Examples with MoleculeModel uk.ac.sussex.gdsc.smlm.model.MoleculeModel used on opensource projects

Example 1 with MoleculeModel

use of uk.ac.sussex.gdsc.smlm.model.MoleculeModel in project GDSC-SMLM by aherbert.

the class CreateData method createCompoundMolecules.

private List<CompoundMoleculeModel> createCompoundMolecules() {
    // Diffusion rate is um^2/sec. Convert to pixels per simulation frame.
    final double diffusionFactor = (1000000.0 / (settings.getPixelPitch() * settings.getPixelPitch())) / settings.getStepsPerSecond();
    List<CompoundMoleculeModel> compounds;
    if (settings.getCompoundMolecules()) {
        // Try and load the compounds from the text specification
        try {
            // Convert from the serialised objects to the compound model
            final String text = settings.getCompoundText();
            final Mixture.Builder builder = Mixture.newBuilder();
            TextFormat.merge(text, builder);
            compounds = new ArrayList<>(builder.getMoleculeCount());
            int id = 1;
            compoundNames = new ArrayList<>(builder.getMoleculeCount());
            for (final Molecule m : builder.getMoleculeList()) {
                final MoleculeModel[] molecules = new MoleculeModel[m.getAtomCount()];
                for (int i = 0; i < molecules.length; i++) {
                    final AtomOrBuilder a = m.getAtomOrBuilder(i);
                    molecules[i] = new MoleculeModel(a.getMass(), a.getX(), a.getY(), a.getZ());
                }
                final CompoundMoleculeModel cm = new CompoundMoleculeModel(id++, 0, 0, 0, Arrays.asList(molecules));
                cm.setFraction(m.getFraction());
                cm.setDiffusionRate(m.getDiffusionRate() * diffusionFactor);
                cm.setDiffusionType(DiffusionType.fromString(m.getDiffusionType()));
                compounds.add(cm);
                compoundNames.add(String.format("Fraction=%s, D=%s um^2/s", MathUtils.rounded(cm.getFraction()), MathUtils.rounded(m.getDiffusionRate())));
            }
            // Convert coordinates from nm to pixels
            final double scaleFactor = 1.0 / settings.getPixelPitch();
            for (final CompoundMoleculeModel c : compounds) {
                c.scale(scaleFactor);
            }
        } catch (final IOException ex) {
            IJ.error(TITLE, "Unable to create compound molecules");
            return null;
        }
    } else {
        // Create a simple compound with one molecule at the origin
        compounds = new ArrayList<>(1);
        final CompoundMoleculeModel m = new CompoundMoleculeModel(1, 0, 0, 0, Arrays.asList(new MoleculeModel(0, 0, 0, 0)));
        m.setDiffusionRate(settings.getDiffusionRate() * diffusionFactor);
        m.setDiffusionType(CreateDataSettingsHelper.getDiffusionType(settings.getDiffusionType()));
        compounds.add(m);
    }
    return compounds;
}

Example 2 with MoleculeModel

use of uk.ac.sussex.gdsc.smlm.model.MoleculeModel in project GDSC-SMLM by aherbert.

the class CreateData method convertRelativeToAbsolute.

/**
 * Update the fluorophores relative coordinates to absolute.
 *
 * @param molecules the molecules
 */
@SuppressWarnings("unused")
private static void convertRelativeToAbsolute(List<CompoundMoleculeModel> molecules) {
    for (final CompoundMoleculeModel c : molecules) {
        final double[] xyz = c.getCoordinates();
        for (int n = c.getSize(); n-- > 0; ) {
            final MoleculeModel m = c.getMolecule(n);
            final double[] xyz2 = m.getCoordinates();
            for (int i = 0; i < 3; i++) {
                xyz2[i] += xyz[i];
            }
        }
    }
}

Example 3 with MoleculeModel

use of uk.ac.sussex.gdsc.smlm.model.MoleculeModel in project GDSC-SMLM by aherbert.

the class BlinkEstimatorTest method estimateBlinking.

