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

Example 6 with StoredDataStatistics

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

the class PsfCreator method runUsingFitting.

private void runUsingFitting() {
    if (!showFittingDialog()) {
        return;
    }
    if (!loadConfiguration()) {
        return;
    }
    final BasePoint[] spots = getSpots(0, true);
    if (spots.length == 0) {
        IJ.error(TITLE, "No spots without neighbours within " + (boxRadius * 2) + "px");
        return;
    }
    final ImageStack stack = getImageStack();
    final int width = imp.getWidth();
    final int height = imp.getHeight();
    final int currentSlice = imp.getSlice();
    // Adjust settings for a single maxima
    config.setIncludeNeighbours(false);
    final ArrayList<double[]> centres = new ArrayList<>(spots.length);
    final int iterations = 1;
    final LoessInterpolator loess = new LoessInterpolator(settings.getSmoothing(), iterations);
    // TODO - The fitting routine may not produce many points. In this instance the LOESS
    // interpolator
    // fails to smooth the data very well. A higher bandwidth helps this but perhaps
    // try a different smoothing method.
    // For each spot
    ImageJUtils.log(TITLE + ": " + imp.getTitle());
    ImageJUtils.log("Finding spot locations...");
    ImageJUtils.log("  %d spot%s without neighbours within %dpx", spots.length, ((spots.length == 1) ? "" : "s"), (boxRadius * 2));
    final StoredDataStatistics averageSd = new StoredDataStatistics();
    final StoredDataStatistics averageA = new StoredDataStatistics();
    final Statistics averageRange = new Statistics();
    final MemoryPeakResults allResults = new MemoryPeakResults();
    allResults.setCalibration(fitConfig.getCalibration());
    allResults.setPsf(fitConfig.getPsf());
    allResults.setName(TITLE);
    allResults.setBounds(new Rectangle(0, 0, width, height));
    MemoryPeakResults.addResults(allResults);
    for (int n = 1; n <= spots.length; n++) {
        final BasePoint spot = spots[n - 1];
        final int x = (int) spot.getX();
        final int y = (int) spot.getY();
        final MemoryPeakResults results = fitSpot(stack, width, height, x, y);
        allResults.add(results);
        if (results.size() < 5) {
            ImageJUtils.log("  Spot %d: Not enough fit results %d", n, results.size());
            continue;
        }
        // Get the results for the spot centre and width
        final double[] z = new double[results.size()];
        final double[] xCoord = new double[z.length];
        final double[] yCoord = new double[z.length];
        final double[] sd;
        final double[] a;
        final Counter counter = new Counter();
        // We have fit the results so they will be in the preferred units
        results.forEach(new PeakResultProcedure() {

