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//
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#include "precomp.hpp"
#include <limits>
using namespace cv;
template<typename _Tp> static int solveQuadratic(_Tp a, _Tp b, _Tp c, _Tp& x1, _Tp& x2)
{
if( a == 0 )
{
if( b == 0 )
{
x1 = x2 = 0;
return c == 0;
}
x1 = x2 = -c/b;
return 1;
}
_Tp d = b*b - 4*a*c;
if( d < 0 )
{
x1 = x2 = 0;
return 0;
}
if( d > 0 )
{
d = std::sqrt(d);
double s = 1/(2*a);
x1 = (-b - d)*s;
x2 = (-b + d)*s;
if( x1 > x2 )
std::swap(x1, x2);
return 2;
}
x1 = x2 = -b/(2*a);
return 1;
}
//for android ndk
#undef _S
static inline Point2f applyHomography( const Mat_<double>& H, const Point2f& pt )
{
double z = H(2,0)*pt.x + H(2,1)*pt.y + H(2,2);
if( z )
{
double w = 1./z;
return Point2f( (float)((H(0,0)*pt.x + H(0,1)*pt.y + H(0,2))*w), (float)((H(1,0)*pt.x + H(1,1)*pt.y + H(1,2))*w) );
}
return Point2f( std::numeric_limits<float>::max(), std::numeric_limits<float>::max() );
}
static inline void linearizeHomographyAt( const Mat_<double>& H, const Point2f& pt, Mat_<double>& A )
{
A.create(2,2);
double p1 = H(0,0)*pt.x + H(0,1)*pt.y + H(0,2),
p2 = H(1,0)*pt.x + H(1,1)*pt.y + H(1,2),
p3 = H(2,0)*pt.x + H(2,1)*pt.y + H(2,2),
p3_2 = p3*p3;
if( p3 )
{
A(0,0) = H(0,0)/p3 - p1*H(2,0)/p3_2; // fxdx
A(0,1) = H(0,1)/p3 - p1*H(2,1)/p3_2; // fxdy
A(1,0) = H(1,0)/p3 - p2*H(2,0)/p3_2; // fydx
A(1,1) = H(1,1)/p3 - p2*H(2,1)/p3_2; // fydx
}
else
A.setTo(Scalar::all(std::numeric_limits<double>::max()));
}
class EllipticKeyPoint
{
public:
EllipticKeyPoint();
EllipticKeyPoint( const Point2f& _center, const Scalar& _ellipse );
static void convert( const std::vector<KeyPoint>& src, std::vector<EllipticKeyPoint>& dst );
static void convert( const std::vector<EllipticKeyPoint>& src, std::vector<KeyPoint>& dst );
static Mat_<double> getSecondMomentsMatrix( const Scalar& _ellipse );
Mat_<double> getSecondMomentsMatrix() const;
void calcProjection( const Mat_<double>& H, EllipticKeyPoint& projection ) const;
static void calcProjection( const std::vector<EllipticKeyPoint>& src, const Mat_<double>& H, std::vector<EllipticKeyPoint>& dst );
Point2f center;
Scalar ellipse; // 3 elements a, b, c: ax^2+2bxy+cy^2=1
Size_<float> axes; // half length of ellipse axes
Size_<float> boundingBox; // half sizes of bounding box which sides are parallel to the coordinate axes
};
EllipticKeyPoint::EllipticKeyPoint()
{
*this = EllipticKeyPoint(Point2f(0,0), Scalar(1, 0, 1) );
}
EllipticKeyPoint::EllipticKeyPoint( const Point2f& _center, const Scalar& _ellipse )
{
center = _center;
ellipse = _ellipse;
double a = ellipse[0], b = ellipse[1], c = ellipse[2];
double ac_b2 = a*c - b*b;
double x1, x2;
solveQuadratic(1., -(a+c), ac_b2, x1, x2);
axes.width = (float)(1/sqrt(x1));
axes.height = (float)(1/sqrt(x2));
