Examples with FastCorrelator gdsc.core.utils.FastCorrelator used on opensource projects

Example 1 with FastCorrelator

use of gdsc.core.utils.FastCorrelator in project GDSC-SMLM by aherbert.

the class BenchmarkSpotFit method summariseResults.

private void summariseResults(TIntObjectHashMap<FilterCandidates> filterCandidates, long runTime, final PreprocessedPeakResult[] preprocessedPeakResults, int nUniqueIDs) {
    createTable();
    // Summarise the fitting results. N fits, N failures. 
    // Optimal match statistics if filtering is perfect (since fitting is not perfect).
    StoredDataStatistics distanceStats = new StoredDataStatistics();
    StoredDataStatistics depthStats = new StoredDataStatistics();
    // Get stats for all fitted results and those that match 
    // Signal, SNR, Width, xShift, yShift, Precision
    createFilterCriteria();
    StoredDataStatistics[][] stats = new StoredDataStatistics[3][filterCriteria.length];
    for (int i = 0; i < stats.length; i++) for (int j = 0; j < stats[i].length; j++) stats[i][j] = new StoredDataStatistics();
    final double nmPerPixel = simulationParameters.a;
    double tp = 0, fp = 0;
    int failcTP = 0, failcFP = 0;
    int cTP = 0, cFP = 0;
    int[] singleStatus = null, multiStatus = null, doubletStatus = null, multiDoubletStatus = null;
    singleStatus = new int[FitStatus.values().length];
    multiStatus = new int[singleStatus.length];
    doubletStatus = new int[singleStatus.length];
    multiDoubletStatus = new int[singleStatus.length];
    // Easier to materialise the values since we have a lot of non final variables to manipulate
    final int[] frames = new int[filterCandidates.size()];
    final FilterCandidates[] candidates = new FilterCandidates[filterCandidates.size()];
    final int[] counter = new int[1];
    filterCandidates.forEachEntry(new TIntObjectProcedure<FilterCandidates>() {

        public boolean execute(int a, FilterCandidates b) {
            frames[counter[0]] = a;
            candidates[counter[0]] = b;
            counter[0]++;
            return true;
        }
    });
    for (FilterCandidates result : candidates) {
        // Count the number of fit results that matched (tp) and did not match (fp)
        tp += result.tp;
        fp += result.fp;
        for (int i = 0; i < result.fitResult.length; i++) {
            if (result.spots[i].match)
                cTP++;
            else
                cFP++;
            final MultiPathFitResult fitResult = result.fitResult[i];
            if (singleStatus != null && result.spots[i].match) {
                // Debugging reasons for fit failure
                addStatus(singleStatus, fitResult.getSingleFitResult());
                addStatus(multiStatus, fitResult.getMultiFitResult());
                addStatus(doubletStatus, fitResult.getDoubletFitResult());
                addStatus(multiDoubletStatus, fitResult.getMultiDoubletFitResult());
            }
            if (noMatch(fitResult)) {
                if (result.spots[i].match)
                    failcTP++;
                else
                    failcFP++;
            }
            // We have multi-path results.
            // We want statistics for:
            // [0] all fitted spots
            // [1] fitted spots that match a result
            // [2] fitted spots that do not match a result
            addToStats(fitResult.getSingleFitResult(), stats);
            addToStats(fitResult.getMultiFitResult(), stats);
            addToStats(fitResult.getDoubletFitResult(), stats);
            addToStats(fitResult.getMultiDoubletFitResult(), stats);
        }
        // Statistics on spots that fit an actual result
        for (int i = 0; i < result.match.length; i++) {
            if (!result.match[i].isFitResult())
                // For now just ignore the candidates that matched
                continue;
            FitMatch fitMatch = (FitMatch) result.match[i];
            distanceStats.add(fitMatch.d * nmPerPixel);
            depthStats.add(fitMatch.z * nmPerPixel);
        }
    }
    // Store data for computing correlation
    double[] i1 = new double[depthStats.getN()];
    double[] i2 = new double[i1.length];
    double[] is = new double[i1.length];
    int ci = 0;
    for (FilterCandidates result : candidates) {
