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

Example 1 with FastCorrelator

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

the class BenchmarkSpotFilter method summariseResults.

private BenchmarkSpotFilterResult summariseResults(TIntObjectHashMap<FilterResult> filterResults, FitEngineConfiguration config, MaximaSpotFilter spotFilter, boolean batchSummary) {
    final BenchmarkSpotFilterResult filterResult = new BenchmarkSpotFilterResult(simulationParameters.id, 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.
    final double[][] cumul = histogramFailures(filterResult);
    // Create the overall match score
    final double[] total = new double[3];
    final ArrayList<ScoredSpot> allSpots = new ArrayList<>();
    filterResults.forEachValue(result -> {
        total[0] += result.result.getTruePositives();
        total[1] += result.result.getFalsePositives();
        total[2] += result.result.getFalseNegatives();
        allSpots.addAll(Arrays.asList(result.spots));
        return true;
    });
    double tp = total[0];
    double fp = total[1];
    final double fn = total[2];
    final FractionClassificationResult allResult = new FractionClassificationResult(tp, fp, 0, fn);
    // The number of actual results
    final double numberOfResults = (tp + fn);
    final StringBuilder sb = new StringBuilder();
    final 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 = border.width;
    final int h = border.height;
    sb.append(w).append('\t');
    sb.append(h).append('\t');
    sb.append(MathUtils.rounded(numberOfResults)).append('\t');
    final double density = (numberOfResults / imp.getStackSize()) / (w * h) / (simulationParameters.pixelPitch * simulationParameters.pixelPitch / 1e6);
    sb.append(MathUtils.rounded(density)).append('\t');
    sb.append(MathUtils.rounded(signal)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.sd)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.pixelPitch)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.depth)).append('\t');
    sb.append(simulationParameters.fixedDepth).append('\t');
    // Camera specific
    CreateData.addCameraDescription(sb, simulationParameters).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.background)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.noise)).append('\t');
    sb.append(MathUtils.rounded(signal / simulationParameters.noise)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.sd / simulationParameters.pixelPitch)).append('\t');
    sb.append(config.getDataFilterType()).append('\t');
    sb.append(spotFilter.getSearch()).append('\t');
    sb.append(spotFilter.getBorder()).append('\t');
    sb.append(MathUtils.rounded(spotFilter.getSpread())).append('\t');
    sb.append(config.getDataFilterMethod(0)).append('\t');
    final double param = config.getDataFilterParameterValue(0);
    final boolean absolute = config.getDataFilterParameterAbsolute(0);
    final double hwhmMin = config.getHwhmMin();
    if (absolute) {
        sb.append(MathUtils.rounded(param)).append('\t');
        sb.append(MathUtils.roundUsingDecimalPlacesToBigDecimal(param / hwhmMin, 3)).append('\t');
    } else {
        sb.append(MathUtils.roundUsingDecimalPlacesToBigDecimal(param * hwhmMin, 3)).append('\t');
        sb.append(MathUtils.rounded(param)).append('\t');
    }
    sb.append(spotFilter.getDescription()).append('\t');
    sb.append(border.x).append('\t');
    sb.append(Settings.MATCHING_METHOD[settings.matchingMethod]).append('\t');
    sb.append(MathUtils.rounded(lowerMatchDistance)).append('\t');
    sb.append(MathUtils.rounded(matchDistance)).append('\t');
    sb.append(MathUtils.rounded(settings.lowerSignalFactor)).append('\t');
    sb.append(MathUtils.rounded(settings.upperSignalFactor));
    filterResult.resultPrefix = sb.toString();
    // Add the results
    sb.append('\t');
    // Rank the scored spots by intensity
    Collections.sort(allSpots, ScoredSpot::compare);
    // Produce Recall, Precision, Jaccard for each cut of the spot candidates
    final double[] recall = new double[allSpots.size() + 1];
    final double[] precision = new double[recall.length];
    final double[] jaccard = new double[recall.length];
    final double[] correlation = new double[recall.length];
    final double[] truePositives = new double[recall.length];
    final double[] falsePositives = new double[recall.length];
    final double[] intensity = new double[recall.length];
