProcessor bp = null;
    double maskScale = 0;
    if (settings.clusterSimulation > 0) {
        // Simulate clusters.
        // Note: In the Veatch et al. paper (Plos 1, e31457) correlation functions are built using
        // circles with small radii of 4-8 Arbitrary Units (AU) or large radii of 10-30 AU. A
        // fluctuations model is created at T = 1.075 Tc. It is not clear exactly how the particles
        // are distributed.
        // It may be that a mask is created first using the model. The particles are placed on the
        // mask using a specified density. This simulation produces a figure to show either a damped
        // cosine function (circles) or an exponential (fluctuations). The number of particles in
        // each circle may be randomly determined just by density. The figure does not discuss the
        // derivation of the cluster size statistic.
        // 
        // If this plugin simulation is run with a uniform distribution and blinking rate of 1 then
        // the damped cosine function is reproduced. The curve crosses g(r)=1 at a value equivalent
        // to the average distance to the centre-of-mass of each drawn cluster, not the input cluster
        // radius parameter (which is a hard upper limit on the distance to centre).
        final int maskSize = settings.lowResolutionImageSize;
        int[] mask = null;
        // scale is in nm/pixel
        maskScale = width / maskSize;
        final ArrayList<double[]> clusterCentres = new ArrayList<>();
        int totalSteps = 1 + (int) Math.ceil(settings.numberOfMolecules / settings.clusterNumber);
        if (settings.clusterSimulation == 2 || settings.clusterSimulation == 3) {
            // Clusters are non-overlapping circles
            // Ensure the circles do not overlap by using an exclusion mask that accumulates
            // out-of-bounds pixels by drawing the last cluster (plus some border) on an image. When no
            // more pixels are available then stop generating molecules.
            // This is done by cumulatively filling a mask and using the MaskDistribution to select
            // a new point. This may be slow but it works.
            // TODO - Allow clusters of different sizes...
            mask = new int[maskSize * maskSize];
            Arrays.fill(mask, 255);
            MaskDistribution maskDistribution = new MaskDistribution(mask, maskSize, maskSize, 0, maskScale, maskScale, rng);
            double[] centre;
            IJ.showStatus("Computing clusters mask");
            final int roiRadius = (int) Math.round((settings.clusterRadius * 2) / maskScale);
            if (settings.clusterSimulation == 3) {
                // Generate a mask of circles then sample from that.
                // If we want to fill the mask completely then adjust the total steps to be the number of
                // circles that can fit inside the mask.
                totalSteps = (int) (maskSize * maskSize / (Math.PI * MathUtils.pow2(settings.clusterRadius / maskScale)));
            }
            while ((centre = maskDistribution.next()) != null && clusterCentres.size() < totalSteps) {
                IJ.showProgress(clusterCentres.size(), totalSteps);
                // The mask returns the coordinates with the centre of the image at 0,0
                centre[0] += width / 2;
                centre[1] += width / 2;
                clusterCentres.add(centre);
                // Fill in the mask around the centre to exclude any more circles that could overlap
                final double cx = centre[0] / maskScale;
                final double cy = centre[1] / maskScale;
                fillMask(mask, maskSize, (int) cx, (int) cy, roiRadius, 0);
                try {
                    maskDistribution = new MaskDistribution(mask, maskSize, maskSize, 0, maskScale, maskScale, rng);
                } catch (final IllegalArgumentException ex) {
                    // This can happen when there are no more non-zero pixels
                    log("WARNING: No more room for clusters on the mask area (created %d of estimated %d)", clusterCentres.size(), totalSteps);
                    break;
                }
            }
            ImageJUtils.finished();
        } else {
            // Pick centres randomly from the distribution
            while (clusterCentres.size() < totalSteps) {
                clusterCentres.add(dist.next());
            }
        }
        final double scaledRadius = settings.clusterRadius / maskScale;
        if (settings.showClusterMask || settings.clusterSimulation == 3) {
            // Show the mask for the clusters
            if (mask == null) {
                mask = new int[maskSize * maskSize];
            } else {
                Arrays.fill(mask, 0);
            }
            final int roiRadius = (int) Math.round(scaledRadius);
            for (final double[] c : clusterCentres) {
                final double cx = c[0] / maskScale;
                final double cy = c[1] / maskScale;
                fillMask(mask, maskSize, (int) cx, (int) cy, roiRadius, 1);
            }
            if (settings.clusterSimulation == 3) {
                // We have the mask. Now pick points at random from the mask.