        for (int i = 0; i < result.match.length; i++) {
            if (!result.match[i].isFitResult())
                // For now just ignore the candidates that matched
                continue;
            FitMatch fitMatch = (FitMatch) result.match[i];
            ScoredSpot spot = result.spots[fitMatch.i];
            i1[ci] = fitMatch.predictedSignal;
            i2[ci] = fitMatch.actualSignal;
            is[ci] = spot.spot.intensity;
            ci++;
        }
    }
    // We want to compute the Jaccard against the spot metric
    // Filter the results using the multi-path filter
    ArrayList<MultiPathFitResults> multiPathResults = new ArrayList<MultiPathFitResults>(filterCandidates.size());
    for (int i = 0; i < frames.length; i++) {
        int frame = frames[i];
        MultiPathFitResult[] multiPathFitResults = candidates[i].fitResult;
        int totalCandidates = candidates[i].spots.length;
        int nActual = actualCoordinates.get(frame).size();
        multiPathResults.add(new MultiPathFitResults(frame, multiPathFitResults, totalCandidates, nActual));
    }
    // Score the results and count the number returned
    List<FractionalAssignment[]> assignments = new ArrayList<FractionalAssignment[]>();
    final TIntHashSet set = new TIntHashSet(nUniqueIDs);
    FractionScoreStore scoreStore = new FractionScoreStore() {

        public void add(int uniqueId) {
            set.add(uniqueId);
        }
    };
    MultiPathFitResults[] multiResults = multiPathResults.toArray(new MultiPathFitResults[multiPathResults.size()]);
    // Filter with no filter
    MultiPathFilter mpf = new MultiPathFilter(new SignalFilter(0), null, multiFilter.residualsThreshold);
    FractionClassificationResult fractionResult = mpf.fractionScoreSubset(multiResults, Integer.MAX_VALUE, this.results.size(), assignments, scoreStore, CoordinateStoreFactory.create(imp.getWidth(), imp.getHeight(), fitConfig.getDuplicateDistance()));
    double nPredicted = fractionResult.getTP() + fractionResult.getFP();
    final double[][] matchScores = new double[set.size()][];
    int count = 0;
    for (int i = 0; i < assignments.size(); i++) {
        FractionalAssignment[] a = assignments.get(i);
        if (a == null)
            continue;
        for (int j = 0; j < a.length; j++) {
            final PreprocessedPeakResult r = ((PeakFractionalAssignment) a[j]).peakResult;
            set.remove(r.getUniqueId());
            final double precision = Math.sqrt(r.getLocationVariance());
            final double signal = r.getSignal();
            final double snr = r.getSNR();
            final double width = r.getXSDFactor();
            final double xShift = r.getXRelativeShift2();
            final double yShift = r.getYRelativeShift2();
            // Since these two are combined for filtering and the max is what matters.
            final double shift = (xShift > yShift) ? Math.sqrt(xShift) : Math.sqrt(yShift);
            final double eshift = Math.sqrt(xShift + yShift);
            final double[] score = new double[8];
            score[FILTER_SIGNAL] = signal;
            score[FILTER_SNR] = snr;
            score[FILTER_MIN_WIDTH] = width;
            score[FILTER_MAX_WIDTH] = width;
            score[FILTER_SHIFT] = shift;
            score[FILTER_ESHIFT] = eshift;
            score[FILTER_PRECISION] = precision;
            score[FILTER_PRECISION + 1] = a[j].getScore();
            matchScores[count++] = score;
        }
    }
    // Add the rest
    set.forEach(new CustomTIntProcedure(count) {

        public boolean execute(int uniqueId) {
            // This should not be null or something has gone wrong
            PreprocessedPeakResult r = preprocessedPeakResults[uniqueId];
            if (r == null)
                throw new RuntimeException("Missing result: " + uniqueId);
            final double precision = Math.sqrt(r.getLocationVariance());
            final double signal = r.getSignal();
            final double snr = r.getSNR();
            final double width = r.getXSDFactor();
            final double xShift = r.getXRelativeShift2();
            final double yShift = r.getYRelativeShift2();
            // Since these two are combined for filtering and the max is what matters.
