MSDFErrorCorrection.cpp

#include "MSDFErrorCorrection.h"

#include <cstring>
#include "arithmetics.hpp"
#include "equation-solver.h"
#include "EdgeColor.h"
#include "bitmap-interpolation.hpp"
#include "edge-selectors.h"
#include "contour-combiners.h"
#include "ShapeDistanceFinder.h"
#include "generator-config.h"

namespace msdfgen {

#define ARTIFACT_T_EPSILON .01
#define PROTECTION_RADIUS_TOLERANCE 1.001

#define CLASSIFIER_FLAG_CANDIDATE 0x01
#define CLASSIFIER_FLAG_ARTIFACT 0x02

MSDFGEN_PUBLIC const double ErrorCorrectionConfig::defaultMinDeviationRatio = 1.11111111111111111;
MSDFGEN_PUBLIC const double ErrorCorrectionConfig::defaultMinImproveRatio = 1.11111111111111111;

/// The base artifact classifier recognizes artifacts based on the contents of the SDF alone.
class BaseArtifactClassifier {
public:
    inline BaseArtifactClassifier(double span, bool protectedFlag) : span(span), protectedFlag(protectedFlag) { }
    /// Evaluates if the median value xm interpolated at xt in the range between am at at and bm at bt indicates an artifact.
    inline int rangeTest(double at, double bt, double xt, float am, float bm, float xm) const {
        // For protected texels, only consider inversion artifacts (interpolated median has different sign than boundaries). For the rest, it is sufficient that the interpolated median is outside its boundaries.
        if ((am > .5f && bm > .5f && xm <= .5f) || (am < .5f && bm < .5f && xm >= .5f) || (!protectedFlag && median(am, bm, xm) != xm)) {
            double axSpan = (xt-at)*span, bxSpan = (bt-xt)*span;
            // Check if the interpolated median's value is in the expected range based on its distance (span) from boundaries a, b.
            if (!(xm >= am-axSpan && xm <= am+axSpan && xm >= bm-bxSpan && xm <= bm+bxSpan))
                return CLASSIFIER_FLAG_CANDIDATE|CLASSIFIER_FLAG_ARTIFACT;
            return CLASSIFIER_FLAG_CANDIDATE;
        }
        return 0;
    }
    /// Returns true if the combined results of the tests performed on the median value m interpolated at t indicate an artifact.
    inline bool evaluate(double t, float m, int flags) const {
        return (flags&2) != 0;
    }
private:
    double span;
    bool protectedFlag;
};

/// The shape distance checker evaluates the exact shape distance to find additional artifacts at a significant performance cost.
template <template <typename> class ContourCombiner, int N>
class ShapeDistanceChecker {
public:
    class ArtifactClassifier : public BaseArtifactClassifier {
    public:
        inline ArtifactClassifier(ShapeDistanceChecker *parent, const Vector2 &direction, double span) : BaseArtifactClassifier(span, parent->protectedFlag), parent(parent), direction(direction) { }
        /// Returns true if the combined results of the tests performed on the median value m interpolated at t indicate an artifact.
        inline bool evaluate(double t, float m, int flags) const {
            if (flags&CLASSIFIER_FLAG_CANDIDATE) {
                // Skip expensive distance evaluation if the point has already been classified as an artifact by the base classifier.
                if (flags&CLASSIFIER_FLAG_ARTIFACT)
                    return true;
                Vector2 tVector = t*direction;
                float oldMSD[N], newMSD[3];
                // Compute the color that would be currently interpolated at the artifact candidate's position.
                Point2 sdfCoord = parent->sdfCoord+tVector;
                interpolate(oldMSD, parent->sdf, sdfCoord);
                // Compute the color that would be interpolated at the artifact candidate's position if error correction was applied on the current texel.
                double aWeight = (1-fabs(tVector.x))*(1-fabs(tVector.y));
                float aPSD = median(parent->msd[0], parent->msd[1], parent->msd[2]);
                newMSD[0] = float(oldMSD[0]+aWeight*(aPSD-parent->msd[0]));
                newMSD[1] = float(oldMSD[1]+aWeight*(aPSD-parent->msd[1]));
                newMSD[2] = float(oldMSD[2]+aWeight*(aPSD-parent->msd[2]));
                // Compute the evaluated distance (interpolated median) before and after error correction, as well as the exact shape distance.
                float oldPSD = median(oldMSD[0], oldMSD[1], oldMSD[2]);
                float newPSD = median(newMSD[0], newMSD[1], newMSD[2]);
                float refPSD = float(parent->distanceMapping(parent->distanceFinder.distance(parent->shapeCoord+tVector*parent->texelSize)));
                // Compare the differences of the exact distance and the before and after distances.
                return parent->minImproveRatio*fabsf(newPSD-refPSD) < double(fabsf(oldPSD-refPSD));
            }
            return false;
        }
    private:
        ShapeDistanceChecker *parent;
        Vector2 direction;
    };
    Point2 shapeCoord, sdfCoord;
    const float *msd;
    bool protectedFlag;
    inline ShapeDistanceChecker(const BitmapConstRef<float, N> &sdf, const Shape &shape, const Projection &projection, DistanceMapping distanceMapping, double minImproveRatio) : distanceFinder(shape), sdf(sdf), distanceMapping(distanceMapping), minImproveRatio(minImproveRatio) {
        texelSize = projection.unprojectVector(Vector2(1));
        if (shape.inverseYAxis)
            texelSize.y = -texelSize.y;
    }
    inline ArtifactClassifier classifier(const Vector2 &direction, double span) {
        return ArtifactClassifier(this, direction, span);
    }
private:
    ShapeDistanceFinder<ContourCombiner<PerpendicularDistanceSelector> > distanceFinder;
    BitmapConstRef<float, N> sdf;
    DistanceMapping distanceMapping;
    Vector2 texelSize;
    double minImproveRatio;
};