                final MaskDistribution maskDistribution = new MaskDistribution(mask, maskSize, maskSize, 0, maskScale, maskScale, rng);
                // Allocate each molecule position to a parent circle so defining clusters.
                final int[][] clusters = new int[clusterCentres.size()][];
                final int[] clusterSize = new int[clusters.length];
                for (int i = 0; i < settings.numberOfMolecules; i++) {
                    final double[] centre = maskDistribution.next();
                    // The mask returns the coordinates with the centre of the image at 0,0
                    centre[0] += width / 2;
                    centre[1] += width / 2;
                    xyz.add(centre);
                    // Output statistics on cluster size and number.
                    // TODO - Finding the closest cluster could be done better than an all-vs-all comparison
                    double max = distance2(centre, clusterCentres.get(0));
                    int cluster = 0;
                    for (int j = 1; j < clusterCentres.size(); j++) {
                        final double d2 = distance2(centre, clusterCentres.get(j));
                        if (d2 < max) {
                            max = d2;
                            cluster = j;
                        }
                    }
                    // Assign point i to cluster
                    centre[2] = cluster;
                    if (clusterSize[cluster] == 0) {
                        clusters[cluster] = new int[10];
                    }
                    if (clusters[cluster].length <= clusterSize[cluster]) {
                        clusters[cluster] = Arrays.copyOf(clusters[cluster], (int) (clusters[cluster].length * 1.5));
                    }
                    clusters[cluster][clusterSize[cluster]++] = i;
                }
                // Generate real cluster size statistics
                for (int j = 0; j < clusterSize.length; j++) {
                    final int size = clusterSize[j];
                    if (size == 0) {
                        continue;
                    }
                    statsSize.add(size);
                    if (size == 1) {
                        statsRadius.add(0);
                        continue;
                    }
                    // Find centre of cluster and add the distance to each point
                    final double[] com = new double[2];
                    for (int n = 0; n < size; n++) {
                        final double[] xy = xyz.get(clusters[j][n]);
                        for (int k = 0; k < 2; k++) {
                            com[k] += xy[k];
                        }
                    }
                    for (int k = 0; k < 2; k++) {
                        com[k] /= size;
                    }
                    for (int n = 0; n < size; n++) {
                        final double dx = xyz.get(clusters[j][n])[0] - com[0];
                        final double dy = xyz.get(clusters[j][n])[1] - com[1];
                        statsRadius.add(Math.sqrt(dx * dx + dy * dy));
                    }
                }
            }
            if (settings.showClusterMask) {
                bp = new ByteProcessor(maskSize, maskSize);
                for (int i = 0; i < mask.length; i++) {
                    if (mask[i] != 0) {
                        bp.set(i, 128);
                    }
                }
                ImageJUtils.display(maskTitle, bp);
            }
        }
        // Use the simulated cluster centres to create clusters of the desired size
        if (settings.clusterSimulation == 1 || settings.clusterSimulation == 2) {
            for (final double[] clusterCentre : clusterCentres) {
                final int clusterN = (int) Math.round((settings.clusterNumberStdDev > 0) ? settings.clusterNumber + gauss.sample() * settings.clusterNumberStdDev : settings.clusterNumber);
                if (clusterN < 1) {
                    continue;
                }
                if (clusterN == 1) {
                    // No need for a cluster around a point
                    xyz.add(clusterCentre);
                    statsRadius.add(0);
                    statsSize.add(1);
                } else {
                    // Generate N random points within a circle of the chosen cluster radius.