            final double shift = (xShift > yShift) ? Math.sqrt(xShift) : Math.sqrt(yShift);
            final double eshift = Math.sqrt(xShift + yShift);
            final double[] score = new double[8];
            score[FILTER_SIGNAL] = signal;
            score[FILTER_SNR] = snr;
            score[FILTER_MIN_WIDTH] = width;
            score[FILTER_MAX_WIDTH] = width;
            score[FILTER_SHIFT] = shift;
            score[FILTER_ESHIFT] = eshift;
            score[FILTER_PRECISION] = precision;
            matchScores[c++] = score;
            return true;
        }
    });
    // Debug the reasons the fit failed
    if (singleStatus != null) {
        String name = PeakFit.getSolverName(fitConfig);
        if (fitConfig.getFitSolver() == FitSolver.MLE && fitConfig.isModelCamera())
            name += " Camera";
        System.out.println("Failure counts: " + name);
        printFailures("Single", singleStatus);
        printFailures("Multi", multiStatus);
        printFailures("Doublet", doubletStatus);
        printFailures("Multi doublet", multiDoubletStatus);
    }
    StringBuilder sb = new StringBuilder(300);
    // Add information about the simulation
    //(simulationParameters.minSignal + simulationParameters.maxSignal) * 0.5;
    final double signal = simulationParameters.signalPerFrame;
    final int n = results.size();
    sb.append(imp.getStackSize()).append("\t");
    final int w = imp.getWidth();
    final int h = imp.getHeight();
    sb.append(w).append("\t");
    sb.append(h).append("\t");
    sb.append(n).append("\t");
    double density = ((double) n / imp.getStackSize()) / (w * h) / (simulationParameters.a * simulationParameters.a / 1e6);
    sb.append(Utils.rounded(density)).append("\t");
    sb.append(Utils.rounded(signal)).append("\t");
    sb.append(Utils.rounded(simulationParameters.s)).append("\t");
    sb.append(Utils.rounded(simulationParameters.a)).append("\t");
    sb.append(Utils.rounded(simulationParameters.depth)).append("\t");
    sb.append(simulationParameters.fixedDepth).append("\t");
    sb.append(Utils.rounded(simulationParameters.gain)).append("\t");
    sb.append(Utils.rounded(simulationParameters.readNoise)).append("\t");
    sb.append(Utils.rounded(simulationParameters.b)).append("\t");
    sb.append(Utils.rounded(simulationParameters.b2)).append("\t");
    // Compute the noise
    double noise = simulationParameters.b2;
    if (simulationParameters.emCCD) {
        // The b2 parameter was computed without application of the EM-CCD noise factor of 2.
        //final double b2 = backgroundVariance + readVariance
        //                = simulationParameters.b + readVariance
        // This should be applied only to the background variance.
        final double readVariance = noise - simulationParameters.b;
        noise = simulationParameters.b * 2 + readVariance;
    }
    if (simulationParameters.fullSimulation) {
    // The total signal is spread over frames
    }
    sb.append(Utils.rounded(signal / Math.sqrt(noise))).append("\t");
    sb.append(Utils.rounded(simulationParameters.s / simulationParameters.a)).append("\t");
    sb.append(spotFilter.getDescription());
    // nP and nN is the fractional score of the spot candidates 
    addCount(sb, nP + nN);
    addCount(sb, nP);
    addCount(sb, nN);
    addCount(sb, fP);
    addCount(sb, fN);
    String name = PeakFit.getSolverName(fitConfig);
    if (fitConfig.getFitSolver() == FitSolver.MLE && fitConfig.isModelCamera())
        name += " Camera";
    add(sb, name);
    add(sb, config.getFitting());
    resultPrefix = sb.toString();
    // Q. Should I add other fit configuration here?
    // The fraction of positive and negative candidates that were included
    add(sb, (100.0 * cTP) / nP);
    add(sb, (100.0 * cFP) / nN);
    // Score the fitting results compared to the original simulation.