MSDFErrorCorrection::MSDFErrorCorrection() { }

MSDFErrorCorrection::MSDFErrorCorrection(const BitmapRef<byte, 1> &stencil, const SDFTransformation &transformation) : stencil(stencil), transformation(transformation) {
    minDeviationRatio = ErrorCorrectionConfig::defaultMinDeviationRatio;
    minImproveRatio = ErrorCorrectionConfig::defaultMinImproveRatio;
    memset(stencil.pixels, 0, sizeof(byte)*stencil.width*stencil.height);
}

void MSDFErrorCorrection::setMinDeviationRatio(double minDeviationRatio) {
    this->minDeviationRatio = minDeviationRatio;
}

void MSDFErrorCorrection::setMinImproveRatio(double minImproveRatio) {
    this->minImproveRatio = minImproveRatio;
}

void MSDFErrorCorrection::protectCorners(const Shape &shape) {
    for (std::vector<Contour>::const_iterator contour = shape.contours.begin(); contour != shape.contours.end(); ++contour)
        if (!contour->edges.empty()) {
            const EdgeSegment *prevEdge = contour->edges.back();
            for (std::vector<EdgeHolder>::const_iterator edge = contour->edges.begin(); edge != contour->edges.end(); ++edge) {
                int commonColor = prevEdge->color&(*edge)->color;
                // If the color changes from prevEdge to edge, this is a corner.
                if (!(commonColor&(commonColor-1))) {
                    // Find the four texels that envelop the corner and mark them as protected.
                    Point2 p = transformation.project((*edge)->point(0));
                    int l = (int) floor(p.x-.5);
                    int b = (int) floor(p.y-.5);
                    if (shape.inverseYAxis)
                        b = stencil.height-b-2;
                    int r = l+1;
                    int t = b+1;
                    // Check that the positions are within bounds.
                    if (l < stencil.width && b < stencil.height && r >= 0 && t >= 0) {
                        if (l >= 0 && b >= 0)
                            *stencil(l, b) |= (byte) PROTECTED;
                        if (r < stencil.width && b >= 0)
                            *stencil(r, b) |= (byte) PROTECTED;
                        if (l >= 0 && t < stencil.height)
                            *stencil(l, t) |= (byte) PROTECTED;
                        if (r < stencil.width && t < stencil.height)
                            *stencil(r, t) |= (byte) PROTECTED;
                    }
                }
                prevEdge = *edge;
            }
        }
}