    // Note: fn = n - tp
    tp = fp = 0;
    int index = 1;
    precision[0] = 1;
    final FastCorrelator corr = new FastCorrelator();
    double lastCorrelation = 0;
    double[] i1 = new double[recall.length];
    double[] i2 = new double[recall.length];
    int ci = 0;
    final SimpleRegression regression = new SimpleRegression(false);
    for (final 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 = Math.round(spotIntensity);
            final long v2 = Math.round(s.intensity);
            regression.addData(spotIntensity, s.intensity);
            i1[ci] = spotIntensity;
            i2[ci] = s.intensity;
            ci++;
            corr.add(v1, v2);
            lastCorrelation = corr.getCorrelation();
        } else {
            fp++;
        }
        recall[index] = tp / numberOfResults;
        precision[index] = tp / (tp + fp);
        // (tp+fp+fn) == (fp+n) since tp+fn=n
        jaccard[index] = tp / (fp + numberOfResults);
        correlation[index] = lastCorrelation;
        truePositives[index] = tp;
        falsePositives[index] = fp;
        intensity[index] = s.getIntensity();
        index++;
    }
    i1 = Arrays.copyOf(i1, ci);
    i2 = Arrays.copyOf(i2, ci);
    final double slope = regression.getSlope();
    sb.append(MathUtils.rounded(slope)).append('\t');
    addResult(sb, allResult, correlation[correlation.length - 1]);
    // Output the match results when the recall achieves the fraction of the maximum.
    double target = recall[recall.length - 1];
    if (settings.recallFraction < 100) {
        target *= settings.recallFraction / 100.0;
    }
    int fractionIndex = 0;
    while (fractionIndex < recall.length && recall[fractionIndex] < target) {
        fractionIndex++;
    }
    if (fractionIndex == recall.length) {
        fractionIndex--;
    }
    sb.append('\t');
    addResult(sb, new FractionClassificationResult(truePositives[fractionIndex], falsePositives[fractionIndex], 0, numberOfResults - truePositives[fractionIndex]), correlation[fractionIndex]);
    // Output the match results at the maximum jaccard score
    int maxIndex = 0;
    for (int ii = 1; ii < recall.length; ii++) {
        if (jaccard[maxIndex] < jaccard[ii]) {
            maxIndex = ii;
        }
    }
    sb.append('\t');
    addResult(sb, new FractionClassificationResult(truePositives[maxIndex], falsePositives[maxIndex], 0, numberOfResults - truePositives[maxIndex]), correlation[maxIndex]);
    sb.append(MathUtils.rounded(time / 1e6));
    // Calculate AUC (Average precision == Area Under Precision-Recall curve)
    final double auc = AucCalculator.auc(precision, recall);
    // Compute the AUC using the adjusted precision curve
    // which uses the maximum precision for recall >= r
    final double[] maxp = new double[precision.length];
    double max = 0;
    for (int k = maxp.length; k-- > 0; ) {
        if (max < precision[k]) {
            max = precision[k];
        }
        maxp[k] = max;
    }
    final double auc2 = AucCalculator.auc(maxp, recall);
    sb.append('\t').append(MathUtils.rounded(auc));
    sb.append('\t').append(MathUtils.rounded(auc2));
    // positives
    if (cumul[0].length != 0) {
        sb.append('\t').append(MathUtils.rounded(getFailures(cumul, 0.80)));
        sb.append('\t').append(MathUtils.rounded(getFailures(cumul, 0.90)));
        sb.append('\t').append(MathUtils.rounded(getFailures(cumul, 0.95)));
        sb.append('\t').append(MathUtils.rounded(getFailures(cumul, 0.99)));
        sb.append('\t').append(MathUtils.rounded(cumul[0][cumul[0].length - 1]));
    } else {
        sb.append("\t\t\t\t\t");
    }
    getTable(batchSummary).append(sb.toString());
    // Store results
    filterResult.auc = auc;
    filterResult.auc2 = auc2;
    filterResult.recall = recall;
    filterResult.precision = precision;
    filterResult.jaccard = jaccard;
    filterResult.correlation = correlation;
    filterResult.maxIndex = maxIndex;
    filterResult.fractionIndex = fractionIndex;
    filterResult.cumul = cumul;
    filterResult.slope = slope;
    filterResult.i1 = i1;
    filterResult.i2 = i2;
    filterResult.intensity = intensity;
    filterResult.time = time;
    filterResult.analysisBorder = this.border;
    return filterResult;
}

Example 2 with FastCorrelator

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

the class BenchmarkSpotFit method summariseResults.