    // Score the candidate selection:
    add(sb, cTP + cFP);
    add(sb, cTP);
    add(sb, cFP);
    // TP are all candidates that can be matched to a spot
    // FP are all candidates that cannot be matched to a spot
    // FN = The number of missed spots
    FractionClassificationResult m = new FractionClassificationResult(cTP, cFP, 0, simulationParameters.molecules - cTP);
    add(sb, m.getRecall());
    add(sb, m.getPrecision());
    add(sb, m.getF1Score());
    add(sb, m.getJaccard());
    // Score the fitting results:
    add(sb, failcTP);
    add(sb, failcFP);
    // TP are all fit results that can be matched to a spot
    // FP are all fit results that cannot be matched to a spot
    // FN = The number of missed spots
    add(sb, tp);
    add(sb, fp);
    m = new FractionClassificationResult(tp, fp, 0, simulationParameters.molecules - tp);
    add(sb, m.getRecall());
    add(sb, m.getPrecision());
    add(sb, m.getF1Score());
    add(sb, m.getJaccard());
    // Do it again but pretend we can perfectly filter all the false positives
    //add(sb, tp);
    m = new FractionClassificationResult(tp, 0, 0, simulationParameters.molecules - tp);
    // Recall is unchanged
    // Precision will be 100%
    add(sb, m.getF1Score());
    add(sb, m.getJaccard());
    // The mean may be subject to extreme outliers so use the median
    double median = distanceStats.getMedian();
    add(sb, median);
    WindowOrganiser wo = new WindowOrganiser();
    String label = String.format("Recall = %s. n = %d. Median = %s nm. SD = %s nm", Utils.rounded(m.getRecall()), distanceStats.getN(), Utils.rounded(median), Utils.rounded(distanceStats.getStandardDeviation()));
    int id = Utils.showHistogram(TITLE, distanceStats, "Match Distance (nm)", 0, 0, 0, label);
    if (Utils.isNewWindow())
        wo.add(id);
    median = depthStats.getMedian();
    add(sb, median);
    // Sort by spot intensity and produce correlation
    int[] indices = Utils.newArray(i1.length, 0, 1);
    if (showCorrelation)
        Sort.sort(indices, is, rankByIntensity);
    double[] r = (showCorrelation) ? new double[i1.length] : null;
    double[] sr = (showCorrelation) ? new double[i1.length] : null;
    double[] rank = (showCorrelation) ? new double[i1.length] : null;
    ci = 0;
    FastCorrelator fastCorrelator = new FastCorrelator();
    ArrayList<Ranking> pc1 = new ArrayList<Ranking>();
    ArrayList<Ranking> pc2 = new ArrayList<Ranking>();
    for (int ci2 : indices) {
        fastCorrelator.add((long) Math.round(i1[ci2]), (long) Math.round(i2[ci2]));
        pc1.add(new Ranking(i1[ci2], ci));
        pc2.add(new Ranking(i2[ci2], ci));
        if (showCorrelation) {
            r[ci] = fastCorrelator.getCorrelation();
            sr[ci] = Correlator.correlation(rank(pc1), rank(pc2));
            if (rankByIntensity)
                rank[ci] = is[0] - is[ci];
            else
                rank[ci] = ci;
        }
        ci++;
    }
    final double pearsonCorr = fastCorrelator.getCorrelation();
    final double rankedCorr = Correlator.correlation(rank(pc1), rank(pc2));
    // Get the regression
    SimpleRegression regression = new SimpleRegression(false);
    for (int i = 0; i < pc1.size(); i++) regression.addData(pc1.get(i).value, pc2.get(i).value);
    //final double intercept = regression.getIntercept();
    final double slope = regression.getSlope();
    if (showCorrelation) {
        String title = TITLE + " Intensity";
        Plot plot = new Plot(title, "Candidate", "Spot");
        double[] limits1 = Maths.limits(i1);
        double[] limits2 = Maths.limits(i2);
        plot.setLimits(limits1[0], limits1[1], limits2[0], limits2[1]);
        label = String.format("Correlation=%s; Ranked=%s; Slope=%s", Utils.rounded(pearsonCorr), Utils.rounded(rankedCorr), Utils.rounded(slope));
        plot.addLabel(0, 0, label);
        plot.setColor(Color.red);
        plot.addPoints(i1, i2, Plot.DOT);
        if (slope > 1)
            plot.drawLine(limits1[0], limits1[0] * slope, limits1[1], limits1[1] * slope);
        else
            plot.drawLine(limits2[0] / slope, limits2[0], limits2[1] / slope, limits2[1]);
        PlotWindow pw = Utils.display(title, plot);
        if (Utils.isNewWindow())
            wo.add(pw);
        title = TITLE + " Correlation";
        plot = new Plot(title, "Spot Rank", "Correlation");
        double[] xlimits = Maths.limits(rank);
        double[] ylimits = Maths.limits(r);
        ylimits = Maths.limits(ylimits, sr);
        plot.setLimits(xlimits[0], xlimits[1], ylimits[0], ylimits[1]);
        plot.setColor(Color.red);
        plot.addPoints(rank, r, Plot.LINE);
        plot.setColor(Color.blue);
        plot.addPoints(rank, sr, Plot.LINE);
        plot.setColor(Color.black);
        plot.addLabel(0, 0, label);