            @Override
            public void execute(PeakResult peak) {
                final int i = counter.getAndIncrement();
                z[i] = peak.getFrame();
                xCoord[i] = peak.getXPosition() - x;
                yCoord[i] = peak.getYPosition() - y;
            }
        });
        final WidthResultProcedure wp = new WidthResultProcedure(results, DistanceUnit.PIXEL);
        wp.getW();
        sd = SimpleArrayUtils.toDouble(wp.wx);
        final HeightResultProcedure hp = new HeightResultProcedure(results, IntensityUnit.COUNT);
        hp.getH();
        a = SimpleArrayUtils.toDouble(hp.heights);
        // Smooth the amplitude plot
        final double[] smoothA = loess.smooth(z, a);
        // Find the maximum amplitude
        int maximumIndex = findMaximumIndex(smoothA);
        // Find the range at a fraction of the max. This is smoothed to find the X/Y centre
        int start = 0;
        int stop = smoothA.length - 1;
        final double limit = smoothA[maximumIndex] * settings.getAmplitudeFraction();
        for (int j = 0; j < smoothA.length; j++) {
            if (smoothA[j] > limit) {
                start = j;
                break;
            }
        }
        for (int j = smoothA.length; j-- > 0; ) {
            if (smoothA[j] > limit) {
                stop = j;
                break;
            }
        }
        averageRange.add(stop - start + 1);
        // Extract xy centre coords and smooth
        double[] smoothX = new double[stop - start + 1];
        double[] smoothY = new double[smoothX.length];
        double[] smoothSd = new double[smoothX.length];
        final double[] newZ = new double[smoothX.length];
        for (int j = start, k = 0; j <= stop; j++, k++) {
            smoothX[k] = xCoord[j];
            smoothY[k] = yCoord[j];
            smoothSd[k] = sd[j];
            newZ[k] = z[j];
        }
        smoothX = loess.smooth(newZ, smoothX);
        smoothY = loess.smooth(newZ, smoothY);
        smoothSd = loess.smooth(newZ, smoothSd);
        // Since the amplitude is not very consistent move from this peak to the
        // lowest width which is the in-focus spot.
        maximumIndex = findMinimumIndex(smoothSd, maximumIndex - start);
        // Find the centre at the amplitude peak
        final double cx = smoothX[maximumIndex] + x;
        final double cy = smoothY[maximumIndex] + y;
        int cz = (int) newZ[maximumIndex];
        double csd = smoothSd[maximumIndex];
        double ca = smoothA[maximumIndex + start];
        // The average should weight the SD using the signal for each spot
        averageSd.add(smoothSd[maximumIndex]);
        averageA.add(ca);
        if (ignoreSpot(n, z, a, smoothA, xCoord, yCoord, sd, newZ, smoothX, smoothY, smoothSd, cx, cy, cz, csd)) {
            ImageJUtils.log("  Spot %d was ignored", n);
            continue;
        }
        // Store result - it may have been moved interactively
        maximumIndex += this.slice - cz;
        cz = (int) newZ[maximumIndex];
        csd = smoothSd[maximumIndex];
        ca = smoothA[maximumIndex + start];
        ImageJUtils.log("  Spot %d => x=%.2f, y=%.2f, z=%d, sd=%.2f, A=%.2f", n, cx, cy, cz, csd, ca);
        centres.add(new double[] { cx, cy, cz, csd, n });
    }
    if (settings.getInteractiveMode()) {
        imp.setSlice(currentSlice);
        imp.setOverlay(null);
        // Hide the amplitude and spot plots
        ImageJUtils.hide(TITLE_AMPLITUDE);
        ImageJUtils.hide(TITLE_PSF_PARAMETERS);
    }
    if (centres.isEmpty()) {
        final String msg = "No suitable spots could be identified";
        ImageJUtils.log(msg);
        IJ.error(TITLE, msg);
        return;
    }
    // Find the limits of the z-centre
    int minz = (int) centres.get(0)[2];
    int maxz = minz;
    for (final double[] centre : centres) {
        if (minz > centre[2]) {
            minz = (int) centre[2];
        } else if (maxz < centre[2]) {
            maxz = (int) centre[2];
        }
    }
    IJ.showStatus("Creating PSF image");
    // Create a stack that can hold all the data.
    final ImageStack psf = createStack(stack, minz, maxz, settings.getMagnification());
    // For each spot
    final Statistics stats = new Statistics();
    boolean ok = true;
    for (int i = 0; ok && i < centres.size(); i++) {