private void summariseResults(BenchmarkSpotFitResult spotFitResults, long runTime, final PreprocessedPeakResult[] preprocessedPeakResults, int uniqueIdCount, CandidateData candidateData, TIntObjectHashMap<List<Coordinate>> actualCoordinates) {
    // Summarise the fitting results. N fits, N failures.
    // Optimal match statistics if filtering is perfect (since fitting is not perfect).
    final StoredDataStatistics distanceStats = new StoredDataStatistics();
    final StoredDataStatistics depthStats = new StoredDataStatistics();
    // Get stats for all fitted results and those that match
    // Signal, SNR, Width, xShift, yShift, Precision
    createFilterCriteria();
    final 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.pixelPitch;
    double tp = 0;
    double fp = 0;
    int failCtp = 0;
    int failCfp = 0;
    int ctp = 0;
    int cfp = 0;
    final int[] singleStatus = new int[FitStatus.values().length];
    final int[] multiStatus = new int[singleStatus.length];
    final int[] doubletStatus = new int[singleStatus.length];
    final int[] multiDoubletStatus = new int[singleStatus.length];
    // Easier to materialise the values since we have a lot of non final variables to manipulate
    final TIntObjectHashMap<FilterCandidates> fitResults = spotFitResults.fitResults;
    final int[] frames = new int[fitResults.size()];
    final FilterCandidates[] candidates = new FilterCandidates[fitResults.size()];
    final int[] counter = new int[1];
    fitResults.forEachEntry((frame, candidate) -> {
        frames[counter[0]] = frame;
        candidates[counter[0]] = candidate;
        counter[0]++;
        return true;
    });
    for (final 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;
            }
            final FitMatch fitMatch = (FitMatch) result.match[i];
            distanceStats.add(fitMatch.distance * nmPerPixel);
            depthStats.add(fitMatch.zdepth * nmPerPixel);
        }
    }
    if (tp == 0) {
        IJ.error(TITLE, "No fit results matched the simulation actual results");
        return;
    }
    // Store data for computing correlation
    final double[] i1 = new double[depthStats.getN()];
    final double[] i2 = new double[i1.length];
    final double[] is = new double[i1.length];
    int ci = 0;
    for (final 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;
            }
            final FitMatch fitMatch = (FitMatch) result.match[i];
            final ScoredSpot spot = result.spots[fitMatch.index];
            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
    final ArrayList<MultiPathFitResults> multiPathResults = new ArrayList<>(fitResults.size());
    for (int i = 0; i < frames.length; i++) {
        final int frame = frames[i];
        final MultiPathFitResult[] multiPathFitResults = candidates[i].fitResult;
        final int totalCandidates = candidates[i].spots.length;
        final List<Coordinate> list = actualCoordinates.get(frame);
        final int nActual = (list == null) ? 0 : list.size();
        multiPathResults.add(new MultiPathFitResults(frame, multiPathFitResults, totalCandidates, nActual));
    }
    // Score the results and count the number returned
    final List<FractionalAssignment[]> assignments = new ArrayList<>();
    final TIntHashSet set = new TIntHashSet(uniqueIdCount);
    final FractionScoreStore scoreStore = set::add;
    final MultiPathFitResults[] multiResults = multiPathResults.toArray(new MultiPathFitResults[0]);
    // Filter with no filter
    final MultiPathFilter mpf = new MultiPathFilter(new SignalFilter(0), null, multiFilter.residualsThreshold);
    mpf.fractionScoreSubset(multiResults, NullFailCounter.INSTANCE, this.results.size(), assignments, scoreStore, CoordinateStoreFactory.create(0, 0, imp.getWidth(), imp.getHeight(), config.convertUsingHwhMax(config.getDuplicateDistanceParameter())));
    final double[][] matchScores = new double[set.size()][];