/// Determines if the channel contributes to an edge between the two texels a, b.
static bool edgeBetweenTexelsChannel(const float *a, const float *b, int channel) {
    // Find interpolation ratio t (0 < t < 1) where an edge is expected (mix(a[channel], b[channel], t) == 0.5).
    double t = (a[channel]-.5)/(a[channel]-b[channel]);
    if (t > 0 && t < 1) {
        // Interpolate channel values at t.
        float c[3] = {
            mix(a[0], b[0], t),
            mix(a[1], b[1], t),
            mix(a[2], b[2], t)
        };
        // This is only an edge if the zero-distance channel is the median.
        return median(c[0], c[1], c[2]) == c[channel];
    }
    return false;
}

/// Returns a bit mask of which channels contribute to an edge between the two texels a, b.
static int edgeBetweenTexels(const float *a, const float *b) {
    return (
        RED*edgeBetweenTexelsChannel(a, b, 0)+
        GREEN*edgeBetweenTexelsChannel(a, b, 1)+
        BLUE*edgeBetweenTexelsChannel(a, b, 2)
    );
}

/// Marks texel as protected if one of its non-median channels is present in the channel mask.
static void protectExtremeChannels(byte *stencil, const float *msd, float m, int mask) {
    if (
        (mask&RED && msd[0] != m) ||
        (mask&GREEN && msd[1] != m) ||
        (mask&BLUE && msd[2] != m)
    )
        *stencil |= (byte) MSDFErrorCorrection::PROTECTED;
}

template <int N>
void MSDFErrorCorrection::protectEdges(const BitmapConstRef<float, N> &sdf) {
    float radius;
    // Horizontal texel pairs
    radius = float(PROTECTION_RADIUS_TOLERANCE*transformation.unprojectVector(Vector2(transformation.distanceMapping(DistanceMapping::Delta(1)), 0)).length());
    for (int y = 0; y < sdf.height; ++y) {
        const float *left = sdf(0, y);
        const float *right = sdf(1, y);
        for (int x = 0; x < sdf.width-1; ++x) {
            float lm = median(left[0], left[1], left[2]);
            float rm = median(right[0], right[1], right[2]);
            if (fabsf(lm-.5f)+fabsf(rm-.5f) < radius) {
                int mask = edgeBetweenTexels(left, right);
                protectExtremeChannels(stencil(x, y), left, lm, mask);
                protectExtremeChannels(stencil(x+1, y), right, rm, mask);
            }
            left += N, right += N;
        }
    }
    // Vertical texel pairs
    radius = float(PROTECTION_RADIUS_TOLERANCE*transformation.unprojectVector(Vector2(0, transformation.distanceMapping(DistanceMapping::Delta(1)))).length());
    for (int y = 0; y < sdf.height-1; ++y) {
        const float *bottom = sdf(0, y);
        const float *top = sdf(0, y+1);
        for (int x = 0; x < sdf.width; ++x) {
            float bm = median(bottom[0], bottom[1], bottom[2]);
            float tm = median(top[0], top[1], top[2]);
            if (fabsf(bm-.5f)+fabsf(tm-.5f) < radius) {
                int mask = edgeBetweenTexels(bottom, top);
                protectExtremeChannels(stencil(x, y), bottom, bm, mask);
                protectExtremeChannels(stencil(x, y+1), top, tm, mask);
            }
            bottom += N, top += N;
        }
    }
    // Diagonal texel pairs
    radius = float(PROTECTION_RADIUS_TOLERANCE*transformation.unprojectVector(Vector2(transformation.distanceMapping(DistanceMapping::Delta(1)))).length());
    for (int y = 0; y < sdf.height-1; ++y) {
        const float *lb = sdf(0, y);
        const float *rb = sdf(1, y);
        const float *lt = sdf(0, y+1);
        const float *rt = sdf(1, y+1);
        for (int x = 0; x < sdf.width-1; ++x) {
            float mlb = median(lb[0], lb[1], lb[2]);
            float mrb = median(rb[0], rb[1], rb[2]);
            float mlt = median(lt[0], lt[1], lt[2]);
            float mrt = median(rt[0], rt[1], rt[2]);
            if (fabsf(mlb-.5f)+fabsf(mrt-.5f) < radius) {
                int mask = edgeBetweenTexels(lb, rt);
                protectExtremeChannels(stencil(x, y), lb, mlb, mask);
                protectExtremeChannels(stencil(x+1, y+1), rt, mrt, mask);
            }
            if (fabsf(mrb-.5f)+fabsf(mlt-.5f) < radius) {
                int mask = edgeBetweenTexels(rb, lt);
                protectExtremeChannels(stencil(x+1, y), rb, mrb, mask);
                protectExtremeChannels(stencil(x, y+1), lt, mlt, mask);
            }
            lb += N, rb += N, lt += N, rt += N;
        }
    }
}