                    // Locate the centre-of-mass and the average distance to the centre.
                    final double[] com = new double[3];
                    int size = 0;
                    while (size < clusterN) {
                        // Generate a random point within a circle uniformly
                        // http://stackoverflow.com/questions/5837572/generate-a-random-point-within-a-circle-uniformly
                        final double t = 2.0 * Math.PI * rng.nextDouble();
                        final double u = rng.nextDouble() + rng.nextDouble();
                        final double r = settings.clusterRadius * ((u > 1) ? 2 - u : u);
                        final double x = r * Math.cos(t);
                        final double y = r * Math.sin(t);
                        final double[] xy = new double[] { clusterCentre[0] + x, clusterCentre[1] + y };
                        xyz.add(xy);
                        for (int k = 0; k < 2; k++) {
                            com[k] += xy[k];
                        }
                        size++;
                    }
                    // Add the distance of the points from the centre of the cluster.
                    // Note this does not account for the movement due to precision.
                    statsSize.add(size);
                    if (size == 1) {
                        statsRadius.add(0);
                    } else {
                        for (int k = 0; k < 2; k++) {
                            com[k] /= size;
                        }
                        while (size > 0) {
                            final double dx = xyz.get(xyz.size() - size)[0] - com[0];
                            final double dy = xyz.get(xyz.size() - size)[1] - com[1];
                            statsRadius.add(Math.sqrt(dx * dx + dy * dy));
                            size--;
                        }
                    }
                }
            }
        }
    } else {
        // Random distribution
        for (int i = 0; i < settings.numberOfMolecules; i++) {
            xyz.add(dist.next());
        }
    }
    // The Gaussian sigma should be applied so the overall distance from the centre
    // ( sqrt(x^2+y^2) ) has a standard deviation of sigmaS?
    final double sigma1D = settings.sigmaS / Math.sqrt(2);
    // Show optional histograms
    StoredDataStatistics intraDistances = null;
    StoredData blinks = null;
    if (settings.showHistograms) {
        final int capacity = (int) (xyz.size() * settings.blinkingRate);
        intraDistances = new StoredDataStatistics(capacity);
        blinks = new StoredData(capacity);
    }
    final Statistics statsSigma = new Statistics();
    for (int i = 0; i < xyz.size(); i++) {
        int occurrences = getBlinks(rng, settings.blinkingRate);
        if (blinks != null) {
            blinks.add(occurrences);
        }
        final int size = settings.molecules.size();
        // Get coordinates in nm
        final double[] moleculeXyz = xyz.get(i);
        if (bp != null && occurrences > 0) {
            bp.putPixel((int) Math.round(moleculeXyz[0] / maskScale), (int) Math.round(moleculeXyz[1] / maskScale), 255);
        }
        while (occurrences-- > 0) {
            final double[] localisationXy = Arrays.copyOf(moleculeXyz, 2);
            // Add random precision
            if (sigma1D > 0) {
                final double dx = gauss.sample() * sigma1D;
                final double dy = gauss.sample() * sigma1D;
                localisationXy[0] += dx;
                localisationXy[1] += dy;
                if (!dist.isWithinXy(localisationXy)) {
                    continue;
                }
                // Calculate mean-squared displacement
                statsSigma.add(dx * dx + dy * dy);
            }
            final double x = localisationXy[0];
            final double y = localisationXy[1];
            settings.molecules.add(new Molecule(x, y, i, 1));
            // Store in pixels
            final float xx = (float) (x / nmPerPixel);
            final float yy = (float) (y / nmPerPixel);
            final float[] params = PeakResult.createParams(0, 0, xx, yy, 0);
            settings.results.add(i + 1, (int) xx, (int) yy, 0, 0, 0, 0, params, null);
        }