boundingBox.width = (float)sqrt(ellipse[2]/ac_b2);
boundingBox.height = (float)sqrt(ellipse[0]/ac_b2);
}
Mat_<double> EllipticKeyPoint::getSecondMomentsMatrix( const Scalar& _ellipse )
{
Mat_<double> M(2, 2);
M(0,0) = _ellipse[0];
M(1,0) = M(0,1) = _ellipse[1];
M(1,1) = _ellipse[2];
return M;
}
Mat_<double> EllipticKeyPoint::getSecondMomentsMatrix() const
{
return getSecondMomentsMatrix(ellipse);
}
void EllipticKeyPoint::calcProjection( const Mat_<double>& H, EllipticKeyPoint& projection ) const
{
Point2f dstCenter = applyHomography(H, center);
Mat_<double> invM; invert(getSecondMomentsMatrix(), invM);
Mat_<double> Aff; linearizeHomographyAt(H, center, Aff);
Mat_<double> dstM; invert(Aff*invM*Aff.t(), dstM);
projection = EllipticKeyPoint( dstCenter, Scalar(dstM(0,0), dstM(0,1), dstM(1,1)) );
}
void EllipticKeyPoint::convert( const std::vector<KeyPoint>& src, std::vector<EllipticKeyPoint>& dst )
{
if( !src.empty() )
{
dst.resize(src.size());
for( size_t i = 0; i < src.size(); i++ )
{
float rad = src[i].size/2;
CV_Assert( rad );
float fac = 1.f/(rad*rad);
dst[i] = EllipticKeyPoint( src[i].pt, Scalar(fac, 0, fac) );
}
}
}
void EllipticKeyPoint::convert( const std::vector<EllipticKeyPoint>& src, std::vector<KeyPoint>& dst )
{
if( !src.empty() )
{
dst.resize(src.size());
for( size_t i = 0; i < src.size(); i++ )
{
Size_<float> axes = src[i].axes;
float rad = sqrt(axes.height*axes.width);
dst[i] = KeyPoint(src[i].center, 2*rad );
}
}
}
void EllipticKeyPoint::calcProjection( const std::vector<EllipticKeyPoint>& src, const Mat_<double>& H, std::vector<EllipticKeyPoint>& dst )
{
if( !src.empty() )
{
CV_Assert( !H.empty() && H.cols == 3 && H.rows == 3);
dst.resize(src.size());
std::vector<EllipticKeyPoint>::const_iterator srcIt = src.begin();
std::vector<EllipticKeyPoint>::iterator dstIt = dst.begin();
for( ; srcIt != src.end(); ++srcIt, ++dstIt )
srcIt->calcProjection(H, *dstIt);
}
}
static void filterEllipticKeyPointsByImageSize( std::vector<EllipticKeyPoint>& keypoints, const Size& imgSize )
{
if( !keypoints.empty() )
{
std::vector<EllipticKeyPoint> filtered;
filtered.reserve(keypoints.size());
std::vector<EllipticKeyPoint>::const_iterator it = keypoints.begin();
for( int i = 0; it != keypoints.end(); ++it, i++ )
{
if( it->center.x + it->boundingBox.width < imgSize.width &&
it->center.x - it->boundingBox.width > 0 &&
it->center.y + it->boundingBox.height < imgSize.height &&
it->center.y - it->boundingBox.height > 0 )
filtered.push_back(*it);
}
keypoints.assign(filtered.begin(), filtered.end());
}
}
struct IntersectAreaCounter
{
IntersectAreaCounter( float _dr, int _minx,
int _miny, int _maxy,
const Point2f& _diff,
const Scalar& _ellipse1, const Scalar& _ellipse2 ) :
dr(_dr), bua(0), bna(0), minx(_minx), miny(_miny), maxy(_maxy),