private TIntHashSet estimateBlinking(UniformRandomProvider rg, double blinkingRate, double ton, double toff, int particles, double fixedFraction, boolean timeAtLowerBound, boolean doAssert) {
    Assumptions.assumeTrue(TestSettings.allow(TestComplexity.MAXIMUM));
    final SpatialIllumination activationIllumination = new UniformIllumination(100);
    int totalSteps = 100;
    final double eAct = totalSteps * 0.3 * activationIllumination.getAveragePhotons();
    final ImageModel imageModel = new ActivationEnergyImageModel(eAct, activationIllumination, ton, 0, toff, 0, blinkingRate, rg);
    final double[] max = new double[] { 256, 256, 32 };
    final double[] min = new double[3];
    final SpatialDistribution distribution = new UniformDistribution(min, max, rg.nextInt());
    final List<CompoundMoleculeModel> compounds = new ArrayList<>(1);
    final CompoundMoleculeModel c = new CompoundMoleculeModel(1, 0, 0, 0, Arrays.asList(new MoleculeModel(0, 0, 0, 0)));
    c.setDiffusionRate(diffusionRate);
    c.setDiffusionType(DiffusionType.RANDOM_WALK);
    compounds.add(c);
    final List<CompoundMoleculeModel> molecules = imageModel.createMolecules(compounds, particles, distribution, false);
    // Activate fluorophores
    final List<? extends FluorophoreSequenceModel> fluorophores = imageModel.createFluorophores(molecules, totalSteps);
    totalSteps = checkTotalSteps(totalSteps, fluorophores);
    final List<LocalisationModel> localisations = imageModel.createImage(molecules, fixedFraction, totalSteps, photons, 0.5, false);
    // // Remove localisations to simulate missed counts.
    // List<LocalisationModel> newLocalisations = new
    // ArrayList<LocalisationModel>(localisations.size());
    // boolean[] id = new boolean[fluorophores.size() + 1];
    // Statistics photonStats = new Statistics();
    // for (LocalisationModel l : localisations)
    // {
    // photonStats.add(l.getIntensity());
    // // Remove by intensity threshold and optionally at random.
    // if (l.getIntensity() < minPhotons || rand.nextDouble() < pDelete)
    // continue;
    // newLocalisations.add(l);
    // id[l.getId()] = true;
    // }
    // localisations = newLocalisations;
    // logger.info("Photons = %f", photonStats.getMean());
    // 
    // List<FluorophoreSequenceModel> newFluorophores = new
    // ArrayList<FluorophoreSequenceModel>(fluorophores.size());
    // for (FluorophoreSequenceModel f : fluorophores)
    // {
    // if (id[f.getId()])
    // newFluorophores.add(f);
    // }
    // fluorophores = newFluorophores;
    final MemoryPeakResults results = new MemoryPeakResults();
    final CalibrationWriter calibration = new CalibrationWriter();
    calibration.setNmPerPixel(pixelPitch);
    calibration.setExposureTime(msPerFrame);
    calibration.setCountPerPhoton(1);
    results.setCalibration(calibration.getCalibration());
    results.setPsf(PsfHelper.create(PSFType.ONE_AXIS_GAUSSIAN_2D));
    final float b = 0;
    float intensity;
    final float z = 0;
    for (final LocalisationModel l : localisations) {
        // Remove by intensity threshold and optionally at random.
        if (l.getIntensity() < minPhotons || rg.nextDouble() < probabilityDelete) {
            continue;
        }
        final int frame = l.getTime();
        intensity = (float) l.getIntensity();
        final float x = (float) l.getX();
        final float y = (float) l.getY();
        final float[] params = Gaussian2DPeakResultHelper.createParams(b, intensity, x, y, z, psfWidth);
        results.add(frame, 0, 0, 0, 0, 0, 0, params, null);
    }
    // Add random localisations
    // Intensity doesn't matter at the moment for tracing
    intensity = (float) photons;
    for (int i = (int) (localisations.size() * probabilityAdd); i-- > 0; ) {
        final int frame = 1 + rg.nextInt(totalSteps);