        if (settings.molecules.size() > size) {
            count++;
            if (intraDistances != null) {
                final int newCount = settings.molecules.size() - size;
                if (newCount == 1) {
                    // No intra-molecule distances
                    continue;
                }
                // Get the distance matrix between these molecules
                final double[][] matrix = new double[newCount][newCount];
                for (int ii = size, x = 0; ii < settings.molecules.size(); ii++, x++) {
                    for (int jj = size + 1, y = 1; jj < settings.molecules.size(); jj++, y++) {
                        final double d2 = settings.molecules.get(ii).distance2(settings.molecules.get(jj));
                        matrix[x][y] = matrix[y][x] = d2;
                    }
                }
                // Get the maximum distance for particle linkage clustering of this molecule
                double max = 0;
                for (int x = 0; x < newCount; x++) {
                    // Compare to all-other molecules and get the minimum distance
                    // needed to join at least one
                    double linkDistance = Double.POSITIVE_INFINITY;
                    for (int y = 0; y < newCount; y++) {
                        if (x == y) {
                            continue;
                        }
                        if (matrix[x][y] < linkDistance) {
                            linkDistance = matrix[x][y];
                        }
                    }
                    // Check if this is larger
                    if (max < linkDistance) {
                        max = linkDistance;
                    }
                }
                intraDistances.add(Math.sqrt(max));
            }
        }
    }
    settings.results.end();
    if (bp != null) {
        final ImagePlus imp = ImageJUtils.display(maskTitle, bp);
        final Calibration cal = imp.getCalibration();
        cal.setUnit("nm");
        cal.pixelWidth = cal.pixelHeight = maskScale;
    }
    log("Simulation results");
    log("  * Molecules = %d (%d activated)", xyz.size(), count);
    log("  * Blinking rate = %s", MathUtils.rounded((double) settings.molecules.size() / xyz.size(), 4));
    log("  * Precision (Mean-displacement) = %s nm", (statsSigma.getN() > 0) ? MathUtils.rounded(Math.sqrt(statsSigma.getMean()), 4) : "0");
    if (intraDistances != null) {
        if (intraDistances.getN() == 0) {
            log("  * Mean Intra-Molecule particle linkage distance = 0 nm");
            log("  * Fraction of inter-molecule particle linkage @ 0 nm = 0 %%");
        } else {
            plot(blinks, "Blinks/Molecule", true);
            final double[][] intraHist = plot(intraDistances, "Intra-molecule particle linkage distance", false);
            // Determine 95th and 99th percentile
            // Will not be null as we requested a non-integer histogram.
            int p99 = intraHist[0].length - 1;
            final double limit1 = 0.99 * intraHist[1][p99];
            final double limit2 = 0.95 * intraHist[1][p99];
            while (intraHist[1][p99] > limit1 && p99 > 0) {
                p99--;
            }
            int p95 = p99;
            while (intraHist[1][p95] > limit2 && p95 > 0) {
                p95--;
            }
            log("  * Mean Intra-Molecule particle linkage distance = %s nm" + " (95%% = %s, 99%% = %s, 100%% = %s)", MathUtils.rounded(intraDistances.getMean(), 4), MathUtils.rounded(intraHist[0][p95], 4), MathUtils.rounded(intraHist[0][p99], 4), MathUtils.rounded(intraHist[0][intraHist[0].length - 1], 4));
            if (settings.distanceAnalysis) {
                performDistanceAnalysis(intraHist, p99);
            }
        }
    }
    if (settings.clusterSimulation > 0) {
        log("  * Cluster number = %s +/- %s", MathUtils.rounded(statsSize.getMean(), 4), MathUtils.rounded(statsSize.getStandardDeviation(), 4));
        log("  * Cluster radius = %s +/- %s nm (mean distance to centre-of-mass)", MathUtils.rounded(statsRadius.getMean(), 4), MathUtils.rounded(statsRadius.getStandardDeviation(), 4));
    }
}

Example 28 with StoredDataStatistics

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

the class PsfEstimator method calculateStatistics.