        final double increment = 1.0 / (stack.getSize() * centres.size());
        setProgress((double) i / centres.size());
        final double[] centre = centres.get(i);
        // Extract the spot
        final float[][] spot = new float[stack.getSize()][];
        Rectangle regionBounds = null;
        for (int slice = 1; slice <= stack.getSize(); slice++) {
            final ImageExtractor ie = ImageExtractor.wrap((float[]) stack.getPixels(slice), width, height);
            if (regionBounds == null) {
                regionBounds = ie.getBoxRegionBounds((int) centre[0], (int) centre[1], boxRadius);
            }
            spot[slice - 1] = ie.crop(regionBounds);
        }
        if (regionBounds == null) {
            // Empty stack
            continue;
        }
        final int n = (int) centre[4];
        final float b = getBackground(n, spot);
        if (!subtractBackgroundAndWindow(spot, b, regionBounds.width, regionBounds.height, centre, loess)) {
            ImageJUtils.log("  Spot %d was ignored", n);
            continue;
        }
        stats.add(b);
        // Adjust the centre using the crop
        centre[0] -= regionBounds.x;
        centre[1] -= regionBounds.y;
        // This takes a long time so this should track progress
        ok = addToPsf(maxz, settings.getMagnification(), psf, centre, spot, regionBounds, increment, settings.getCentreEachSlice());
    }
    if (settings.getInteractiveMode()) {
        ImageJUtils.hide(TITLE_INTENSITY);
    }
    IJ.showProgress(1);
    if (!ok || stats.getN() == 0) {
        return;
    }
    final double avSd = getAverage(averageSd, averageA, 2);
    ImageJUtils.log("  Average background = %.2f, Av. SD = %s px", stats.getMean(), MathUtils.rounded(avSd, 4));
    normalise(psf, maxz, avSd * settings.getMagnification(), false);
    IJ.showProgress(1);
    psfImp = ImageJUtils.display(TITLE_PSF, psf);
    psfImp.setSlice(maxz);
    psfImp.resetDisplayRange();
    psfImp.updateAndDraw();
    final double[][] fitCom = new double[2][psf.getSize()];
    Arrays.fill(fitCom[0], Double.NaN);
    Arrays.fill(fitCom[1], Double.NaN);
    final double fittedSd = fitPsf(psf, loess, maxz, averageRange.getMean(), fitCom);
    // Compute the drift in the PSF:
    // - Use fitted centre if available; otherwise find CoM for each frame
    // - express relative to the average centre
    final double[][] com = calculateCentreOfMass(psf, fitCom, nmPerPixel / settings.getMagnification());
    final double[] slice = SimpleArrayUtils.newArray(psf.getSize(), 1, 1.0);
    final String title = TITLE + " CoM Drift";
    final Plot plot = new Plot(title, "Slice", "Drift (nm)");
    plot.addLabel(0, 0, "Red = X; Blue = Y");
    // double[] limitsX = Maths.limits(com[0]);
    // double[] limitsY = Maths.limits(com[1]);
    final double[] limitsX = getLimits(com[0]);
    final double[] limitsY = getLimits(com[1]);
    plot.setLimits(1, psf.getSize(), Math.min(limitsX[0], limitsY[0]), Math.max(limitsX[1], limitsY[1]));
    plot.setColor(Color.red);
    plot.addPoints(slice, com[0], Plot.DOT);
    plot.addPoints(slice, loess.smooth(slice, com[0]), Plot.LINE);
    plot.setColor(Color.blue);
    plot.addPoints(slice, com[1], Plot.DOT);
    plot.addPoints(slice, loess.smooth(slice, com[1]), Plot.LINE);
    ImageJUtils.display(title, plot);
    // TODO - Redraw the PSF with drift correction applied.
    // This means that the final image should have no drift.
    // This is relevant when combining PSF images. It doesn't matter too much for simulations
    // unless the drift is large.
    // Add Image properties containing the PSF details
    final double fwhm = getFwhm(psf, maxz);
    psfImp.setProperty("Info", ImagePsfHelper.toString(ImagePsfHelper.create(maxz, nmPerPixel / settings.getMagnification(), settings.getNmPerSlice(), stats.getN(), fwhm, createNote())));
    ImageJUtils.log("%s : z-centre = %d, nm/Pixel = %s, nm/Slice = %s, %d images, " + "PSF SD = %s nm, FWHM = %s px\n", psfImp.getTitle(), maxz, MathUtils.rounded(nmPerPixel / settings.getMagnification(), 3), MathUtils.rounded(settings.getNmPerSlice(), 3), stats.getN(), MathUtils.rounded(fittedSd * nmPerPixel, 4), MathUtils.rounded(fwhm));
    createInteractivePlots(psf, maxz, nmPerPixel / settings.getMagnification(), fittedSd * nmPerPixel);
    IJ.showStatus("");
}