        final float x = (float) (rg.nextDouble() * max[0]);
        final float y = (float) (rg.nextDouble() * max[1]);
        final float[] params = Gaussian2DPeakResultHelper.createParams(b, intensity, x, y, z, psfWidth);
        results.add(frame, 0, 0, 0, 0, 0, 0, params, null);
    }
    // Get actual simulated stats ...
    final Statistics statsNBlinks = new Statistics();
    final Statistics statsTOn = new Statistics();
    final Statistics statsTOff = new Statistics();
    final Statistics statsSampledNBlinks = new Statistics();
    final Statistics statsSampledTOn = new Statistics();
    final StoredDataStatistics statsSampledTOff = new StoredDataStatistics();
    for (final FluorophoreSequenceModel f : fluorophores) {
        statsNBlinks.add(f.getNumberOfBlinks());
        statsTOn.add(f.getOnTimes());
        statsTOff.add(f.getOffTimes());
        final int[] on = f.getSampledOnTimes();
        statsSampledNBlinks.add(on.length);
        statsSampledTOn.add(on);
        statsSampledTOff.add(f.getSampledOffTimes());
    }
    logger.info(FunctionUtils.getSupplier("N = %d (%d), N-blinks = %f, tOn = %f, tOff = %f, Fixed = %f", fluorophores.size(), localisations.size(), blinkingRate, ton, toff, fixedFraction));
    logger.info(FunctionUtils.getSupplier("Actual N-blinks = %f (%f), tOn = %f (%f), tOff = %f (%f), 95%% = %f, max = %f", statsNBlinks.getMean(), statsSampledNBlinks.getMean(), statsTOn.getMean(), statsSampledTOn.getMean(), statsTOff.getMean(), statsSampledTOff.getMean(), statsSampledTOff.getStatistics().getPercentile(95), statsSampledTOff.getStatistics().getMax()));
    logger.info("-=-=--=-");
    final BlinkEstimator be = new BlinkEstimator();
    be.setMaxDarkTime((int) (toff * 10));
    be.setMsPerFrame(msPerFrame);
    be.setRelativeDistance(false);
    final double d = ImageModel.getRandomMoveDistance(diffusionRate);
    be.setSearchDistance((fixedFraction < 1) ? Math.sqrt(2 * d * d) * 3 : 0);
    be.setTimeAtLowerBound(timeAtLowerBound);
    // Assertions.assertTrue("Max dark time must exceed the dark time of the data (otherwise no
    // plateau)",
    // be.maxDarkTime > statsSampledTOff.getStatistics().getMax());
    final int nMolecules = fluorophores.size();
    if (usePopulationStatistics) {
        blinkingRate = statsNBlinks.getMean();
        toff = statsTOff.getMean();
    } else {
        blinkingRate = statsSampledNBlinks.getMean();
        toff = statsSampledTOff.getMean();
    }
    // See if any fitting regime gets a correct answer
    final TIntHashSet ok = new TIntHashSet();
    for (int numberOfFittedPoints = MIN_FITTED_POINTS; numberOfFittedPoints <= MAX_FITTED_POINTS; numberOfFittedPoints++) {
        be.setNumberOfFittedPoints(numberOfFittedPoints);
        be.computeBlinkingRate(results, true);
        final double moleculesError = DoubleEquality.relativeError(nMolecules, be.getNMolecules());
        final double blinksError = DoubleEquality.relativeError(blinkingRate, be.getNBlinks());
        final double offError = DoubleEquality.relativeError(toff * msPerFrame, be.getTOff());
        logger.info(FunctionUtils.getSupplier("Error %d: N = %f, blinks = %f, tOff = %f : %f", numberOfFittedPoints, moleculesError, blinksError, offError, (moleculesError + blinksError + offError) / 3));
        if (moleculesError < relativeError && blinksError < relativeError && offError < relativeError) {
            ok.add(numberOfFittedPoints);
            logger.info("-=-=--=-");
            logger.info(FunctionUtils.getSupplier("*** Correct at %d fitted points ***", numberOfFittedPoints));
            if (doAssert) {
                break;
            }
        }
    // if (!be.isIncreaseNFittedPoints())
    // break;
    }
    logger.info("-=-=--=-");
    if (doAssert) {
        Assertions.assertFalse(ok.isEmpty());
    }
    // relativeError);
    return ok;
}