    int count = 0;
    for (int i = 0; i < assignments.size(); i++) {
        final 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) {

        @Override
        public boolean execute(int uniqueId) {
            // This should not be null or something has gone wrong
            final PreprocessedPeakResult r = preprocessedPeakResults[uniqueId];
            if (r == null) {
                throw new IllegalArgumentException("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[count++] = score;
            return true;
        }
    });
    final FitConfiguration fitConfig = config.getFitConfiguration();
    // Debug the reasons the fit failed
    if (singleStatus != null) {
        String name = PeakFit.getSolverName(fitConfig);
        if (fitConfig.getFitSolver() == FitSolver.MLE && fitConfig.isModelCamera()) {
            name += " Camera";
        }
        IJ.log("Failure counts: " + name);
        printFailures("Single", singleStatus);
        printFailures("Multi", multiStatus);
        printFailures("Doublet", doubletStatus);
        printFailures("Multi doublet", multiDoubletStatus);
    }
    final StringBuilder sb = new StringBuilder(300);
    // Add information about the simulation
    final double signal = simulationParameters.averageSignal;
    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');
    final double density = ((double) n / imp.getStackSize()) / (w * h) / (simulationParameters.pixelPitch * simulationParameters.pixelPitch / 1e6);
    sb.append(MathUtils.rounded(density)).append('\t');
    sb.append(MathUtils.rounded(signal)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.sd)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.pixelPitch)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.depth)).append('\t');
    sb.append(simulationParameters.fixedDepth).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.gain)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.readNoise)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.background)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.noise)).append('\t');
    if (simulationParameters.fullSimulation) {
    // The total signal is spread over frames
    }
    sb.append(MathUtils.rounded(signal / simulationParameters.noise)).append('\t');
    sb.append(MathUtils.rounded(simulationParameters.sd / simulationParameters.pixelPitch)).append('\t');
    sb.append(spotFilter.getDescription());
    // nP and nN is the fractional score of the spot candidates
    addCount(sb, (double) candidateData.countPositive + candidateData.countNegative);
    addCount(sb, candidateData.countPositive);
    addCount(sb, candidateData.countNegative);
    addCount(sb, candidateData.fractionPositive);
    addCount(sb, candidateData.fractionNegative);
    String name = PeakFit.getSolverName(fitConfig);
    if (fitConfig.getFitSolver() == FitSolver.MLE && fitConfig.isModelCamera()) {
        name += " Camera";
    }
    add(sb, name);
    add(sb, config.getFitting());
    spotFitResults.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) / candidateData.countPositive);
    add(sb, (100.0 * cfp) / candidateData.countNegative);
    // 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 match = new FractionClassificationResult(ctp, cfp, 0, simulationParameters.molecules - ctp);
    add(sb, match.getRecall());
    add(sb, match.getPrecision());
    add(sb, match.getF1Score());
    add(sb, match.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);
    match = new FractionClassificationResult(tp, fp, 0, simulationParameters.molecules - tp);
    add(sb, match.getRecall());
    add(sb, match.getPrecision());
    add(sb, match.getF1Score());
    add(sb, match.getJaccard());
    // Do it again but pretend we can perfectly filter all the false positives
    // add(sb, tp);
    match = new FractionClassificationResult(tp, 0, 0, simulationParameters.molecules - tp);
    // Recall is unchanged