private boolean calculateStatistics(PeakFit fitter, double[] params, double[] paramsDev) {
    debug("  Fitting PSF");
    swapStatistics();
    // Create the fit engine using the PeakFit plugin
    final FitConfiguration fitConfig = config.getFitConfiguration();
    fitConfig.setInitialPeakStdDev0((float) params[1]);
    try {
        fitConfig.setInitialPeakStdDev1((float) params[2]);
        fitConfig.setInitialAngle((float) Math.toRadians(params[0]));
    } catch (IllegalStateException ex) {
    // Ignore this as the current PSF is not a 2 axis and theta Gaussian PSF
    }
    final ImageStack stack = imp.getImageStack();
    final Rectangle roi = stack.getProcessor(1).getRoi();
    ImageSource source = new IJImageSource(imp);
    // Allow interlaced data by wrapping the image source
    if (interlacedData) {
        source = new InterlacedImageSource(source, dataStart, dataBlock, dataSkip);
    }
    // Allow frame aggregation by wrapping the image source
    if (integrateFrames > 1) {
        source = new AggregatedImageSource(source, integrateFrames);
    }
    fitter.initialiseImage(source, roi, true);
    fitter.addPeakResults(this);
    fitter.initialiseFitting();
    final FitEngine engine = fitter.createFitEngine();
    // Use random slices
    final int[] slices = new int[stack.getSize()];
    for (int i = 0; i < slices.length; i++) {
        slices[i] = i + 1;
    }
    RandomUtils.shuffle(slices, UniformRandomProviders.create());
    IJ.showStatus("Fitting ...");
    // Use multi-threaded code for speed
    int sliceIndex;
    for (sliceIndex = 0; sliceIndex < slices.length; sliceIndex++) {
        final int slice = slices[sliceIndex];
        IJ.showProgress(size(), settings.getNumberOfPeaks());
        final ImageProcessor ip = stack.getProcessor(slice);
        // stack processor does not set the bounds required by ImageConverter
        ip.setRoi(roi);
        final FitJob job = new FitJob(slice, ImageJImageConverter.getData(ip), roi);
        engine.run(job);
        if (sampleSizeReached() || ImageJUtils.isInterrupted()) {
            break;
        }
    }
    if (ImageJUtils.isInterrupted()) {
        IJ.showProgress(1);
        engine.end(true);
        return false;
    }
    // Wait until we have enough results
    while (!sampleSizeReached() && !engine.isQueueEmpty()) {
        IJ.showProgress(size(), settings.getNumberOfPeaks());
        try {
            Thread.sleep(50);
        } catch (final InterruptedException ex) {
            Thread.currentThread().interrupt();
            throw new ConcurrentRuntimeException("Unexpected interruption", ex);
        }
    }
    // End now if we have enough samples
    engine.end(sampleSizeReached());
    ImageJUtils.finished();
    // This count will be an over-estimate given that the provider is ahead of the consumer
    // in this multi-threaded system
    debug("  Processed %d/%d slices (%d peaks)", sliceIndex, slices.length, size());
    setParams(ANGLE, params, paramsDev, sampleNew[ANGLE]);
    setParams(X, params, paramsDev, sampleNew[X]);
    setParams(Y, params, paramsDev, sampleNew[Y]);
    if (settings.getShowHistograms()) {
        final HistogramPlotBuilder builder = new HistogramPlotBuilder(TITLE).setNumberOfBins(settings.getHistogramBins());
        final WindowOrganiser wo = new WindowOrganiser();
        for (int ii = 0; ii < 3; ii++) {
            if (sampleNew[ii].getN() == 0) {
                continue;
            }
            final StoredDataStatistics stats = StoredDataStatistics.create(sampleNew[ii].getValues());
            builder.setData(stats).setName(NAMES[ii]).setPlotLabel("Mean = " + MathUtils.rounded(stats.getMean()) + ". Median = " + MathUtils.rounded(sampleNew[ii].getPercentile(50))).show(wo);
        }
        wo.tile();
    }
    if (size() < 2) {
        log("ERROR: Insufficient number of fitted peaks, terminating ...");
        return false;
    }
    return true;
}

Example 29 with StoredDataStatistics

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

the class MeanVarianceTest method run.