Example 4 with MoleculeModel

use of uk.ac.sussex.gdsc.smlm.model.MoleculeModel in project GDSC-SMLM by aherbert.

the class DiffusionRateTest method showExample.

private void showExample(int totalSteps, double diffusionSigma, UniformRandomProvider rng) {
    final MoleculeModel m = new MoleculeModel(0, new double[3]);
    final float[] xValues = new float[totalSteps];
    final float[] x = new float[totalSteps];
    final float[] y = new float[totalSteps];
    final DiffusionType diffusionType = CreateDataSettingsHelper.getDiffusionType(settings.getDiffusionType());
    double[] axis;
    if (diffusionType == DiffusionType.LINEAR_WALK) {
        axis = nextVector(SamplerUtils.createNormalizedGaussianSampler(rng));
    } else {
        axis = null;
    }
    for (int j = 0; j < totalSteps; j++) {
        if (diffusionType == DiffusionType.GRID_WALK) {
            m.walk(diffusionSigma, rng);
        } else if (diffusionType == DiffusionType.LINEAR_WALK) {
            m.slide(diffusionSigma, axis, rng);
        } else {
            m.move(diffusionSigma, rng);
        }
        x[j] = (float) (m.getX());
        y[j] = (float) (m.getY());
        xValues[j] = (float) ((j + 1) / settings.getStepsPerSecond());
    }
    // Plot x and y coords on a timeline
    final String title = TITLE + " example coordinates";
    final Plot plot = new Plot(title, "Time (seconds)", "Distance (um)");
    final float[] xUm = convertToUm(x);
    final float[] yUm = convertToUm(y);
    float[] limits = MathUtils.limits(xUm);
    limits = MathUtils.limits(limits, yUm);
    plot.setLimits(0, totalSteps / settings.getStepsPerSecond(), limits[0], limits[1]);
    plot.setColor(Color.red);
    plot.addPoints(xValues, xUm, Plot.LINE);
    plot.setColor(Color.blue);
    plot.addPoints(xValues, yUm, Plot.LINE);
    ImageJUtils.display(title, plot);
    // Scale up and draw 2D position
    for (int j = 0; j < totalSteps; j++) {
        x[j] *= pluginSettings.magnification;
        y[j] *= pluginSettings.magnification;
    }
    final float[] limitsx = getLimits(x);
    final float[] limitsy = getLimits(y);
    int width = (int) (limitsx[1] - limitsx[0]);
    int height = (int) (limitsy[1] - limitsy[0]);
    // Ensure we draw something, even it is a simple dot at the centre for no diffusion
    if (width == 0) {
        width = (int) (32 * pluginSettings.magnification);
        limitsx[0] = -width / 2.0f;
    }
    if (height == 0) {
        height = (int) (32 * pluginSettings.magnification);
        limitsy[0] = -height / 2.0f;
    }
    final ImageProcessor ip = new ByteProcessor(width, height);
    // Adjust x and y using the minimum to centre
    x[0] -= limitsx[0];
    y[0] -= limitsy[0];
    for (int j = 1; j < totalSteps; j++) {
        // Adjust x and y using the minimum to centre
        x[j] -= limitsx[0];
        y[j] -= limitsy[0];
        // Draw a line
        ip.setColor(32 + (223 * j) / (totalSteps - 1));
        ip.drawLine(round(x[j - 1]), round(y[j - 1]), round(x[j]), round(y[j]));
    }
    // Draw the final position
    ip.putPixel(round(x[totalSteps - 1]), round(y[totalSteps - 1]), 255);
    final ImagePlus imp = ImageJUtils.display(TITLE + " example", ip);
    // Apply the fire lookup table
    WindowManager.setTempCurrentImage(imp);
    final LutLoader lut = new LutLoader();
    lut.run("fire");
    WindowManager.setTempCurrentImage(null);
}

Example 5 with MoleculeModel

use of uk.ac.sussex.gdsc.smlm.model.MoleculeModel in project GDSC-SMLM by aherbert.

the class DiffusionRateTest method run.

