Examples with LoessInterpolator org.apache.commons.math3.analysis.interpolation.LoessInterpolator used on opensource projects

Example 6 with LoessInterpolator

use of org.apache.commons.math3.analysis.interpolation.LoessInterpolator in project GDSC-SMLM by aherbert.

the class FIRE method runQEstimation.

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

Example 7 with LoessInterpolator

use of org.apache.commons.math3.analysis.interpolation.LoessInterpolator in project GDSC-SMLM by aherbert.

the class BenchmarkFilterAnalysis method depthAnalysis.

/**
	 * Depth analysis.
	 *
	 * @param allAssignments
	 *            The assignments generated from running the filter (or null)
	 * @param filter
	 *            the filter
	 * @return the assignments
	 */
private ArrayList<FractionalAssignment[]> depthAnalysis(ArrayList<FractionalAssignment[]> allAssignments, DirectFilter filter) {
    if (!depthRecallAnalysis || simulationParameters.fixedDepth)
        return null;
    // Build a histogram of the number of spots at different depths
    final double[] depths = depthStats.getValues();
    double[] limits = Maths.limits(depths);
    //final int bins = Math.max(10, nActual / 100);
    //final int bins = Utils.getBinsSturges(depths.length);
    final int bins = Utils.getBinsSqrt(depths.length);
    double[][] h1 = Utils.calcHistogram(depths, limits[0], limits[1], bins);
    double[][] h2 = Utils.calcHistogram(depthFitStats.getValues(), limits[0], limits[1], bins);
    // manually to get the results that pass.
    if (allAssignments == null)
        allAssignments = getAssignments(filter);
    double[] depths2 = new double[results.size()];
    int count = 0;
    for (FractionalAssignment[] assignments : allAssignments) {
        if (assignments == null)
            continue;
        for (int i = 0; i < assignments.length; i++) {
            final CustomFractionalAssignment c = (CustomFractionalAssignment) assignments[i];
            depths2[count++] = c.peak.error;
        }
    }
    depths2 = Arrays.copyOf(depths2, count);
    // Build a histogram using the same limits
    double[][] h3 = Utils.calcHistogram(depths2, limits[0], limits[1], bins);
    // Convert pixel depth to nm
    for (int i = 0; i < h1[0].length; i++) h1[0][i] *= simulationParameters.a;
    limits[0] *= simulationParameters.a;
    limits[1] *= simulationParameters.a;
    // Produce a histogram of the number of spots at each depth
    String title1 = TITLE + " Depth Histogram";
    Plot2 plot1 = new Plot2(title1, "Depth (nm)", "Frequency");
    plot1.setLimits(limits[0], limits[1], 0, Maths.max(h1[1]));
    plot1.setColor(Color.black);
    plot1.addPoints(h1[0], h1[1], Plot2.BAR);
    plot1.addLabel(0, 0, "Black = Spots; Blue = Fitted; Red = Filtered");
    plot1.setColor(Color.blue);
    plot1.addPoints(h1[0], h2[1], Plot2.BAR);
    plot1.setColor(Color.red);
    plot1.addPoints(h1[0], h3[1], Plot2.BAR);
    plot1.setColor(Color.magenta);
    PlotWindow pw1 = Utils.display(title1, plot1);
    if (Utils.isNewWindow())
        wo.add(pw1);
    // Interpolate
    final double halfBinWidth = (h1[0][1] - h1[0][0]) * 0.5;
    // Remove final value of the histogram as this is at the upper limit of the range (i.e. count zero)
    h1[0] = Arrays.copyOf(h1[0], h1[0].length - 1);
    h1[1] = Arrays.copyOf(h1[1], h1[0].length);
    h2[1] = Arrays.copyOf(h2[1], h1[0].length);
    h3[1] = Arrays.copyOf(h3[1], h1[0].length);