@Override
public void run(String arg) {
    SmlmUsageTracker.recordPlugin(this.getClass(), arg);
    settings = Settings.load();
    settings.save();
    String helpKey = "mean-variance-test";
    if (ImageJUtils.isExtraOptions()) {
        final ImagePlus imp = WindowManager.getCurrentImage();
        if (imp.getStackSize() > 1) {
            final GenericDialog gd = new GenericDialog(TITLE);
            gd.addMessage("Perform single image analysis on the current image?");
            gd.addNumericField("Bias", settings.bias, 0);
            gd.addHelp(HelpUrls.getUrl(helpKey));
            gd.showDialog();
            if (gd.wasCanceled()) {
                return;
            }
            singleImage = true;
            settings.bias = Math.abs(gd.getNextNumber());
        } else {
            IJ.error(TITLE, "Single-image mode requires a stack");
            return;
        }
    }
    List<ImageSample> images;
    String inputDirectory = "";
    if (singleImage) {
        IJ.showStatus("Loading images...");
        images = getImages();
        if (images.size() == 0) {
            IJ.error(TITLE, "Not enough images for analysis");
            return;
        }
    } else {
        inputDirectory = IJ.getDirectory("Select image series ...");
        if (inputDirectory == null) {
            return;
        }
        final SeriesOpener series = new SeriesOpener(inputDirectory);
        series.setVariableSize(true);
        if (series.getNumberOfImages() < 3) {
            IJ.error(TITLE, "Not enough images in the selected directory");
            return;
        }
        if (!IJ.showMessageWithCancel(TITLE, String.format("Analyse %d images, first image:\n%s", series.getNumberOfImages(), series.getImageList()[0]))) {
            return;
        }
        IJ.showStatus("Loading images");
        images = getImages(series);
        if (images.size() < 3) {
            IJ.error(TITLE, "Not enough images for analysis");
            return;
        }
        if (images.get(0).exposure != 0) {
            IJ.error(TITLE, "First image in series must have exposure 0 (Bias image)");
            return;
        }
    }
    final boolean emMode = (arg != null && arg.contains("em"));
    GenericDialog gd = new GenericDialog(TITLE);
    gd.addMessage("Set the output options:");
    gd.addCheckbox("Show_table", settings.showTable);
    gd.addCheckbox("Show_charts", settings.showCharts);
    if (emMode) {
        // Ask the user for the camera gain ...
        gd.addMessage("Estimating the EM-gain requires the camera gain without EM readout enabled");
        gd.addNumericField("Camera_gain (Count/e-)", settings.cameraGain, 4);
    }
    if (emMode) {
        helpKey += "-em-ccd";
    }
    gd.addHelp(HelpUrls.getUrl(helpKey));
    gd.showDialog();
    if (gd.wasCanceled()) {
        return;
    }
    settings.showTable = gd.getNextBoolean();
    settings.showCharts = gd.getNextBoolean();
    if (emMode) {
        settings.cameraGain = gd.getNextNumber();
    }
    IJ.showStatus("Computing mean & variance");
    final double nImages = images.size();
    for (int i = 0; i < images.size(); i++) {
        IJ.showStatus(String.format("Computing mean & variance %d/%d", i + 1, images.size()));
        images.get(i).compute(singleImage, i / nImages, (i + 1) / nImages);
    }
    IJ.showProgress(1);
    IJ.showStatus("Computing results");
    // Allow user to input multiple bias images
    int start = 0;
    final Statistics biasStats = new Statistics();
    final Statistics noiseStats = new Statistics();
    final double bias;
    if (singleImage) {
        bias = settings.bias;
    } else {
        while (start < images.size()) {
            final ImageSample sample = images.get(start);
            if (sample.exposure == 0) {
                biasStats.add(sample.means);
                for (final PairSample pair : sample.samples) {
                    noiseStats.add(pair.variance);
                }
                start++;
            } else {
                break;
            }
        }
        bias = biasStats.getMean();
    }
    // Get the mean-variance data
    int total = 0;
    for (int i = start; i < images.size(); i++) {
        total += images.get(i).samples.size();
    }
    if (settings.showTable && total > 2000) {
        gd = new GenericDialog(TITLE);