        pw = Utils.display(title, plot);
        if (Utils.isNewWindow())
            wo.add(pw);
    }
    add(sb, pearsonCorr);
    add(sb, rankedCorr);
    add(sb, slope);
    label = String.format("n = %d. Median = %s nm", depthStats.getN(), Utils.rounded(median));
    id = Utils.showHistogram(TITLE, depthStats, "Match Depth (nm)", 0, 1, 0, label);
    if (Utils.isNewWindow())
        wo.add(id);
    // Plot histograms of the stats on the same window
    double[] lower = new double[filterCriteria.length];
    double[] upper = new double[lower.length];
    min = new double[lower.length];
    max = new double[lower.length];
    for (int i = 0; i < stats[0].length; i++) {
        double[] limits = showDoubleHistogram(stats, i, wo, matchScores, nPredicted);
        lower[i] = limits[0];
        upper[i] = limits[1];
        min[i] = limits[2];
        max[i] = limits[3];
    }
    // Reconfigure some of the range limits
    // Make this a bit bigger
    upper[FILTER_SIGNAL] *= 2;
    // Make this a bit bigger
    upper[FILTER_SNR] *= 2;
    double factor = 0.25;
    if (lower[FILTER_MIN_WIDTH] != 0)
        // (assuming lower is less than 1)
        upper[FILTER_MIN_WIDTH] = 1 - Math.max(0, factor * (1 - lower[FILTER_MIN_WIDTH]));
    if (upper[FILTER_MIN_WIDTH] != 0)
        // (assuming upper is more than 1)
        lower[FILTER_MAX_WIDTH] = 1 + Math.max(0, factor * (upper[FILTER_MAX_WIDTH] - 1));
    // Round the ranges
    final double[] interval = new double[stats[0].length];
    interval[FILTER_SIGNAL] = SignalFilter.DEFAULT_INCREMENT;
    interval[FILTER_SNR] = SNRFilter.DEFAULT_INCREMENT;
    interval[FILTER_MIN_WIDTH] = WidthFilter2.DEFAULT_MIN_INCREMENT;
    interval[FILTER_MAX_WIDTH] = WidthFilter.DEFAULT_INCREMENT;
    interval[FILTER_SHIFT] = ShiftFilter.DEFAULT_INCREMENT;
    interval[FILTER_ESHIFT] = EShiftFilter.DEFAULT_INCREMENT;
    interval[FILTER_PRECISION] = PrecisionFilter.DEFAULT_INCREMENT;
    interval[FILTER_ITERATIONS] = 0.1;
    interval[FILTER_EVALUATIONS] = 0.1;
    // Create a range increment
    double[] increment = new double[lower.length];
    for (int i = 0; i < increment.length; i++) {
        lower[i] = Maths.floor(lower[i], interval[i]);
        upper[i] = Maths.ceil(upper[i], interval[i]);
        double range = upper[i] - lower[i];
        // Allow clipping if the range is small compared to the min increment
        double multiples = range / interval[i];
        // Use 8 multiples for the equivalent of +/- 4 steps around the centre
        if (multiples < 8) {
            multiples = Math.ceil(multiples);
        } else
            multiples = 8;
        increment[i] = Maths.ceil(range / multiples, interval[i]);
        if (i == FILTER_MIN_WIDTH)
            // Requires clipping based on the upper limit
            lower[i] = upper[i] - increment[i] * multiples;
        else
            upper[i] = lower[i] + increment[i] * multiples;
    }
    for (int i = 0; i < stats[0].length; i++) {
        lower[i] = Maths.round(lower[i]);
        upper[i] = Maths.round(upper[i]);
        min[i] = Maths.round(min[i]);
        max[i] = Maths.round(max[i]);
        increment[i] = Maths.round(increment[i]);
        sb.append("\t").append(min[i]).append(':').append(lower[i]).append('-').append(upper[i]).append(':').append(max[i]);
    }
    // Disable some filters
    increment[FILTER_SIGNAL] = Double.POSITIVE_INFINITY;
    //increment[FILTER_SHIFT] = Double.POSITIVE_INFINITY;
    increment[FILTER_ESHIFT] = Double.POSITIVE_INFINITY;
    wo.tile();
    sb.append("\t").append(Utils.timeToString(runTime / 1000000.0));
    summaryTable.append(sb.toString());
    if (saveFilterRange) {
        GlobalSettings gs = SettingsManager.loadSettings();
        FilterSettings filterSettings = gs.getFilterSettings();
        String filename = (silent) ? filterSettings.filterSetFilename : Utils.getFilename("Filter_range_file", filterSettings.filterSetFilename);
        if (filename == null)
            return;
        // Remove extension to store the filename
        filename = Utils.replaceExtension(filename, ".xml");
        filterSettings.filterSetFilename = filename;
        // Create a filter set using the ranges
        ArrayList<Filter> filters = new ArrayList<Filter>(3);
        filters.add(new MultiFilter2(lower[0], (float) lower[1], lower[2], lower[3], lower[4], lower[5], lower[6]));
        filters.add(new MultiFilter2(upper[0], (float) upper[1], upper[2], upper[3], upper[4], upper[5], upper[6]));
        filters.add(new MultiFilter2(increment[0], (float) increment[1], increment[2], increment[3], increment[4], increment[5], increment[6]));
        if (saveFilters(filename, filters))
            SettingsManager.saveSettings(gs);
        // Create a filter set using the min/max and the initial bounds.