    // Precision will be 100%
    add(sb, match.getF1Score());
    add(sb, match.getJaccard());
    // The mean may be subject to extreme outliers so use the median
    double median = distanceStats.getMedian();
    add(sb, median);
    final WindowOrganiser wo = new WindowOrganiser();
    String label = String.format("Recall = %s. n = %d. Median = %s nm. SD = %s nm", MathUtils.rounded(match.getRecall()), distanceStats.getN(), MathUtils.rounded(median), MathUtils.rounded(distanceStats.getStandardDeviation()));
    new HistogramPlotBuilder(TITLE, distanceStats, "Match Distance (nm)").setPlotLabel(label).show(wo);
    median = depthStats.getMedian();
    add(sb, median);
    // Sort by spot intensity and produce correlation
    double[] correlation = null;
    double[] rankCorrelation = null;
    double[] rank = null;
    final FastCorrelator fastCorrelator = new FastCorrelator();
    final ArrayList<Ranking> pc1 = new ArrayList<>();
    final ArrayList<Ranking> pc2 = new ArrayList<>();
    ci = 0;
    if (settings.showCorrelation) {
        final int[] indices = SimpleArrayUtils.natural(i1.length);
        SortUtils.sortData(indices, is, settings.rankByIntensity, true);
        correlation = new double[i1.length];
        rankCorrelation = new double[i1.length];
        rank = new double[i1.length];
        for (final int ci2 : indices) {
            fastCorrelator.add(Math.round(i1[ci2]), Math.round(i2[ci2]));
            pc1.add(new Ranking(i1[ci2], ci));
            pc2.add(new Ranking(i2[ci2], ci));
            correlation[ci] = fastCorrelator.getCorrelation();
            rankCorrelation[ci] = Correlator.correlation(rank(pc1), rank(pc2));
            if (settings.rankByIntensity) {
                rank[ci] = is[0] - is[ci];
            } else {
                rank[ci] = ci;
            }
            ci++;
        }
    } else {
        for (int i = 0; i < i1.length; i++) {
            fastCorrelator.add(Math.round(i1[i]), Math.round(i2[i]));
            pc1.add(new Ranking(i1[i], i));
            pc2.add(new Ranking(i2[i], i));
        }
    }
    final double pearsonCorr = fastCorrelator.getCorrelation();
    final double rankedCorr = Correlator.correlation(rank(pc1), rank(pc2));
    // Get the regression
    final 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 (settings.showCorrelation) {
        String title = TITLE + " Intensity";
        Plot plot = new Plot(title, "Candidate", "Spot");
        final double[] limits1 = MathUtils.limits(i1);
        final double[] limits2 = MathUtils.limits(i2);
        plot.setLimits(limits1[0], limits1[1], limits2[0], limits2[1]);
        label = String.format("Correlation=%s; Ranked=%s; Slope=%s", MathUtils.rounded(pearsonCorr), MathUtils.rounded(rankedCorr), MathUtils.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]);
        }
        ImageJUtils.display(title, plot, wo);
        title = TITLE + " Correlation";
        plot = new Plot(title, "Spot Rank", "Correlation");
        final double[] xlimits = MathUtils.limits(rank);
        double[] ylimits = MathUtils.limits(correlation);
        ylimits = MathUtils.limits(ylimits, rankCorrelation);
        plot.setLimits(xlimits[0], xlimits[1], ylimits[0], ylimits[1]);
        plot.setColor(Color.red);
        plot.addPoints(rank, correlation, Plot.LINE);
        plot.setColor(Color.blue);
        plot.addPoints(rank, rankCorrelation, Plot.LINE);
        plot.setColor(Color.black);
        plot.addLabel(0, 0, label);
        ImageJUtils.display(title, plot, wo);
    }
    add(sb, pearsonCorr);
    add(sb, rankedCorr);
    add(sb, slope);
    label = String.format("n = %d. Median = %s nm", depthStats.getN(), MathUtils.rounded(median));
    new HistogramPlotBuilder(TITLE, depthStats, "Match Depth (nm)").setRemoveOutliersOption(1).setPlotLabel(label).show(wo);
    // Plot histograms of the stats on the same window
    final double[] lower = new double[filterCriteria.length];