Example 7 with StoredDataStatistics

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

the class Fire method calculatePrecisionHistogram.

/**
 * Calculate a histogram of the precision. The precision can be either stored in the results or
 * calculated using the Mortensen formula. If the precision method for Q estimation is not fixed
 * then the histogram is fitted with a Gaussian to create an initial estimate.
 *
 * @return The precision histogram
 */
private PrecisionHistogram calculatePrecisionHistogram() {
    final boolean logFitParameters = false;
    final String title = results.getName() + " Precision Histogram";
    // Check if the results has the precision already or if it can be computed.
    final boolean canUseStored = canUseStoredPrecision(results);
    final boolean canCalculatePrecision = canCalculatePrecision(results);
    // Set the method to compute a histogram. Default to the user selected option.
    PrecisionMethod method = null;
    if ((canUseStored && precisionMethod == PrecisionMethod.STORED) || (canCalculatePrecision && precisionMethod == PrecisionMethod.CALCULATE)) {
        method = precisionMethod;
    }
    if (method == null) {
        // We only have two choices so if one is available then select it.
        if (canUseStored) {
            method = PrecisionMethod.STORED;
        } else if (canCalculatePrecision) {
            method = PrecisionMethod.CALCULATE;
        }
        // If the user selected a method not available then log a warning
        if (method != null && precisionMethod != PrecisionMethod.FIXED) {
            IJ.log(String.format("%s : Selected precision method '%s' not available, switching to '%s'", pluginTitle, precisionMethod, method.getName()));
        }
        if (method == null) {
            // This does not matter if the user has provide a fixed input.
            if (precisionMethod == PrecisionMethod.FIXED) {
                final PrecisionHistogram histogram = new PrecisionHistogram(title);
                histogram.mean = settings.mean;
                histogram.sigma = settings.sigma;
                return histogram;
            }
            // No precision
            return null;
        }
    }
    // We get here if we can compute precision.
    // Build the histogram
    StoredDataStatistics precision = new StoredDataStatistics(results.size());
    if (method == PrecisionMethod.STORED) {
        final StoredDataStatistics p = precision;
        results.forEach((PeakResultProcedure) result -> p.add(result.getPrecision()));
    } else {
        precision.add(pp.precisions);
    }
    double yMin = Double.NEGATIVE_INFINITY;
    double yMax = 0;
    // Set the min and max y-values using 1.5 x IQR
    final DescriptiveStatistics stats = precision.getStatistics();
    final double lower = stats.getPercentile(25);
    final double upper = stats.getPercentile(75);
    if (Double.isNaN(lower) || Double.isNaN(upper)) {
        if (logFitParameters) {
            ImageJUtils.log("Error computing IQR: %f - %f", lower, upper);
        }
    } else {
        final double iqr = upper - lower;
        yMin = Math.max(lower - iqr, stats.getMin());
        yMax = Math.min(upper + iqr, stats.getMax());
        if (logFitParameters) {
            ImageJUtils.log("  Data range: %f - %f. Plotting 1.5x IQR: %f - %f", stats.getMin(), stats.getMax(), yMin, yMax);
        }
    }
    if (yMin == Double.NEGATIVE_INFINITY) {
        final int n = 5;
        yMin = Math.max(stats.getMin(), stats.getMean() - n * stats.getStandardDeviation());
        yMax = Math.min(stats.getMax(), stats.getMean() + n * stats.getStandardDeviation());
        if (logFitParameters) {
            ImageJUtils.log("  Data range: %f - %f. Plotting mean +/- %dxSD: %f - %f", stats.getMin(), stats.getMax(), n, yMin, yMax);
        }
    }
    // Get the data within the range
    final double[] data = precision.getValues();
    precision = new StoredDataStatistics(data.length);
    for (final double d : data) {
        if (d < yMin || d > yMax) {
            continue;
        }
        precision.add(d);
    }
    final int histogramBins = HistogramPlot.getBins(precision, HistogramPlot.BinMethod.SCOTT);
    final float[][] hist = HistogramPlot.calcHistogram(precision.getFloatValues(), yMin, yMax, histogramBins);
    final PrecisionHistogram histogram = new PrecisionHistogram(hist, precision, title);
    if (precisionMethod == PrecisionMethod.FIXED) {
        histogram.mean = settings.mean;
        histogram.sigma = settings.sigma;
        return histogram;
    }
    // Fitting of the histogram to produce the initial estimate
    // Extract non-zero data
    float[] x = Arrays.copyOf(hist[0], hist[0].length);
    float[] y = Arrays.copyOf(hist[1], hist[1].length);
    int count = 0;
    for (int i = 0; i < y.length; i++) {
        if (y[i] > 0) {
            x[count] = x[i];
            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
    final double[] stats2 = HistogramPlot.getHistogramStatistics(x, y);
    if (logFitParameters) {
        ImageJUtils.log("  Initial Statistics: %f +/- %f", stats2[0], stats2[1]);
    }
    histogram.mean = stats2[0];
    histogram.sigma = stats2[1];
    // Standard Gaussian fit
    final double[] parameters = fitGaussian(x, y);
    if (parameters == null) {
        ImageJUtils.log("  Failed to fit initial Gaussian");
        return histogram;
    }
    final double newMean = parameters[1];
    final double error = Math.abs(stats2[0] - newMean) / stats2[1];
    if (error > 3) {
        ImageJUtils.log("  Failed to fit Gaussian: %f standard deviations from histogram mean", error);
        return histogram;
    }
    if (newMean < yMin || newMean > yMax) {
        ImageJUtils.log("  Failed to fit Gaussian: %f outside data range %f - %f", newMean, yMin, yMax);
        return histogram;
    }
    if (logFitParameters) {
        ImageJUtils.log("  Initial Gaussian: %f @ %f +/- %f", parameters[0], parameters[1], parameters[2]);
    }
    histogram.mean = parameters[1];
    histogram.sigma = parameters[2];
    return histogram;
}