        // Set sensible limits
        min[FILTER_SIGNAL] = Math.max(min[FILTER_SIGNAL], 30);
        max[FILTER_PRECISION] = Math.min(max[FILTER_PRECISION], 100);
        // Commented this out so that the 4-set filters are the same as the 3-set filters.
        // The difference leads to differences when optimising.
        //			// Use half the initial bounds (hoping this is a good starting guess for the optimum)
        //			final boolean[] limitToLower = new boolean[min.length];
        //			limitToLower[FILTER_SIGNAL] = true;
        //			limitToLower[FILTER_SNR] = true;
        //			limitToLower[FILTER_MIN_WIDTH] = true;
        //			limitToLower[FILTER_MAX_WIDTH] = false;
        //			limitToLower[FILTER_SHIFT] = false;
        //			limitToLower[FILTER_ESHIFT] = false;
        //			limitToLower[FILTER_PRECISION] = true;
        //			for (int i = 0; i < limitToLower.length; i++)
        //			{
        //				final double range = (upper[i] - lower[i]) / 2;
        //				if (limitToLower[i])
        //					upper[i] = lower[i] + range;
        //				else
        //					lower[i] = upper[i] - range;
        //			}
        filters = new ArrayList<Filter>(4);
        filters.add(new MultiFilter2(min[0], (float) min[1], min[2], min[3], min[4], min[5], min[6]));
        filters.add(new MultiFilter2(lower[0], (float) lower[1], lower[2], lower[3], lower[4], lower[5], lower[6]));
        filters.add(new MultiFilter2(upper[0], (float) upper[1], upper[2], upper[3], upper[4], upper[5], upper[6]));
        filters.add(new MultiFilter2(max[0], (float) max[1], max[2], max[3], max[4], max[5], max[6]));
        saveFilters(Utils.replaceExtension(filename, ".4.xml"), filters);
    }
}

Example 2 with FastCorrelator

use of gdsc.core.utils.FastCorrelator in project GDSC-SMLM by aherbert.

the class BenchmarkSpotFilter method summariseResults.

private BenchmarkFilterResult summariseResults(TIntObjectHashMap<FilterResult> filterResults, FitEngineConfiguration config, MaximaSpotFilter spotFilter, boolean relativeDistances, boolean batchSummary) {
    BenchmarkFilterResult filterResult = new BenchmarkFilterResult(filterResults, config, spotFilter);
    // Note: 
    // Although we can compute the TP/FP score as each additional spot is added
    // using the RankedScoreCalculator this is not applicable to the PeakFit method.
    // The method relies on all spot candidates being present in order to make a
    // decision to fit the candidate as a multiple. So scoring the filter candidates using
    // for example the top 10 may get a better score than if all candidates were scored
    // and the scores accumulated for the top 10, it is not how the algorithm will use the 
    // candidate set. I.e. It does not use the top 10, then top 20 to refine the fit, etc. 
    // (the method is not iterative) .
    // We require an assessment of how a subset of the scored candidates
    // in ranked order contributes to the overall score, i.e. are the candidates ranked
    // in the correct order, those most contributing to the match to the underlying data 
    // should be higher up and those least contributing will be at the end.