    final double[] upper = new double[lower.length];
    final double[] min = new double[lower.length];
    final double[] max = new double[lower.length];
    for (int i = 0; i < stats[0].length; i++) {
        final double[] limits = showDoubleHistogram(stats, i, wo, matchScores);
        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;
    final 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
    final double[] increment = new double[lower.length];
    for (int i = 0; i < increment.length; i++) {
        lower[i] = MathUtils.floor(lower[i], interval[i]);
        upper[i] = MathUtils.ceil(upper[i], interval[i]);
        final 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] = MathUtils.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] = MathUtils.round(lower[i]);
        upper[i] = MathUtils.round(upper[i]);
        min[i] = MathUtils.round(min[i]);
        max[i] = MathUtils.round(max[i]);
        increment[i] = MathUtils.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(TextUtils.nanosToString(runTime));
    createTable().append(sb.toString());
    if (settings.saveFilterRange) {
        GUIFilterSettings filterSettings = SettingsManager.readGuiFilterSettings(0);
        String filename = (silent) ? filterSettings.getFilterSetFilename() : ImageJUtils.getFilename("Filter_range_file", filterSettings.getFilterSetFilename());
        if (filename == null) {
            return;
        }
        // Remove extension to store the filename
        filename = FileUtils.replaceExtension(filename, ".xml");
        filterSettings = filterSettings.toBuilder().setFilterSetFilename(filename).build();
        // Create a filter set using the ranges
        final ArrayList<Filter> filters = new ArrayList<>(4);
        // Create the multi-filter using the same precision type as that used during fitting.
        // Currently no support for z-filter as 3D astigmatism fitting is experimental.
        final PrecisionMethod precisionMethod = getPrecisionMethod((DirectFilter) multiFilter.getFilter());
        Function<double[], Filter> generator;
        if (precisionMethod == PrecisionMethod.POISSON_CRLB) {
            generator = parameters -> new MultiFilterCrlb(parameters[FILTER_SIGNAL], (float) parameters[FILTER_SNR], parameters[FILTER_MIN_WIDTH], parameters[FILTER_MAX_WIDTH], parameters[FILTER_SHIFT], parameters[FILTER_ESHIFT], parameters[FILTER_PRECISION], 0f, 0f);
        } else if (precisionMethod == PrecisionMethod.MORTENSEN) {
            generator = parameters -> new MultiFilter(parameters[FILTER_SIGNAL], (float) parameters[FILTER_SNR], parameters[FILTER_MIN_WIDTH], parameters[FILTER_MAX_WIDTH], parameters[FILTER_SHIFT], parameters[FILTER_ESHIFT], parameters[FILTER_PRECISION], 0f, 0f);
        } else {
            // Default
            generator = parameters -> new MultiFilter2(parameters[FILTER_SIGNAL], (float) parameters[FILTER_SNR], parameters[FILTER_MIN_WIDTH], parameters[FILTER_MAX_WIDTH], parameters[FILTER_SHIFT], parameters[FILTER_ESHIFT], parameters[FILTER_PRECISION], 0f, 0f);
        }
        filters.add(generator.apply(lower));
        filters.add(generator.apply(upper));
        filters.add(generator.apply(increment));
        if (saveFilters(filename, filters)) {
            SettingsManager.writeSettings(filterSettings);
        }
        // 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_SNR] = Math.min(max[FILTER_SNR], 10000);
        max[FILTER_PRECISION] = Math.min(max[FILTER_PRECISION], 100);
        // Make the 4-set filters the same as the 3-set filters.
        filters.clear();
        filters.add(generator.apply(min));
        filters.add(generator.apply(lower));
        filters.add(generator.apply(upper));
        filters.add(generator.apply(max));
        saveFilters(FileUtils.replaceExtension(filename, ".4.xml"), filters);
    }
    spotFitResults.min = min;
    spotFitResults.max = max;
}