@Override
public void run(String arg) {
    SmlmUsageTracker.recordPlugin(this.getClass(), arg);
    pluginSettings = Settings.load();
    pluginSettings.save();
    if (IJ.controlKeyDown()) {
        simpleTest();
        return;
    }
    extraOptions = ImageJUtils.isExtraOptions();
    if (!showDialog()) {
        return;
    }
    lastSimulation.set(null);
    final int totalSteps = (int) Math.ceil(settings.getSeconds() * settings.getStepsPerSecond());
    conversionFactor = 1000000.0 / (settings.getPixelPitch() * settings.getPixelPitch());
    // Diffusion rate is um^2/sec. Convert to pixels per simulation frame.
    final double diffusionRateInPixelsPerSecond = settings.getDiffusionRate() * conversionFactor;
    final double diffusionRateInPixelsPerStep = diffusionRateInPixelsPerSecond / settings.getStepsPerSecond();
    final double precisionInPixels = myPrecision / settings.getPixelPitch();
    final boolean addError = myPrecision != 0;
    ImageJUtils.log(TITLE + " : D = %s um^2/sec, Precision = %s nm", MathUtils.rounded(settings.getDiffusionRate(), 4), MathUtils.rounded(myPrecision, 4));
    ImageJUtils.log("Mean-displacement per dimension = %s nm/sec", MathUtils.rounded(1e3 * ImageModel.getRandomMoveDistance(settings.getDiffusionRate()), 4));
    if (extraOptions) {
        ImageJUtils.log("Step size = %s, precision = %s", MathUtils.rounded(ImageModel.getRandomMoveDistance(diffusionRateInPixelsPerStep)), MathUtils.rounded(precisionInPixels));
    }
    // Convert diffusion co-efficient into the standard deviation for the random walk
    final DiffusionType diffusionType = CreateDataSettingsHelper.getDiffusionType(settings.getDiffusionType());
    final double diffusionSigma = ImageModel.getRandomMoveDistance(diffusionRateInPixelsPerStep);
    ImageJUtils.log("Simulation step-size = %s nm", MathUtils.rounded(settings.getPixelPitch() * diffusionSigma, 4));
    // Move the molecules and get the diffusion rate
    IJ.showStatus("Simulating ...");
    final long start = System.nanoTime();
    final UniformRandomProvider random = UniformRandomProviders.create();
    final Statistics[] stats2D = new Statistics[totalSteps];
    final Statistics[] stats3D = new Statistics[totalSteps];
    final StoredDataStatistics jumpDistances2D = new StoredDataStatistics(totalSteps);
    final StoredDataStatistics jumpDistances3D = new StoredDataStatistics(totalSteps);
    for (int j = 0; j < totalSteps; j++) {
        stats2D[j] = new Statistics();
        stats3D[j] = new Statistics();
    }
    final SphericalDistribution dist = new SphericalDistribution(settings.getConfinementRadius() / settings.getPixelPitch());
    final Statistics asymptote = new Statistics();
    // Save results to memory
    final MemoryPeakResults results = new MemoryPeakResults(totalSteps);
    results.setCalibration(CalibrationHelper.create(settings.getPixelPitch(), 1, 1000.0 / settings.getStepsPerSecond()));
    results.setName(TITLE);
    results.setPsf(PsfHelper.create(PSFType.CUSTOM));
    int peak = 0;
    // Store raw coordinates
    final ArrayList<Point> points = new ArrayList<>(totalSteps);
    final StoredData totalJumpDistances1D = new StoredData(settings.getParticles());
    final StoredData totalJumpDistances2D = new StoredData(settings.getParticles());
    final StoredData totalJumpDistances3D = new StoredData(settings.getParticles());
    final NormalizedGaussianSampler gauss = SamplerUtils.createNormalizedGaussianSampler(random);
    for (int i = 0; i < settings.getParticles(); i++) {
        if (i % 16 == 0) {
            IJ.showProgress(i, settings.getParticles());
            if (ImageJUtils.isInterrupted()) {
                return;
            }
        }
        // Increment the frame so that tracing analysis can distinguish traces
        peak++;
        double[] origin = new double[3];
        final int id = i + 1;
        final MoleculeModel m = new MoleculeModel(id, origin.clone());
        if (addError) {
            origin = addError(origin, precisionInPixels, gauss);
        }
        if (pluginSettings.useConfinement) {
            // Note: When using confinement the average displacement should asymptote
            // at the average distance of a point from the centre of a ball. This is 3r/4.