Example 8 with StoredDataStatistics

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

the class BenchmarkFilterAnalysis method expandFilters.

/**
 * Expand filters. Set the increment for any parameter not expanded to zero. Set the input
 * parameters array to the lower bounds. Set the input parameters2 array to the upper bounds.
 *
 * <p>If a parameter is not expanded since the increment is Infinity the parameter is disabled. If
 * it was not expanded for any other reason (increment is zero, NaN values, etc) the weakest
 * parameter of the two input array is used and set as the lower and upper bounds.
 *
 * @param baseFilter the base filter
 * @param parameters the parameters
 * @param parameters2 the parameters 2
 * @param increment the increment
 * @return the list
 */
private static List<Filter> expandFilters(Filter baseFilter, double[] parameters, double[] parameters2, double[] increment) {
    final int n = baseFilter.getNumberOfParameters();
    if (parameters.length < n || parameters2.length < n || increment.length < n) {
        throw new IllegalArgumentException("Input arrays  must be  at least the length of the number of parameters");
    }
    final double[] increment2 = increment.clone();
    final int capacity = (int) countCombinations(parameters, parameters2, increment);
    final ArrayList<Filter> list = new ArrayList<>(capacity);
    // Initialise with a filter set at the minimum for each parameter.
    // Get the weakest parameters for those not expanded.
    Filter f1 = baseFilter.create(parameters);
    final double[] p = parameters2.clone();
    f1.weakestParameters(p);
    for (int i = 0; i < n; i++) {
        if (increment[i] == 0) {
            // Disable if Infinite increment, otherwise use the weakest parameter
            parameters[i] = parameters2[i] = (Double.isInfinite(increment2[i])) ? baseFilter.getDisabledParameterValue(i) : p[i];
        }
    }
    f1 = baseFilter.create(parameters);
    list.add(f1);
    for (int i = 0; i < n; i++) {
        if (increment[i] == 0) {
            continue;
        }
        final double min = parameters[i];
        final double max = parameters2[i];
        final double inc = increment[i];
        final double max2 = max + inc;
        // Set the upper bounds for the output and store the expansion params
        final StoredDataStatistics stats = new StoredDataStatistics(10);
        for (double value = min + inc; value < max || value - max < max2 - value; value += inc) {
            parameters2[i] = value;
            stats.add(value);
        }
        final double[] values = stats.getValues();
        final ArrayList<Filter> list2 = new ArrayList<>((values.length + 1) * list.size());
        for (int k = 0; k < list.size(); k++) {
            final Filter f = list.get(k);
            // Copy params of the filter
            for (int j = 0; j < n; j++) {
                p[j] = f.getParameterValue(j);
            }
            for (int l = 0; l < values.length; l++) {
                p[i] = values[l];
                list2.add(f.create(p));
            }
        }
        list.addAll(list2);
    }
    // Sort the filters
    Collections.sort(list);
    return list;
}