        gd.addMessage("Table output requires " + total + " entries.\n \nYou may want to disable the table.");
        gd.addCheckbox("Show_table", settings.showTable);
        gd.showDialog();
        if (gd.wasCanceled()) {
            return;
        }
        settings.showTable = gd.getNextBoolean();
    }
    final TextWindow results = (settings.showTable) ? createResultsWindow() : null;
    double[] mean = new double[total];
    double[] variance = new double[mean.length];
    final Statistics gainStats = (singleImage) ? new StoredDataStatistics(total) : new Statistics();
    final WeightedObservedPoints obs = new WeightedObservedPoints();
    for (int i = (singleImage) ? 0 : start, j = 0; i < images.size(); i++) {
        final StringBuilder sb = (settings.showTable) ? new StringBuilder() : null;
        final ImageSample sample = images.get(i);
        for (final PairSample pair : sample.samples) {
            if (j % 16 == 0) {
                IJ.showProgress(j, total);
            }
            mean[j] = pair.getMean();
            variance[j] = pair.variance;
            // Gain is in Count / e
            double gain = variance[j] / (mean[j] - bias);
            gainStats.add(gain);
            obs.add(mean[j], variance[j]);
            if (emMode) {
                gain /= (2 * settings.cameraGain);
            }
            if (sb != null) {
                sb.append(sample.title).append('\t');
                sb.append(sample.exposure).append('\t');
                sb.append(pair.slice1).append('\t');
                sb.append(pair.slice2).append('\t');
                sb.append(IJ.d2s(pair.mean1, 2)).append('\t');
                sb.append(IJ.d2s(pair.mean2, 2)).append('\t');
                sb.append(IJ.d2s(mean[j], 2)).append('\t');
                sb.append(IJ.d2s(variance[j], 2)).append('\t');
                sb.append(MathUtils.rounded(gain, 4)).append("\n");
            }
            j++;
        }
        if (results != null && sb != null) {
            results.append(sb.toString());
        }
    }
    IJ.showProgress(1);
    if (singleImage) {
        StoredDataStatistics stats = (StoredDataStatistics) gainStats;
        ImageJUtils.log(TITLE);
        if (emMode) {
            final double[] values = stats.getValues();
            MathArrays.scaleInPlace(0.5, values);
            stats = StoredDataStatistics.create(values);
        }
        if (settings.showCharts) {
            // Plot the gain over time
            final String title = TITLE + " Gain vs Frame";
            final Plot plot = new Plot(title, "Slice", "Gain");
            plot.addPoints(SimpleArrayUtils.newArray(gainStats.getN(), 1, 1.0), stats.getValues(), Plot.LINE);
            final PlotWindow pw = ImageJUtils.display(title, plot);
            // Show a histogram
            final String label = String.format("Mean = %s, Median = %s", MathUtils.rounded(stats.getMean()), MathUtils.rounded(stats.getMedian()));
            final WindowOrganiser wo = new WindowOrganiser();
            final PlotWindow pw2 = new HistogramPlotBuilder(TITLE, stats, "Gain").setRemoveOutliersOption(1).setPlotLabel(label).show(wo);
            if (wo.isNotEmpty()) {
                final Point point = pw.getLocation();
                point.y += pw.getHeight();
                pw2.setLocation(point);
            }
        }
        ImageJUtils.log("Single-image mode: %s camera", (emMode) ? "EM-CCD" : "Standard");
        final double gain = stats.getMedian();
        if (emMode) {
            final double totalGain = gain;
            final double emGain = totalGain / settings.cameraGain;
            ImageJUtils.log("  Gain = 1 / %s (Count/e-)", MathUtils.rounded(settings.cameraGain, 4));
            ImageJUtils.log("  EM-Gain = %s", MathUtils.rounded(emGain, 4));
            ImageJUtils.log("  Total Gain = %s (Count/e-)", MathUtils.rounded(totalGain, 4));
        } else {
            settings.cameraGain = gain;
            ImageJUtils.log("  Gain = 1 / %s (Count/e-)", MathUtils.rounded(settings.cameraGain, 4));
        }
    } else {
        IJ.showStatus("Computing fit");
        // Sort
        final int[] indices = rank(mean);
        mean = reorder(mean, indices);
        variance = reorder(variance, indices);
        // Compute optimal coefficients.