            // See: http://answers.yahoo.com/question/index?qid=20090131162630AAMTUfM
            // The equivalent in 2D is 2r/3. However although we are plotting 2D distance
            // this is a projection of the 3D position onto the plane and so the particles
            // will not be evenly spread (there will be clustering at centre caused by the
            // poles)
            final double[] axis = (diffusionType == DiffusionType.LINEAR_WALK) ? nextVector(gauss) : null;
            for (int j = 0; j < totalSteps; j++) {
                double[] xyz = m.getCoordinates();
                final double[] originalXyz = xyz.clone();
                for (int n = pluginSettings.confinementAttempts; n-- > 0; ) {
                    if (diffusionType == DiffusionType.GRID_WALK) {
                        m.walk(diffusionSigma, random);
                    } else if (diffusionType == DiffusionType.LINEAR_WALK) {
                        m.slide(diffusionSigma, axis, random);
                    } else {
                        m.move(diffusionSigma, random);
                    }
                    if (!dist.isWithin(m.getCoordinates())) {
                        // Reset position
                        for (int k = 0; k < 3; k++) {
                            xyz[k] = originalXyz[k];
                        }
                    } else {
                        // The move was allowed
                        break;
                    }
                }
                points.add(new Point(id, xyz));
                if (addError) {
                    xyz = addError(xyz, precisionInPixels, gauss);
                }
                peak = record(xyz, id, peak, stats2D[j], stats3D[j], jumpDistances2D, jumpDistances3D, origin, results);
            }
            asymptote.add(distance(m.getCoordinates()));
        } else if (diffusionType == DiffusionType.GRID_WALK) {
            for (int j = 0; j < totalSteps; j++) {
                m.walk(diffusionSigma, random);
                double[] xyz = m.getCoordinates();
                points.add(new Point(id, xyz));
                if (addError) {
                    xyz = addError(xyz, precisionInPixels, gauss);
                }
                peak = record(xyz, id, peak, stats2D[j], stats3D[j], jumpDistances2D, jumpDistances3D, origin, results);
            }
        } else if (diffusionType == DiffusionType.LINEAR_WALK) {
            final double[] axis = nextVector(gauss);
            for (int j = 0; j < totalSteps; j++) {
                m.slide(diffusionSigma, axis, random);
                double[] xyz = m.getCoordinates();
                points.add(new Point(id, xyz));
                if (addError) {
                    xyz = addError(xyz, precisionInPixels, gauss);
                }
                peak = record(xyz, id, peak, stats2D[j], stats3D[j], jumpDistances2D, jumpDistances3D, origin, results);
            }
        } else {
            for (int j = 0; j < totalSteps; j++) {
                m.move(diffusionSigma, random);
                double[] xyz = m.getCoordinates();
                points.add(new Point(id, xyz));
                if (addError) {
                    xyz = addError(xyz, precisionInPixels, gauss);
                }
                peak = record(xyz, id, peak, stats2D[j], stats3D[j], jumpDistances2D, jumpDistances3D, origin, results);
            }
        }
        // Debug: record all the particles so they can be analysed
        // System.out.printf("%f %f %f\n", m.getX(), m.getY(), m.getZ());
        final double[] xyz = m.getCoordinates();
        double d2 = 0;
        totalJumpDistances1D.add(d2 = xyz[0] * xyz[0]);
        totalJumpDistances2D.add(d2 += xyz[1] * xyz[1]);
        totalJumpDistances3D.add(d2 += xyz[2] * xyz[2]);
    }
    final long nanoseconds = System.nanoTime() - start;
    IJ.showProgress(1);
    MemoryPeakResults.addResults(results);
    simulation = new SimulationData(results.getName(), myPrecision);
    // Convert pixels^2/step to um^2/sec
    final double msd2D = (jumpDistances2D.getMean() / conversionFactor) / (results.getCalibrationReader().getExposureTime() / 1000);
    final double msd3D = (jumpDistances3D.getMean() / conversionFactor) / (results.getCalibrationReader().getExposureTime() / 1000);