diff(_diff), ellipse1(_ellipse1), ellipse2(_ellipse2) {}
IntersectAreaCounter( const IntersectAreaCounter& counter, Split )
{
*this = counter;
bua = 0;
bna = 0;
}
void operator()( const BlockedRange& range )
{
CV_Assert( miny < maxy );
CV_Assert( dr > FLT_EPSILON );
int temp_bua = bua, temp_bna = bna;
for( int i = range.begin(); i != range.end(); i++ )
{
float rx1 = minx + i*dr;
float rx2 = rx1 - diff.x;
for( float ry1 = (float)miny; ry1 <= (float)maxy; ry1 += dr )
{
float ry2 = ry1 - diff.y;
//compute the distance from the ellipse center
float e1 = (float)(ellipse1[0]*rx1*rx1 + 2*ellipse1[1]*rx1*ry1 + ellipse1[2]*ry1*ry1);
float e2 = (float)(ellipse2[0]*rx2*rx2 + 2*ellipse2[1]*rx2*ry2 + ellipse2[2]*ry2*ry2);
//compute the area
if( e1<1 && e2<1 ) temp_bna++;
if( e1<1 || e2<1 ) temp_bua++;
}
}
bua = temp_bua;
bna = temp_bna;
}
void join( IntersectAreaCounter& ac )
{
bua += ac.bua;
bna += ac.bna;
}
float dr;
int bua, bna;
int minx;
int miny, maxy;
Point2f diff;
Scalar ellipse1, ellipse2;
};
struct SIdx
{
SIdx() : S(-1), i1(-1), i2(-1) {}
SIdx(float _S, int _i1, int _i2) : S(_S), i1(_i1), i2(_i2) {}
float S;
int i1;
int i2;
bool operator<(const SIdx& v) const { return S > v.S; }
struct UsedFinder
{
UsedFinder(const SIdx& _used) : used(_used) {}
const SIdx& used;
bool operator()(const SIdx& v) const { return (v.i1 == used.i1 || v.i2 == used.i2); }
UsedFinder& operator=(const UsedFinder&);
};
};
static void computeOneToOneMatchedOverlaps( const std::vector<EllipticKeyPoint>& keypoints1, const std::vector<EllipticKeyPoint>& keypoints2t,
bool commonPart, std::vector<SIdx>& overlaps, float minOverlap )
{
CV_Assert( minOverlap >= 0.f );
overlaps.clear();
if( keypoints1.empty() || keypoints2t.empty() )
return;
overlaps.clear();
overlaps.reserve(cvRound(keypoints1.size() * keypoints2t.size() * 0.01));
for( size_t i1 = 0; i1 < keypoints1.size(); i1++ )
{
EllipticKeyPoint kp1 = keypoints1[i1];
float maxDist = sqrt(kp1.axes.width*kp1.axes.height),
fac = 30.f/maxDist;
if( !commonPart )
fac=3;
maxDist = maxDist*4;
fac = 1.f/(fac*fac);
EllipticKeyPoint keypoint1a = EllipticKeyPoint( kp1.center, Scalar(fac*kp1.ellipse[0], fac*kp1.ellipse[1], fac*kp1.ellipse[2]) );
for( size_t i2 = 0; i2 < keypoints2t.size(); i2++ )
{
EllipticKeyPoint kp2 = keypoints2t[i2];
Point2f diff = kp2.center - kp1.center;
if( norm(diff) < maxDist )
{
EllipticKeyPoint keypoint2a = EllipticKeyPoint( kp2.center, Scalar(fac*kp2.ellipse[0], fac*kp2.ellipse[1], fac*kp2.ellipse[2]) );
//find the largest eigenvalue
int maxx = (int)ceil(( keypoint1a.boundingBox.width > (diff.x+keypoint2a.boundingBox.width)) ?
keypoint1a.boundingBox.width : (diff.x+keypoint2a.boundingBox.width));
int minx = (int)floor((-keypoint1a.boundingBox.width < (diff.x-keypoint2a.boundingBox.width)) ?