    // TODO : Fix the smoothing since LOESS sometimes does not work.
    // Perhaps allow configuration of the number of histogram bins and the smoothing bandwidth.
    // Use minimum of 3 points for smoothing
    // Ensure we use at least x% of data
    double bandwidth = Math.max(3.0 / h1[0].length, 0.15);
    LoessInterpolator loess = new LoessInterpolator(bandwidth, 1);
    PolynomialSplineFunction spline1 = loess.interpolate(h1[0], h1[1]);
    PolynomialSplineFunction spline2 = loess.interpolate(h1[0], h2[1]);
    PolynomialSplineFunction spline3 = loess.interpolate(h1[0], h3[1]);
    // Use a second interpolator in case the LOESS fails
    LinearInterpolator lin = new LinearInterpolator();
    PolynomialSplineFunction spline1b = lin.interpolate(h1[0], h1[1]);
    PolynomialSplineFunction spline2b = lin.interpolate(h1[0], h2[1]);
    PolynomialSplineFunction spline3b = lin.interpolate(h1[0], h3[1]);
    // Increase the number of points to show a smooth curve
    double[] points = new double[bins * 5];
    limits = Maths.limits(h1[0]);
    final double interval = (limits[1] - limits[0]) / (points.length - 1);
    double[] v = new double[points.length];
    double[] v2 = new double[points.length];
    double[] v3 = new double[points.length];
    for (int i = 0; i < points.length - 1; i++) {
        points[i] = limits[0] + i * interval;
        v[i] = getSplineValue(spline1, spline1b, points[i]);
        v2[i] = getSplineValue(spline2, spline2b, points[i]);
        v3[i] = getSplineValue(spline3, spline3b, points[i]);
        points[i] += halfBinWidth;
    }
    // Final point on the limit of the spline range
    int ii = points.length - 1;
    v[ii] = getSplineValue(spline1, spline1b, limits[1]);
    v2[ii] = getSplineValue(spline2, spline2b, limits[1]);
    v3[ii] = getSplineValue(spline3, spline3b, limits[1]);
    points[ii] = limits[1] + halfBinWidth;
    // Calculate recall
    for (int i = 0; i < v.length; i++) {
        v2[i] = v2[i] / v[i];
        v3[i] = v3[i] / v[i];
    }
    final double halfSummaryDepth = summaryDepth * 0.5;
    String title2 = TITLE + " Depth Histogram (normalised)";
    Plot2 plot2 = new Plot2(title2, "Depth (nm)", "Recall");
    plot2.setLimits(limits[0] + halfBinWidth, limits[1] + halfBinWidth, 0, Maths.min(1, Maths.max(v2)));
    plot2.setColor(Color.black);
    plot2.addLabel(0, 0, "Blue = Fitted; Red = Filtered");
    plot2.setColor(Color.blue);
    plot2.addPoints(points, v2, Plot2.LINE);
    plot2.setColor(Color.red);
    plot2.addPoints(points, v3, Plot2.LINE);
    plot2.setColor(Color.magenta);
    if (-halfSummaryDepth - halfBinWidth >= limits[0]) {
        plot2.drawLine(-halfSummaryDepth, 0, -halfSummaryDepth, getSplineValue(spline3, spline3b, -halfSummaryDepth - halfBinWidth) / getSplineValue(spline1, spline1b, -halfSummaryDepth - halfBinWidth));
    }
    if (halfSummaryDepth - halfBinWidth <= limits[1]) {
        plot2.drawLine(halfSummaryDepth, 0, halfSummaryDepth, getSplineValue(spline3, spline3b, halfSummaryDepth - halfBinWidth) / getSplineValue(spline1, spline1b, halfSummaryDepth - halfBinWidth));
    }
    PlotWindow pw2 = Utils.display(title2, plot2);
    if (Utils.isNewWindow())
        wo.add(pw2);
    return allAssignments;
}

Example 8 with LoessInterpolator

use of org.apache.commons.math3.analysis.interpolation.LoessInterpolator in project GDSC-SMLM by aherbert.

the class PSFDrift method computeDrift.