void MSDFErrorCorrection::protectAll() {
    byte *end = stencil.pixels+stencil.width*stencil.height;
    for (byte *mask = stencil.pixels; mask < end; ++mask)
        *mask |= (byte) PROTECTED;
}

/// Returns the median of the linear interpolation of texels a, b at t.
static float interpolatedMedian(const float *a, const float *b, double t) {
    return median(
        mix(a[0], b[0], t),
        mix(a[1], b[1], t),
        mix(a[2], b[2], t)
    );
}
/// Returns the median of the bilinear interpolation with the given constant, linear, and quadratic terms at t.
static float interpolatedMedian(const float *a, const float *l, const float *q, double t) {
    return float(median(
        t*(t*q[0]+l[0])+a[0],
        t*(t*q[1]+l[1])+a[1],
        t*(t*q[2]+l[2])+a[2]
    ));
}

/// Determines if the interpolated median xm is an artifact.
static bool isArtifact(bool isProtected, double axSpan, double bxSpan, float am, float bm, float xm) {
    return (
        // For protected texels, only report an artifact if it would cause fill inversion (change between positive and negative distance).
        (!isProtected || (am > .5f && bm > .5f && xm <= .5f) || (am < .5f && bm < .5f && xm >= .5f)) &&
        // This is an artifact if the interpolated median is outside the range of possible values based on its distance from a, b.
        !(xm >= am-axSpan && xm <= am+axSpan && xm >= bm-bxSpan && xm <= bm+bxSpan)
    );
}

/// Checks if a linear interpolation artifact will occur at a point where two specific color channels are equal - such points have extreme median values.
template <class ArtifactClassifier>
static bool hasLinearArtifactInner(const ArtifactClassifier &artifactClassifier, float am, float bm, const float *a, const float *b, float dA, float dB) {
    // Find interpolation ratio t (0 < t < 1) where two color channels are equal (mix(dA, dB, t) == 0).
    double t = (double) dA/(dA-dB);
    if (t > ARTIFACT_T_EPSILON && t < 1-ARTIFACT_T_EPSILON) {
        // Interpolate median at t and let the classifier decide if its value indicates an artifact.
        float xm = interpolatedMedian(a, b, t);
        return artifactClassifier.evaluate(t, xm, artifactClassifier.rangeTest(0, 1, t, am, bm, xm));
    }
    return false;
}

/// Checks if a bilinear interpolation artifact will occur at a point where two specific color channels are equal - such points have extreme median values.
template <class ArtifactClassifier>
static bool hasDiagonalArtifactInner(const ArtifactClassifier &artifactClassifier, float am, float dm, const float *a, const float *l, const float *q, float dA, float dBC, float dD, double tEx0, double tEx1) {
    // Find interpolation ratios t (0 < t[i] < 1) where two color channels are equal.
    double t[2];
    int solutions = solveQuadratic(t, dD-dBC+dA, dBC-dA-dA, dA);
    for (int i = 0; i < solutions; ++i) {
        // Solutions t[i] == 0 and t[i] == 1 are singularities and occur very often because two channels are usually equal at texels.
        if (t[i] > ARTIFACT_T_EPSILON && t[i] < 1-ARTIFACT_T_EPSILON) {
            // Interpolate median xm at t.
            float xm = interpolatedMedian(a, l, q, t[i]);
            // Determine if xm deviates too much from medians of a, d.
            int rangeFlags = artifactClassifier.rangeTest(0, 1, t[i], am, dm, xm);
            // Additionally, check xm against the interpolated medians at the local extremes tEx0, tEx1.
            double tEnd[2];
            float em[2];
            // tEx0
            if (tEx0 > 0 && tEx0 < 1) {
                tEnd[0] = 0, tEnd[1] = 1;
                em[0] = am, em[1] = dm;
                tEnd[tEx0 > t[i]] = tEx0;
                em[tEx0 > t[i]] = interpolatedMedian(a, l, q, tEx0);
                rangeFlags |= artifactClassifier.rangeTest(tEnd[0], tEnd[1], t[i], em[0], em[1], xm);
            }
            // tEx1
            if (tEx1 > 0 && tEx1 < 1) {
                tEnd[0] = 0, tEnd[1] = 1;
                em[0] = am, em[1] = dm;
                tEnd[tEx1 > t[i]] = tEx1;
                em[tEx1 > t[i]] = interpolatedMedian(a, l, q, tEx1);
                rangeFlags |= artifactClassifier.rangeTest(tEnd[0], tEnd[1], t[i], em[0], em[1], xm);
            }
            if (artifactClassifier.evaluate(t[i], xm, rangeFlags))
                return true;
        }
    }
    return false;
}