Example 9 with StoredDataStatistics

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

the class TraceDiffusion method calculateDiffusionCoefficient.

/**
 * Calculate the diffusion coefficient (D) of the molecule. This is done by using the mean-squared
 * deviation between frames divided by the time interval (delta) between frames. This is divided
 * by 4 to produce the diffusion coefficient from two-dimensional distance analysis.
 *
 * <p>See Uphoff, et al, 2013. Single-molecule DNA repair in live bacteria, PNAS 110, 8063-8068
 *
 * @param msdPerMoleculeAdjacent the MSD per molecule adjacent
 * @return The D per molecule
 */
private static StoredDataStatistics calculateDiffusionCoefficient(StoredDataStatistics msdPerMoleculeAdjacent) {
    final StoredDataStatistics dPerMolecule = new StoredDataStatistics();
    final double diffusionCoefficientConversion = 1.0 / 4.0;
    for (final double msd : msdPerMoleculeAdjacent.getValues()) {
        dPerMolecule.add(msd * diffusionCoefficientConversion);
    }
    return dPerMolecule;
}

Example 10 with StoredDataStatistics

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

the class TraceDiffusion method run.

@Override
public void run(String arg) {
    SmlmUsageTracker.recordPlugin(this.getClass(), arg);
    jumpDistanceParametersRef.set(null);
    extraOptions = ImageJUtils.isExtraOptions();
    if (MemoryPeakResults.isMemoryEmpty()) {
        IJ.error(TITLE, "No localisations in memory");
        return;
    }
    settings = Settings.load();
    // Saved by reference so just save now
    settings.save();
    final ArrayList<MemoryPeakResults> allResults = new ArrayList<>();
    // Option to pick multiple input datasets together using a list box.
    if ("multi".equals(arg) && !showMultiDialog(allResults)) {
        return;
    }
    // This shows the dialog for selecting trace options
    if (!showTraceDialog(allResults)) {
        return;
    }
    if (allResults.isEmpty()) {
        return;
    }
    ImageJUtils.log(TITLE + "...");
    // - Trace each single dataset (and store in memory)
    // - Combine trace results held in memory
    final Trace[] traces = getTraces(allResults);
    // This still allows a zero entry in the results table.
    if (traces.length > 0 && !showDialog()) {
        return;
    }
    final int count = traces.length;
    double[] fitMsdResult = null;
    int numberOfDataPoints = 0;
    double[][] jdParams = null;
    if (count > 0) {
        calculatePrecision(traces, allResults.size() > 1);
        // --- MSD Analysis ---
        // Conversion constants
        final double px2ToUm2 = MathUtils.pow2(results.getCalibrationReader().getNmPerPixel()) / 1e6;
        final double px2ToUm2PerSecond = px2ToUm2 / exposureTime;
        // Get the maximum trace length
        int length = clusteringSettings.getMinimumTraceLength();
        if (!clusteringSettings.getTruncate()) {
            for (final Trace trace : traces) {
                if (length < trace.size()) {
                    length = trace.size();
                }
            }
        }
        // Get the localisation error (4s^2) in um^2
        final double error = (clusteringSettings.getPrecisionCorrection()) ? 4 * precision * precision / 1e6 : 0;
        // Pre-calculate MSD correction factors. This accounts for the fact that the distance moved
        // in the start/end frames is reduced due to the averaging of the particle location over the
        // entire frame into a single point. The true MSD may be restored by applying a factor.
        // Note: These are used for the calculation of the diffusion coefficients per molecule and
        // the MSD passed to the Jump Distance analysis. However the error is not included in the
        // jump distance analysis so will be subtracted from the fitted D coefficients later.
        final double[] factors;
        if (clusteringSettings.getMsdCorrection()) {
            factors = new double[length];
            for (int t = 1; t < length; t++) {
                factors[t] = JumpDistanceAnalysis.getConversionfactor(t);