private void computeDrift() {
    // Create a grid of XY offset positions between 0-1 for PSF insert
    final double[] grid = new double[gridSize];
    for (int i = 0; i < grid.length; i++) grid[i] = (double) i / gridSize;
    // Configure fitting region
    final int w = 2 * regionSize + 1;
    centrePixel = w / 2;
    // Check region size using the image PSF
    double newPsfWidth = (double) imp.getWidth() / scale;
    if (Math.ceil(newPsfWidth) > w)
        Utils.log(TITLE + ": Fitted region size (%d) is smaller than the scaled PSF (%.1f)", w, newPsfWidth);
    // Create robust PSF fitting settings
    final double a = psfSettings.nmPerPixel * scale;
    final double sa = PSFCalculator.squarePixelAdjustment(psfSettings.nmPerPixel * (psfSettings.fwhm / Gaussian2DFunction.SD_TO_FWHM_FACTOR), a);
    fitConfig.setInitialPeakStdDev(sa / a);
    fitConfig.setBackgroundFitting(backgroundFitting);
    fitConfig.setNotSignalFitting(false);
    fitConfig.setComputeDeviations(false);
    fitConfig.setDisableSimpleFilter(true);
    // Create the PSF over the desired z-depth
    int depth = (int) Math.round(zDepth / psfSettings.nmPerSlice);
    int startSlice = psfSettings.zCentre - depth;
    int endSlice = psfSettings.zCentre + depth;
    int nSlices = imp.getStackSize();
    startSlice = (startSlice < 1) ? 1 : (startSlice > nSlices) ? nSlices : startSlice;
    endSlice = (endSlice < 1) ? 1 : (endSlice > nSlices) ? nSlices : endSlice;
    ImagePSFModel psf = createImagePSF(startSlice, endSlice);
    int minz = startSlice - psfSettings.zCentre;
    int maxz = endSlice - psfSettings.zCentre;
    final int nZ = maxz - minz + 1;
    final int gridSize2 = grid.length * grid.length;
    total = nZ * gridSize2;
    // Store all the fitting results
    int nStartPoints = getNumberOfStartPoints();
    results = new double[total * nStartPoints][];
    // TODO - Add ability to iterate this, adjusting the current offset in the PSF
    // each iteration
    // Create a pool of workers
    int nThreads = Prefs.getThreads();
    BlockingQueue<Job> jobs = new ArrayBlockingQueue<Job>(nThreads * 2);
    List<Worker> workers = new LinkedList<Worker>();
    List<Thread> threads = new LinkedList<Thread>();
    for (int i = 0; i < nThreads; i++) {
        Worker worker = new Worker(jobs, psf, w, fitConfig);
        Thread t = new Thread(worker);
        workers.add(worker);
        threads.add(t);
        t.start();
    }
    // Fit 
    Utils.showStatus("Fitting ...");
    final int step = Utils.getProgressInterval(total);
    outer: for (int z = minz, i = 0; z <= maxz; z++) {
        for (int x = 0; x < grid.length; x++) for (int y = 0; y < grid.length; y++, i++) {
            if (IJ.escapePressed()) {
                break outer;
            }
            put(jobs, new Job(z, grid[x], grid[y], i));
            if (i % step == 0) {
                IJ.showProgress(i, total);
            }
        }
    }
    // If escaped pressed then do not need to stop the workers, just return
    if (Utils.isInterrupted()) {
        IJ.showProgress(1);
        return;
    }
    // Finish all the worker threads by passing in a null job
    for (int i = 0; i < threads.size(); i++) {
        put(jobs, new Job());
    }
    // Wait for all to finish
    for (int i = 0; i < threads.size(); i++) {
        try {
            threads.get(i).join();
        } catch (InterruptedException e) {
            e.printStackTrace();
        }
    }
    threads.clear();
    IJ.showProgress(1);
    IJ.showStatus("");
    // Plot the average and SE for the drift curve
    // Plot the recall
    double[] zPosition = new double[nZ];
    double[] avX = new double[nZ];
    double[] seX = new double[nZ];
    double[] avY = new double[nZ];
    double[] seY = new double[nZ];
    double[] recall = new double[nZ];
    for (int z = minz, i = 0; z <= maxz; z++, i++) {
        Statistics statsX = new Statistics();