/// Checks if a linear interpolation artifact will occur inbetween two horizontally or vertically adjacent texels a, b.
template <class ArtifactClassifier>
static bool hasLinearArtifact(const ArtifactClassifier &artifactClassifier, float am, const float *a, const float *b) {
    float bm = median(b[0], b[1], b[2]);
    return (
        // Out of the pair, only report artifacts for the texel further from the edge to minimize side effects.
        fabsf(am-.5f) >= fabsf(bm-.5f) && (
            // Check points where each pair of color channels meets.
            hasLinearArtifactInner(artifactClassifier, am, bm, a, b, a[1]-a[0], b[1]-b[0]) ||
            hasLinearArtifactInner(artifactClassifier, am, bm, a, b, a[2]-a[1], b[2]-b[1]) ||
            hasLinearArtifactInner(artifactClassifier, am, bm, a, b, a[0]-a[2], b[0]-b[2])
        )
    );
}

/// Checks if a bilinear interpolation artifact will occur inbetween two diagonally adjacent texels a, d (with b, c forming the other diagonal).
template <class ArtifactClassifier>
static bool hasDiagonalArtifact(const ArtifactClassifier &artifactClassifier, float am, const float *a, const float *b, const float *c, const float *d) {
    float dm = median(d[0], d[1], d[2]);
    // Out of the pair, only report artifacts for the texel further from the edge to minimize side effects.
    if (fabsf(am-.5f) >= fabsf(dm-.5f)) {
        float abc[3] = {
            a[0]-b[0]-c[0],
            a[1]-b[1]-c[1],
            a[2]-b[2]-c[2]
        };
        // Compute the linear terms for bilinear interpolation.
        float l[3] = {
            -a[0]-abc[0],
            -a[1]-abc[1],
            -a[2]-abc[2]
        };
        // Compute the quadratic terms for bilinear interpolation.
        float q[3] = {
            d[0]+abc[0],
            d[1]+abc[1],
            d[2]+abc[2]
        };
        // Compute interpolation ratios tEx (0 < tEx[i] < 1) for the local extremes of each color channel (the derivative 2*q[i]*tEx[i]+l[i] == 0).
        double tEx[3] = {
            -.5*l[0]/q[0],
            -.5*l[1]/q[1],
            -.5*l[2]/q[2]
        };
        // Check points where each pair of color channels meets.
        return (
            hasDiagonalArtifactInner(artifactClassifier, am, dm, a, l, q, a[1]-a[0], b[1]-b[0]+c[1]-c[0], d[1]-d[0], tEx[0], tEx[1]) ||
            hasDiagonalArtifactInner(artifactClassifier, am, dm, a, l, q, a[2]-a[1], b[2]-b[1]+c[2]-c[1], d[2]-d[1], tEx[1], tEx[2]) ||
            hasDiagonalArtifactInner(artifactClassifier, am, dm, a, l, q, a[0]-a[2], b[0]-b[2]+c[0]-c[2], d[0]-d[2], tEx[2], tEx[0])
        );
    }
    return false;
}