        // a - b x
        final double[] init = { 0, 1 / gainStats.getMean() };
        final PolynomialCurveFitter fitter = PolynomialCurveFitter.create(2).withStartPoint(init);
        final double[] best = fitter.fit(obs.toList());
        // Construct the polynomial that best fits the data.
        final PolynomialFunction fitted = new PolynomialFunction(best);
        if (settings.showCharts) {
            // Plot mean verses variance. Gradient is gain in Count/e.
            final String title = TITLE + " results";
            final Plot plot = new Plot(title, "Mean", "Variance");
            final double[] xlimits = MathUtils.limits(mean);
            final double[] ylimits = MathUtils.limits(variance);
            double xrange = (xlimits[1] - xlimits[0]) * 0.05;
            if (xrange == 0) {
                xrange = 0.05;
            }
            double yrange = (ylimits[1] - ylimits[0]) * 0.05;
            if (yrange == 0) {
                yrange = 0.05;
            }
            plot.setLimits(xlimits[0] - xrange, xlimits[1] + xrange, ylimits[0] - yrange, ylimits[1] + yrange);
            plot.setColor(Color.blue);
            plot.addPoints(mean, variance, Plot.CROSS);
            plot.setColor(Color.red);
            plot.addPoints(new double[] { mean[0], mean[mean.length - 1] }, new double[] { fitted.value(mean[0]), fitted.value(mean[mean.length - 1]) }, Plot.LINE);
            ImageJUtils.display(title, plot);
        }
        final double avBiasNoise = Math.sqrt(noiseStats.getMean());
        ImageJUtils.log(TITLE);
        ImageJUtils.log("  Directory = %s", inputDirectory);
        ImageJUtils.log("  Bias = %s +/- %s (Count)", MathUtils.rounded(bias, 4), MathUtils.rounded(avBiasNoise, 4));
        ImageJUtils.log("  Variance = %s + %s * mean", MathUtils.rounded(best[0], 4), MathUtils.rounded(best[1], 4));
        if (emMode) {
            // The gradient is the observed gain of the noise.
            // In an EM-CCD there is a noise factor of 2.
            // Q. Is this true for a correct noise factor calibration:
            // double noiseFactor = (Read Noise EM-CCD) / (Read Noise CCD)
            // Em-gain is the observed gain divided by the noise factor multiplied by camera gain
            final double emGain = best[1] / (2 * settings.cameraGain);
            // Compute total gain
            final double totalGain = emGain * settings.cameraGain;
            final double readNoise = avBiasNoise / settings.cameraGain;
            // Effective noise is standard deviation of the bias image divided by the total gain (in
            // Count/e-)
            final double readNoiseE = avBiasNoise / totalGain;
            ImageJUtils.log("  Read Noise = %s (e-) [%s (Count)]", MathUtils.rounded(readNoise, 4), MathUtils.rounded(avBiasNoise, 4));
            ImageJUtils.log("  Gain = 1 / %s (Count/e-)", MathUtils.rounded(1 / settings.cameraGain, 4));
            ImageJUtils.log("  EM-Gain = %s", MathUtils.rounded(emGain, 4));
            ImageJUtils.log("  Total Gain = %s (Count/e-)", MathUtils.rounded(totalGain, 4));
            ImageJUtils.log("  Effective Read Noise = %s (e-) (Read Noise/Total Gain)", MathUtils.rounded(readNoiseE, 4));
        } else {
            // The gradient is the observed gain of the noise.
            settings.cameraGain = best[1];
            // Noise is standard deviation of the bias image divided by the gain (in Count/e-)
            final double readNoise = avBiasNoise / settings.cameraGain;
            ImageJUtils.log("  Read Noise = %s (e-) [%s (Count)]", MathUtils.rounded(readNoise, 4), MathUtils.rounded(avBiasNoise, 4));
            ImageJUtils.log("  Gain = 1 / %s (Count/e-)", MathUtils.rounded(1 / settings.cameraGain, 4));
        }
    }
    IJ.showStatus("");
}