        Statistics statsY = new Statistics();
        for (int s = 0; s < nStartPoints; s++) {
            int resultPosition = i * gridSize2 + s * total;
            final int endResultPosition = resultPosition + gridSize2;
            while (resultPosition < endResultPosition) {
                if (results[resultPosition] != null) {
                    statsX.add(results[resultPosition][0]);
                    statsY.add(results[resultPosition][1]);
                }
                resultPosition++;
            }
        }
        zPosition[i] = z * psfSettings.nmPerSlice;
        avX[i] = statsX.getMean();
        seX[i] = statsX.getStandardError();
        avY[i] = statsY.getMean();
        seY[i] = statsY.getStandardError();
        recall[i] = (double) statsX.getN() / (nStartPoints * gridSize2);
    }
    // Find the range from the z-centre above the recall limit 
    int centre = 0;
    for (int slice = startSlice, i = 0; slice <= endSlice; slice++, i++) {
        if (slice == psfSettings.zCentre) {
            centre = i;
            break;
        }
    }
    if (recall[centre] < recallLimit)
        return;
    int start = centre, end = centre;
    for (int i = centre; i-- > 0; ) {
        if (recall[i] < recallLimit)
            break;
        start = i;
    }
    for (int i = centre; ++i < recall.length; ) {
        if (recall[i] < recallLimit)
            break;
        end = i;
    }
    int iterations = 1;
    LoessInterpolator loess = null;
    if (smoothing > 0)
        loess = new LoessInterpolator(smoothing, iterations);
    double[][] smoothx = displayPlot("Drift X", "X (nm)", zPosition, avX, seX, loess, start, end);
    double[][] smoothy = displayPlot("Drift Y", "Y (nm)", zPosition, avY, seY, loess, start, end);
    displayPlot("Recall", "Recall", zPosition, recall, null, null, start, end);
    WindowOrganiser wo = new WindowOrganiser();
    wo.tileWindows(idList);
    // Ask the user if they would like to store them in the image
    GenericDialog gd = new GenericDialog(TITLE);
    gd.enableYesNoCancel();
    gd.hideCancelButton();
    startSlice = psfSettings.zCentre - (centre - start);
    endSlice = psfSettings.zCentre + (end - centre);
    gd.addMessage(String.format("Save the drift to the PSF?\n \nSlices %d (%s nm) - %d (%s nm) above recall limit", startSlice, Utils.rounded(zPosition[start]), endSlice, Utils.rounded(zPosition[end])));
    gd.addMessage("Optionally average the end points to set drift outside the limits.\n(Select zero to ignore)");
    gd.addSlider("Number_of_points", 0, 10, positionsToAverage);
    gd.showDialog();
    if (gd.wasOKed()) {
        positionsToAverage = Math.abs((int) gd.getNextNumber());
        ArrayList<PSFOffset> offset = new ArrayList<PSFOffset>();
        final double pitch = psfSettings.nmPerPixel;
        int j = 0, jj = 0;
        for (int i = start, slice = startSlice; i <= end; slice++, i++) {
            j = findCentre(zPosition[i], smoothx, j);
            if (j == -1) {
                Utils.log("Failed to find the offset for depth %.2f", zPosition[i]);
                continue;
            }
            // The offset should store the difference to the centre in pixels so divide by the pixel pitch
            double cx = smoothx[1][j] / pitch;
            double cy = smoothy[1][j] / pitch;
            jj = findOffset(slice, jj);
            if (jj != -1) {
                cx += psfSettings.offset[jj].cx;
                cy += psfSettings.offset[jj].cy;
            }
            offset.add(new PSFOffset(slice, cx, cy));
        }
        addMissingOffsets(startSlice, endSlice, nSlices, offset);
        psfSettings.offset = offset.toArray(new PSFOffset[offset.size()]);
        psfSettings.addNote(TITLE, String.format("Solver=%s, Region=%d", PeakFit.getSolverName(fitConfig), regionSize));
        imp.setProperty("Info", XmlUtils.toXML(psfSettings));
    }
}