template <int N>
void MSDFErrorCorrection::findErrors(const BitmapConstRef<float, N> &sdf) {
    // Compute the expected deltas between values of horizontally, vertically, and diagonally adjacent texels.
    double hSpan = minDeviationRatio*transformation.unprojectVector(Vector2(transformation.distanceMapping(DistanceMapping::Delta(1)), 0)).length();
    double vSpan = minDeviationRatio*transformation.unprojectVector(Vector2(0, transformation.distanceMapping(DistanceMapping::Delta(1)))).length();
    double dSpan = minDeviationRatio*transformation.unprojectVector(Vector2(transformation.distanceMapping(DistanceMapping::Delta(1)))).length();
    // Inspect all texels.
    for (int y = 0; y < sdf.height; ++y) {
        for (int x = 0; x < sdf.width; ++x) {
            const float *c = sdf(x, y);
            float cm = median(c[0], c[1], c[2]);
            bool protectedFlag = (*stencil(x, y)&PROTECTED) != 0;
            const float *l = NULL, *b = NULL, *r = NULL, *t = NULL;
            // Mark current texel c with the error flag if an artifact occurs when it's interpolated with any of its 8 neighbors.
            *stencil(x, y) |= (byte) (ERROR*(
                (x > 0 && ((l = sdf(x-1, y)), hasLinearArtifact(BaseArtifactClassifier(hSpan, protectedFlag), cm, c, l))) ||
                (y > 0 && ((b = sdf(x, y-1)), hasLinearArtifact(BaseArtifactClassifier(vSpan, protectedFlag), cm, c, b))) ||
                (x < sdf.width-1 && ((r = sdf(x+1, y)), hasLinearArtifact(BaseArtifactClassifier(hSpan, protectedFlag), cm, c, r))) ||
                (y < sdf.height-1 && ((t = sdf(x, y+1)), hasLinearArtifact(BaseArtifactClassifier(vSpan, protectedFlag), cm, c, t))) ||
                (x > 0 && y > 0 && hasDiagonalArtifact(BaseArtifactClassifier(dSpan, protectedFlag), cm, c, l, b, sdf(x-1, y-1))) ||
                (x < sdf.width-1 && y > 0 && hasDiagonalArtifact(BaseArtifactClassifier(dSpan, protectedFlag), cm, c, r, b, sdf(x+1, y-1))) ||
                (x > 0 && y < sdf.height-1 && hasDiagonalArtifact(BaseArtifactClassifier(dSpan, protectedFlag), cm, c, l, t, sdf(x-1, y+1))) ||
                (x < sdf.width-1 && y < sdf.height-1 && hasDiagonalArtifact(BaseArtifactClassifier(dSpan, protectedFlag), cm, c, r, t, sdf(x+1, y+1)))
            ));
        }
    }
}