-keypoint1a.boundingBox.width : (diff.x-keypoint2a.boundingBox.width));
int maxy = (int)ceil(( keypoint1a.boundingBox.height > (diff.y+keypoint2a.boundingBox.height)) ?
keypoint1a.boundingBox.height : (diff.y+keypoint2a.boundingBox.height));
int miny = (int)floor((-keypoint1a.boundingBox.height < (diff.y-keypoint2a.boundingBox.height)) ?
-keypoint1a.boundingBox.height : (diff.y-keypoint2a.boundingBox.height));
int mina = (maxx-minx) < (maxy-miny) ? (maxx-minx) : (maxy-miny) ;
//compute the area
float dr = (float)mina/50.f;
int N = (int)floor((float)(maxx - minx) / dr);
IntersectAreaCounter ac( dr, minx, miny, maxy, diff, keypoint1a.ellipse, keypoint2a.ellipse );
parallel_reduce( BlockedRange(0, N+1), ac );
if( ac.bna > 0 )
{
float ov = (float)ac.bna / (float)ac.bua;
if( ov >= minOverlap )
overlaps.push_back(SIdx(ov, (int)i1, (int)i2));
}
}
}
}
std::sort( overlaps.begin(), overlaps.end() );
typedef std::vector<SIdx>::iterator It;
It pos = overlaps.begin();
It end = overlaps.end();
while(pos != end)
{
It prev = pos++;
end = std::remove_if(pos, end, SIdx::UsedFinder(*prev));
}
overlaps.erase(pos, overlaps.end());
}
static void calculateRepeatability( const Mat& img1, const Mat& img2, const Mat& H1to2,
const std::vector<KeyPoint>& _keypoints1, const std::vector<KeyPoint>& _keypoints2,
float& repeatability, int& correspondencesCount,
Mat* thresholdedOverlapMask=0 )
{
std::vector<EllipticKeyPoint> keypoints1, keypoints2, keypoints1t, keypoints2t;
EllipticKeyPoint::convert( _keypoints1, keypoints1 );
EllipticKeyPoint::convert( _keypoints2, keypoints2 );
// calculate projections of key points
EllipticKeyPoint::calcProjection( keypoints1, H1to2, keypoints1t );
Mat H2to1; invert(H1to2, H2to1);
EllipticKeyPoint::calcProjection( keypoints2, H2to1, keypoints2t );
float overlapThreshold;
bool ifEvaluateDetectors = thresholdedOverlapMask == 0;
if( ifEvaluateDetectors )
{
overlapThreshold = 1.f - 0.4f;
// remove key points from outside of the common image part
Size sz1 = img1.size(), sz2 = img2.size();
filterEllipticKeyPointsByImageSize( keypoints1, sz1 );
filterEllipticKeyPointsByImageSize( keypoints1t, sz2 );
filterEllipticKeyPointsByImageSize( keypoints2, sz2 );
filterEllipticKeyPointsByImageSize( keypoints2t, sz1 );
}
else
{
overlapThreshold = 1.f - 0.5f;
thresholdedOverlapMask->create( (int)keypoints1.size(), (int)keypoints2t.size(), CV_8UC1 );
thresholdedOverlapMask->setTo( Scalar::all(0) );
}
size_t size1 = keypoints1.size(), size2 = keypoints2t.size();
size_t minCount = MIN( size1, size2 );
// calculate overlap errors
std::vector<SIdx> overlaps;
computeOneToOneMatchedOverlaps( keypoints1, keypoints2t, ifEvaluateDetectors, overlaps, overlapThreshold/*min overlap*/ );
correspondencesCount = -1;
repeatability = -1.f;
if( overlaps.empty() )
return;
if( ifEvaluateDetectors )
{
// regions one-to-one matching
correspondencesCount = (int)overlaps.size();
repeatability = minCount ? (float)correspondencesCount / minCount : -1;
}
else
{
for( size_t i = 0; i < overlaps.size(); i++ )
{
int y = overlaps[i].i1;
int x = overlaps[i].i2;
thresholdedOverlapMask->at<uchar>(y,x) = 1;
}
}
}