    // TODO We could add some smart filtering of candidates before ranking. This would
    // allow assessment of the candidate set handed to PeakFit. E.g. Threshold the image
    // and only use candidates that are in the foreground region.
    double[][] cumul = histogramFailures(filterResult);
    // Create the overall match score
    final double[] total = new double[3];
    final ArrayList<ScoredSpot> allSpots = new ArrayList<BenchmarkSpotFilter.ScoredSpot>();
    filterResults.forEachValue(new TObjectProcedure<FilterResult>() {

        public boolean execute(FilterResult result) {
            total[0] += result.result.getTP();
            total[1] += result.result.getFP();
            total[2] += result.result.getFN();
            allSpots.addAll(Arrays.asList(result.spots));
            return true;
        }
    });
    double tp = total[0], fp = total[1], fn = total[2];
    FractionClassificationResult allResult = new FractionClassificationResult(tp, fp, 0, fn);
    // The number of actual results
    final double n = (tp + fn);
    StringBuilder sb = new StringBuilder();
    double signal = (simulationParameters.minSignal + simulationParameters.maxSignal) * 0.5;
    // Create the benchmark settings and the fitting settings
    sb.append(imp.getStackSize()).append("\t");
    final int w = lastAnalysisBorder.width;
    final int h = lastAnalysisBorder.height;
    sb.append(w).append("\t");
    sb.append(h).append("\t");
    sb.append(Utils.rounded(n)).append("\t");
    double density = (n / imp.getStackSize()) / (w * h) / (simulationParameters.a * simulationParameters.a / 1e6);
    sb.append(Utils.rounded(density)).append("\t");
    sb.append(Utils.rounded(signal)).append("\t");
    sb.append(Utils.rounded(simulationParameters.s)).append("\t");
    sb.append(Utils.rounded(simulationParameters.a)).append("\t");
    sb.append(Utils.rounded(simulationParameters.depth)).append("\t");
    sb.append(simulationParameters.fixedDepth).append("\t");
    sb.append(Utils.rounded(simulationParameters.gain)).append("\t");
    sb.append(Utils.rounded(simulationParameters.readNoise)).append("\t");
    sb.append(Utils.rounded(simulationParameters.b)).append("\t");
    sb.append(Utils.rounded(simulationParameters.b2)).append("\t");
    // Compute the noise
    double noise = simulationParameters.b2;
    if (simulationParameters.emCCD) {
        // The b2 parameter was computed without application of the EM-CCD noise factor of 2.
        //final double b2 = backgroundVariance + readVariance
        //                = simulationParameters.b + readVariance
        // This should be applied only to the background variance.
        final double readVariance = noise - simulationParameters.b;
        noise = simulationParameters.b * 2 + readVariance;
    }
    sb.append(Utils.rounded(signal / Math.sqrt(noise))).append("\t");
    sb.append(Utils.rounded(simulationParameters.s / simulationParameters.a)).append("\t");
    sb.append(config.getDataFilterType()).append("\t");
    //sb.append(spotFilter.getName()).append("\t");
    sb.append(spotFilter.getSearch()).append("\t");
    sb.append(spotFilter.getBorder()).append("\t");
    sb.append(Utils.rounded(spotFilter.getSpread())).append("\t");
    sb.append(config.getDataFilter(0)).append("\t");
    final double param = config.getSmooth(0);
    final double hwhmMin = config.getHWHMMin();
    if (relativeDistances) {
        sb.append(Utils.rounded(param * hwhmMin)).append("\t");
        sb.append(Utils.rounded(param)).append("\t");
    } else {
        sb.append(Utils.rounded(param)).append("\t");
        sb.append(Utils.rounded(param / hwhmMin)).append("\t");
    }
    sb.append(spotFilter.getDescription()).append("\t");
    sb.append(lastAnalysisBorder.x).append("\t");
    sb.append(MATCHING_METHOD[matchingMethod]).append("\t");
    sb.append(Utils.rounded(lowerMatchDistance)).append("\t");
    sb.append(Utils.rounded(matchDistance)).append("\t");
    sb.append(Utils.rounded(lowerSignalFactor)).append("\t");
    sb.append(Utils.rounded(upperSignalFactor));
    resultPrefix = sb.toString();
    // Add the results
    sb.append("\t");
    // Rank the scored spots by intensity
    Collections.sort(allSpots);
    // Produce Recall, Precision, Jaccard for each cut of the spot candidates
    double[] r = new double[allSpots.size() + 1];
    double[] p = new double[r.length];
    double[] j = new double[r.length];
    double[] c = new double[r.length];
    double[] truePositives = new double[r.length];
    double[] falsePositives = new double[r.length];
    double[] intensity = new double[r.length];
    // Note: fn = n - tp
    tp = fp = 0;
    int i = 1;
    p[0] = 1;
    FastCorrelator corr = new FastCorrelator();
    double lastC = 0;
    double[] i1 = new double[r.length];
    double[] i2 = new double[r.length];
    int ci = 0;
    SimpleRegression regression = new SimpleRegression(false);
    for (ScoredSpot s : allSpots) {
        if (s.match) {
            // Score partial matches as part true-positive and part false-positive.