template <template <typename> class ContourCombiner, int N>
void MSDFErrorCorrection::findErrors(const BitmapConstRef<float, N> &sdf, const Shape &shape) {
    // Compute the expected deltas between values of horizontally, vertically, and diagonally adjacent texels.
    double hSpan = minDeviationRatio*transformation.unprojectVector(Vector2(transformation.distanceMapping(DistanceMapping::Delta(1)), 0)).length();
    double vSpan = minDeviationRatio*transformation.unprojectVector(Vector2(0, transformation.distanceMapping(DistanceMapping::Delta(1)))).length();
    double dSpan = minDeviationRatio*transformation.unprojectVector(Vector2(transformation.distanceMapping(DistanceMapping::Delta(1)))).length();
#ifdef MSDFGEN_USE_OPENMP
    #pragma omp parallel
#endif
    {
        ShapeDistanceChecker<ContourCombiner, N> shapeDistanceChecker(sdf, shape, transformation, transformation.distanceMapping, minImproveRatio);
        bool rightToLeft = false;
        // Inspect all texels.
#ifdef MSDFGEN_USE_OPENMP
        #pragma omp for
#endif
        for (int y = 0; y < sdf.height; ++y) {
            int row = shape.inverseYAxis ? sdf.height-y-1 : y;
            for (int col = 0; col < sdf.width; ++col) {
                int x = rightToLeft ? sdf.width-col-1 : col;
                if ((*stencil(x, row)&ERROR))
                    continue;
                const float *c = sdf(x, row);
                shapeDistanceChecker.shapeCoord = transformation.unproject(Point2(x+.5, y+.5));
                shapeDistanceChecker.sdfCoord = Point2(x+.5, row+.5);
                shapeDistanceChecker.msd = c;
                shapeDistanceChecker.protectedFlag = (*stencil(x, row)&PROTECTED) != 0;
                float cm = median(c[0], c[1], c[2]);
                const float *l = NULL, *b = NULL, *r = NULL, *t = NULL;
                // Mark current texel c with the error flag if an artifact occurs when it's interpolated with any of its 8 neighbors.
                *stencil(x, row) |= (byte) (ERROR*(
                    (x > 0 && ((l = sdf(x-1, row)), hasLinearArtifact(shapeDistanceChecker.classifier(Vector2(-1, 0), hSpan), cm, c, l))) ||
                    (row > 0 && ((b = sdf(x, row-1)), hasLinearArtifact(shapeDistanceChecker.classifier(Vector2(0, -1), vSpan), cm, c, b))) ||
                    (x < sdf.width-1 && ((r = sdf(x+1, row)), hasLinearArtifact(shapeDistanceChecker.classifier(Vector2(+1, 0), hSpan), cm, c, r))) ||
                    (row < sdf.height-1 && ((t = sdf(x, row+1)), hasLinearArtifact(shapeDistanceChecker.classifier(Vector2(0, +1), vSpan), cm, c, t))) ||
                    (x > 0 && row > 0 && hasDiagonalArtifact(shapeDistanceChecker.classifier(Vector2(-1, -1), dSpan), cm, c, l, b, sdf(x-1, row-1))) ||
                    (x < sdf.width-1 && row > 0 && hasDiagonalArtifact(shapeDistanceChecker.classifier(Vector2(+1, -1), dSpan), cm, c, r, b, sdf(x+1, row-1))) ||
                    (x > 0 && row < sdf.height-1 && hasDiagonalArtifact(shapeDistanceChecker.classifier(Vector2(-1, +1), dSpan), cm, c, l, t, sdf(x-1, row+1))) ||
                    (x < sdf.width-1 && row < sdf.height-1 && hasDiagonalArtifact(shapeDistanceChecker.classifier(Vector2(+1, +1), dSpan), cm, c, r, t, sdf(x+1, row+1)))
                ));
            }
        }
    }
}

template <int N>
void MSDFErrorCorrection::apply(const BitmapRef<float, N> &sdf) const {
    int texelCount = sdf.width*sdf.height;
    const byte *mask = stencil.pixels;
    float *texel = sdf.pixels;
    for (int i = 0; i < texelCount; ++i) {
        if (*mask&ERROR) {
            // Set all color channels to the median.
            float m = median(texel[0], texel[1], texel[2]);
            texel[0] = m, texel[1] = m, texel[2] = m;
        }
        ++mask;
        texel += N;
    }
}

BitmapConstRef<byte, 1> MSDFErrorCorrection::getStencil() const {
    return stencil;
}

template void MSDFErrorCorrection::protectEdges(const BitmapConstRef<float, 3> &sdf);
template void MSDFErrorCorrection::protectEdges(const BitmapConstRef<float, 4> &sdf);
template void MSDFErrorCorrection::findErrors(const BitmapConstRef<float, 3> &sdf);
template void MSDFErrorCorrection::findErrors(const BitmapConstRef<float, 4> &sdf);
template void MSDFErrorCorrection::findErrors<SimpleContourCombiner>(const BitmapConstRef<float, 3> &sdf, const Shape &shape);
template void MSDFErrorCorrection::findErrors<SimpleContourCombiner>(const BitmapConstRef<float, 4> &sdf, const Shape &shape);
template void MSDFErrorCorrection::findErrors<OverlappingContourCombiner>(const BitmapConstRef<float, 3> &sdf, const Shape &shape);
template void MSDFErrorCorrection::findErrors<OverlappingContourCombiner>(const BitmapConstRef<float, 4> &sdf, const Shape &shape);
template void MSDFErrorCorrection::apply(const BitmapRef<float, 3> &sdf) const;
template void MSDFErrorCorrection::apply(const BitmapRef<float, 4> &sdf) const;

}