            }
        } else {
            factors = SimpleArrayUtils.newArray(length, 0.0, 1.0);
        }
        // Extract the mean-squared distance statistics
        final Statistics[] stats = new Statistics[length];
        for (int i = 0; i < stats.length; i++) {
            stats[i] = new Statistics();
        }
        final ArrayList<double[]> distances = (settings.saveTraceDistances || settings.displayTraceLength) ? new ArrayList<>(traces.length) : null;
        // Store all the jump distances at the specified interval
        final StoredDataStatistics jumpDistances = new StoredDataStatistics();
        final int jumpDistanceInterval = clusteringSettings.getJumpDistance();
        // Compute squared distances
        final StoredDataStatistics msdPerMoleculeAllVsAll = new StoredDataStatistics();
        final StoredDataStatistics msdPerMoleculeAdjacent = new StoredDataStatistics();
        for (final Trace trace : traces) {
            final PeakResultStoreList results = trace.getPoints();
            // Sum the MSD and the time
            final int traceLength = (clusteringSettings.getTruncate()) ? clusteringSettings.getMinimumTraceLength() : trace.size();
            // Get the mean for each time separation
            final double[] sumDistance = new double[traceLength + 1];
            final double[] sumTime = new double[sumDistance.length];
            // Do the distances to the origin (saving if necessary)
            final float x0 = results.get(0).getXPosition();
            final float y0 = results.get(0).getYPosition();
            if (distances != null) {
                final double[] msd = new double[traceLength - 1];
                for (int j = 1; j < traceLength; j++) {
                    final int t = j;
                    final double d = distance2(x0, y0, results.get(j));
                    msd[j - 1] = px2ToUm2 * d;
                    if (t == jumpDistanceInterval) {
                        jumpDistances.add(msd[j - 1]);
                    }
                    sumDistance[t] += d;
                    sumTime[t] += t;
                }
                distances.add(msd);
            } else {
                for (int j = 1; j < traceLength; j++) {
                    final int t = j;
                    final double d = distance2(x0, y0, results.get(j));
                    if (t == jumpDistanceInterval) {
                        jumpDistances.add(px2ToUm2 * d);
                    }
                    sumDistance[t] += d;
                    sumTime[t] += t;
                }
            }
            if (clusteringSettings.getInternalDistances()) {
                // Do the internal distances
                for (int i = 1; i < traceLength; i++) {
                    final float x = results.get(i).getXPosition();
                    final float y = results.get(i).getYPosition();
                    for (int j = i + 1; j < traceLength; j++) {
                        final int t = j - i;
                        final double d = distance2(x, y, results.get(j));
                        if (t == jumpDistanceInterval) {
                            jumpDistances.add(px2ToUm2 * d);
                        }
                        sumDistance[t] += d;
                        sumTime[t] += t;
                    }
                }
                // Add the average distance per time separation to the population
                for (int t = 1; t < traceLength; t++) {
                    // Note: (traceLength - t) == count
                    stats[t].add(sumDistance[t] / (traceLength - t));
                }
            } else {
                // Add the distance per time separation to the population
                for (int t = 1; t < traceLength; t++) {
                    stats[t].add(sumDistance[t]);
                }
            }
            // Fix this for the precision and MSD adjustment.
            // It may be necessary to:
            // - sum the raw distances for each time interval (this is sumDistance[t])
            // - subtract the precision error