            // TP can be above 1 if we are allowing multiple matches.
            tp += s.getScore();
            fp += s.antiScore();
            // Just use a rounded intensity for now
            final double spotIntensity = s.getIntensity();
            final long v1 = (long) Math.round(spotIntensity);
            final long v2 = (long) Math.round(s.intensity);
            regression.addData(spotIntensity, s.intensity);
            i1[ci] = spotIntensity;
            i2[ci] = s.intensity;
            ci++;
            corr.add(v1, v2);
            lastC = corr.getCorrelation();
        } else
            fp++;
        r[i] = (double) tp / n;
        p[i] = (double) tp / (tp + fp);
        // (tp+fp+fn) == (fp+n) since tp+fn=n;
        j[i] = (double) tp / (fp + n);
        c[i] = lastC;
        truePositives[i] = tp;
        falsePositives[i] = fp;
        intensity[i] = s.getIntensity();
        i++;
    }
    i1 = Arrays.copyOf(i1, ci);
    i2 = Arrays.copyOf(i2, ci);
    final double slope = regression.getSlope();
    sb.append(Utils.rounded(slope)).append("\t");
    addResult(sb, allResult, c[c.length - 1]);
    // Output the match results when the recall achieves the fraction of the maximum.
    double target = r[r.length - 1];
    if (recallFraction < 100)
        target *= recallFraction / 100.0;
    int fractionIndex = 0;
    while (fractionIndex < r.length && r[fractionIndex] < target) {
        fractionIndex++;
    }
    if (fractionIndex == r.length)
        fractionIndex--;
    addResult(sb, new FractionClassificationResult(truePositives[fractionIndex], falsePositives[fractionIndex], 0, n - truePositives[fractionIndex]), c[fractionIndex]);
    // Output the match results at the maximum jaccard score
    int maxIndex = 0;
    for (int ii = 1; ii < r.length; ii++) {
        if (j[maxIndex] < j[ii])
            maxIndex = ii;
    }
    addResult(sb, new FractionClassificationResult(truePositives[maxIndex], falsePositives[maxIndex], 0, n - truePositives[maxIndex]), c[maxIndex]);
    sb.append(Utils.rounded(time / 1e6));
    // Calculate AUC (Average precision == Area Under Precision-Recall curve)
    final double auc = AUCCalculator.auc(p, r);
    // Compute the AUC using the adjusted precision curve
    // which uses the maximum precision for recall >= r
    final double[] maxp = new double[p.length];
    double max = 0;
    for (int k = maxp.length; k-- > 0; ) {
        if (max < p[k])
            max = p[k];
        maxp[k] = max;
    }
    final double auc2 = AUCCalculator.auc(maxp, r);
    sb.append("\t").append(Utils.rounded(auc));
    sb.append("\t").append(Utils.rounded(auc2));
    // Output the number of fit failures that must be processed to capture fractions of the true positives
    if (cumul[0].length != 0) {
        sb.append("\t").append(Utils.rounded(getFailures(cumul, 0.80)));
        sb.append("\t").append(Utils.rounded(getFailures(cumul, 0.90)));
        sb.append("\t").append(Utils.rounded(getFailures(cumul, 0.95)));
        sb.append("\t").append(Utils.rounded(getFailures(cumul, 0.99)));
        sb.append("\t").append(Utils.rounded(cumul[0][cumul[0].length - 1]));
    } else
        sb.append("\t\t\t\t\t");
    BufferedTextWindow resultsTable = getTable(batchSummary);
    resultsTable.append(sb.toString());
    // Store results
    filterResult.auc = auc;
    filterResult.auc2 = auc2;
    filterResult.r = r;
    filterResult.p = p;
    filterResult.j = j;
    filterResult.c = c;
    filterResult.maxIndex = maxIndex;
    filterResult.fractionIndex = fractionIndex;
    filterResult.cumul = cumul;
    filterResult.slope = slope;
    filterResult.i1 = i1;
    filterResult.i2 = i2;
    filterResult.intensity = intensity;
    filterResult.relativeDistances = relativeDistances;
    filterResult.time = time;
    return filterResult;
}