    ImageJUtils.log("Raw data D=%s um^2/s, Precision = %s nm, N=%d, step=%s s, mean2D=%s um^2, " + "MSD 2D = %s um^2/s, mean3D=%s um^2, MSD 3D = %s um^2/s", MathUtils.rounded(settings.getDiffusionRate()), MathUtils.rounded(myPrecision), jumpDistances2D.getN(), MathUtils.rounded(results.getCalibrationReader().getExposureTime() / 1000), MathUtils.rounded(jumpDistances2D.getMean() / conversionFactor), MathUtils.rounded(msd2D), MathUtils.rounded(jumpDistances3D.getMean() / conversionFactor), MathUtils.rounded(msd3D));
    aggregateIntoFrames(points, addError, precisionInPixels, gauss);
    IJ.showStatus("Analysing results ...");
    if (pluginSettings.showDiffusionExample) {
        showExample(totalSteps, diffusionSigma, random);
    }
    // Plot a graph of mean squared distance
    final double[] xValues = new double[stats2D.length];
    final double[] yValues2D = new double[stats2D.length];
    final double[] yValues3D = new double[stats3D.length];
    final double[] upper2D = new double[stats2D.length];
    final double[] lower2D = new double[stats2D.length];
    final double[] upper3D = new double[stats3D.length];
    final double[] lower3D = new double[stats3D.length];
    final SimpleRegression r2D = new SimpleRegression(false);
    final SimpleRegression r3D = new SimpleRegression(false);
    final int firstN = (pluginSettings.useConfinement) ? pluginSettings.fitN : totalSteps;
    for (int j = 0; j < totalSteps; j++) {
        // Convert steps to seconds
        xValues[j] = (j + 1) / settings.getStepsPerSecond();
        // Convert values in pixels^2 to um^2
        final double mean2D = stats2D[j].getMean() / conversionFactor;
        final double mean3D = stats3D[j].getMean() / conversionFactor;
        final double sd2D = stats2D[j].getStandardDeviation() / conversionFactor;
        final double sd3D = stats3D[j].getStandardDeviation() / conversionFactor;
        yValues2D[j] = mean2D;
        yValues3D[j] = mean3D;
        upper2D[j] = mean2D + sd2D;
        lower2D[j] = mean2D - sd2D;
        upper3D[j] = mean3D + sd3D;
        lower3D[j] = mean3D - sd3D;
        if (j < firstN) {
            r2D.addData(xValues[j], yValues2D[j]);
            r3D.addData(xValues[j], yValues3D[j]);
        }
    }
    // TODO - Fit using the equation for 2D confined diffusion:
    // MSD = 4s^2 + R^2 (1 - 0.99e^(-1.84^2 Dt / R^2)
    // s = localisation precision
    // R = confinement radius
    // D = 2D diffusion coefficient
    // t = time
    final PolynomialFunction fitted2D;
    final PolynomialFunction fitted3D;
    if (r2D.getN() > 0) {
        // Do linear regression to get diffusion rate
        final double[] best2D = new double[] { r2D.getIntercept(), r2D.getSlope() };
        fitted2D = new PolynomialFunction(best2D);
        final double[] best3D = new double[] { r3D.getIntercept(), r3D.getSlope() };
        fitted3D = new PolynomialFunction(best3D);
        // For 2D diffusion: d^2 = 4D
        // where: d^2 = mean-square displacement
        double diffCoeff = best2D[1] / 4.0;
        final String msg = "2D Diffusion rate = " + MathUtils.rounded(diffCoeff, 4) + " um^2 / sec (" + TextUtils.nanosToString(nanoseconds) + ")";
        IJ.showStatus(msg);
        ImageJUtils.log(msg);
        diffCoeff = best3D[1] / 6.0;
        ImageJUtils.log("3D Diffusion rate = " + MathUtils.rounded(diffCoeff, 4) + " um^2 / sec (" + TextUtils.nanosToString(nanoseconds) + ")");
    } else {
        fitted2D = fitted3D = null;
    }
    // Create plots
    plotMsd(totalSteps, xValues, yValues2D, lower2D, upper2D, fitted2D, 2);
    plotMsd(totalSteps, xValues, yValues3D, lower3D, upper3D, fitted3D, 3);
    plotJumpDistances(TITLE, jumpDistances2D, 2, 1);
    plotJumpDistances(TITLE, jumpDistances3D, 3, 1);
    // Show the total jump length for debugging
    // plotJumpDistances(TITLE + " total", totalJumpDistances1D, 1, totalSteps);
    // plotJumpDistances(TITLE + " total", totalJumpDistances2D, 2, totalSteps);
    // plotJumpDistances(TITLE + " total", totalJumpDistances3D, 3, totalSteps);
    windowOrganiser.tile();
    if (pluginSettings.useConfinement) {
        ImageJUtils.log("3D asymptote distance = %s nm (expected %.2f)", MathUtils.rounded(asymptote.getMean() * settings.getPixelPitch(), 4), 3 * settings.getConfinementRadius() / 4);
    }
}