            // - apply correction factor for the n-frames to get actual MSD
            // - sum the actual MSD
            double sumD = 0;
            final double sumD_adjacent = Math.max(0, sumDistance[1] - error) * factors[1];
            double sumT = 0;
            final double sumT_adjacent = sumTime[1];
            for (int t = 1; t < traceLength; t++) {
                sumD += Math.max(0, sumDistance[t] - error) * factors[t];
                sumT += sumTime[t];
            }
            // Calculate the average displacement for the trace (do not simply use the largest
            // time separation since this will miss moving molecules that end up at the origin)
            msdPerMoleculeAllVsAll.add(px2ToUm2PerSecond * sumD / sumT);
            msdPerMoleculeAdjacent.add(px2ToUm2PerSecond * sumD_adjacent / sumT_adjacent);
        }
        StoredDataStatistics dperMoleculeAllVsAll = null;
        StoredDataStatistics dperMoleculeAdjacent = null;
        if (settings.saveTraceDistances || (clusteringSettings.getShowHistograms() && settings.displayDHistogram)) {
            dperMoleculeAllVsAll = calculateDiffusionCoefficient(msdPerMoleculeAllVsAll);
            dperMoleculeAdjacent = calculateDiffusionCoefficient(msdPerMoleculeAdjacent);
        }
        if (settings.saveTraceDistances) {
            saveTraceDistances(traces.length, distances, msdPerMoleculeAllVsAll, msdPerMoleculeAdjacent, dperMoleculeAllVsAll, dperMoleculeAdjacent);
        }
        if (settings.displayTraceLength) {
            final StoredDataStatistics lengths = calculateTraceLengths(distances);
            showHistogram(lengths, "Trace length (um)");
        }
        if (settings.displayTraceSize) {
            final StoredDataStatistics sizes = calculateTraceSizes(traces);
            showHistogram(sizes, "Trace size", true);
        }
        // Plot the per-trace histogram of MSD and D
        if (clusteringSettings.getShowHistograms()) {
            if (settings.displayMsdHistogram) {
                showHistogram(msdPerMoleculeAllVsAll, "MSD/Molecule (all-vs-all)");
                showHistogram(msdPerMoleculeAdjacent, "MSD/Molecule (adjacent)");
            }
            if (settings.displayDHistogram) {
                showHistogram(dperMoleculeAllVsAll, "D/Molecule (all-vs-all)");
                showHistogram(dperMoleculeAdjacent, "D/Molecule (adjacent)");
            }
        }
        // Calculate the mean squared distance (MSD)
        final double[] x = new double[stats.length];
        final double[] y = new double[x.length];
        final double[] sd = new double[x.length];
        // Intercept is the 4s^2 (in um^2)
        y[0] = 4 * precision * precision / 1e6;
        for (int i = 1; i < stats.length; i++) {
            x[i] = i * exposureTime;
            y[i] = stats[i].getMean() * px2ToUm2;
            // sd[i] = stats[i].getStandardDeviation() * px2ToUm2;
            sd[i] = stats[i].getStandardError() * px2ToUm2;
        }
        final String title = TITLE + " MSD";
        final Plot plot = plotMsd(x, y, sd, title);
        // Fit the MSD using a linear fit
        fitMsdResult = fitMsd(x, y, title, plot);
        // Jump Distance analysis
        if (settings.saveRawData) {
            saveStatistics(jumpDistances, "Jump Distance", "Distance (um^2)", false);
        }
        // Calculate the cumulative jump-distance histogram
        final double[][] jdHistogram = JumpDistanceAnalysis.cumulativeHistogram(jumpDistances.getValues());
        // Always show the jump distance histogram
        jdTitle = TITLE + " Jump Distance";
        jdPlot = new Plot(jdTitle, "Distance (um^2)", "Cumulative Probability");
        jdPlot.addPoints(jdHistogram[0], jdHistogram[1], Plot.LINE);
        display(jdTitle, jdPlot);
        // Fit Jump Distance cumulative probability
        numberOfDataPoints = jumpDistances.getN();
        jdParams = fitJumpDistance(jumpDistances, jdHistogram);
        jumpDistanceParametersRef.set(jdParams);
    }
    summarise(traces, fitMsdResult, numberOfDataPoints, jdParams);
}