void cv::evaluateFeatureDetector( const Mat& img1, const Mat& img2, const Mat& H1to2,
std::vector<KeyPoint>* _keypoints1, std::vector<KeyPoint>* _keypoints2,
float& repeatability, int& correspCount,
const Ptr<FeatureDetector>& _fdetector )
{
Ptr<FeatureDetector> fdetector(_fdetector);
std::vector<KeyPoint> *keypoints1, *keypoints2, buf1, buf2;
keypoints1 = _keypoints1 != 0 ? _keypoints1 : &buf1;
keypoints2 = _keypoints2 != 0 ? _keypoints2 : &buf2;
if( (keypoints1->empty() || keypoints2->empty()) && !fdetector )
CV_Error( Error::StsBadArg, "fdetector must not be empty when keypoints1 or keypoints2 is empty" );
if( keypoints1->empty() )
fdetector->detect( img1, *keypoints1 );
if( keypoints2->empty() )
fdetector->detect( img2, *keypoints2 );
calculateRepeatability( img1, img2, H1to2, *keypoints1, *keypoints2, repeatability, correspCount );
}
struct DMatchForEvaluation : public DMatch
{
uchar isCorrect;
DMatchForEvaluation( const DMatch &dm ) : DMatch( dm ) {}
};
static inline float recall( int correctMatchCount, int correspondenceCount )
{
return correspondenceCount ? (float)correctMatchCount / (float)correspondenceCount : -1;
}
static inline float precision( int correctMatchCount, int falseMatchCount )
{
return correctMatchCount + falseMatchCount ? (float)correctMatchCount / (float)(correctMatchCount + falseMatchCount) : -1;
}
void cv::computeRecallPrecisionCurve( const std::vector<std::vector<DMatch> >& matches1to2,
const std::vector<std::vector<uchar> >& correctMatches1to2Mask,
std::vector<Point2f>& recallPrecisionCurve )
{
CV_Assert( matches1to2.size() == correctMatches1to2Mask.size() );
std::vector<DMatchForEvaluation> allMatches;
int correspondenceCount = 0;
for( size_t i = 0; i < matches1to2.size(); i++ )
{
for( size_t j = 0; j < matches1to2[i].size(); j++ )
{
DMatchForEvaluation match = matches1to2[i][j];
match.isCorrect = correctMatches1to2Mask[i][j] ;
allMatches.push_back( match );
correspondenceCount += match.isCorrect != 0 ? 1 : 0;
}
}
std::sort( allMatches.begin(), allMatches.end() );
int correctMatchCount = 0, falseMatchCount = 0;
recallPrecisionCurve.resize( allMatches.size() );
for( size_t i = 0; i < allMatches.size(); i++ )
{
if( allMatches[i].isCorrect )
correctMatchCount++;
else
falseMatchCount++;
float r = recall( correctMatchCount, correspondenceCount );
float p = precision( correctMatchCount, falseMatchCount );
recallPrecisionCurve[i] = Point2f(1-p, r);
}
}
float cv::getRecall( const std::vector<Point2f>& recallPrecisionCurve, float l_precision )
{
int nearestPointIndex = getNearestPoint( recallPrecisionCurve, l_precision );
float recall = -1.f;
if( nearestPointIndex >= 0 )
recall = recallPrecisionCurve[nearestPointIndex].y;
return recall;
}
int cv::getNearestPoint( const std::vector<Point2f>& recallPrecisionCurve, float l_precision )
{
int nearestPointIndex = -1;
if( l_precision >= 0 && l_precision <= 1 )
{
float minDiff = FLT_MAX;
for( size_t i = 0; i < recallPrecisionCurve.size(); i++ )
{
float curDiff = std::fabs(l_precision - recallPrecisionCurve[i].x);
if( curDiff <= minDiff )
{
nearestPointIndex = (int)i;
minDiff = curDiff;
}
}
}
return nearestPointIndex;
}