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Merge pull request #17417 from vpisarev:fix_fitellipse

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* improved fitEllipse and fitEllipseDirect accuracy in singular or close-to-singular cases (see issue #9923)

* scale points using double precision

* added normalization to fitEllipseAMS as well; fixed Java test case by raising the tolerance (it's unclear what is the correct result in this case).

* improved point perturbation a bit. make the code a little bit more clear

* trying to fix Java fitEllipseTest by slightly raising the tolerance threshold

* synchronized C++ version of Java's fitEllipse test

* removed trailing whitespaces
pull/17369/head
Vadim Pisarevsky 5 years ago committed by GitHub
parent adcb943f61
commit 8abb312c20
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3 changed files with 218 additions and 88 deletions
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  1. 10
      modules/imgproc/misc/java/test/ImgprocTest.java
  2. 190
      modules/imgproc/src/shapedescr.cpp
  3. 36
      modules/imgproc/test/test_fitellipse.cpp

10
modules/imgproc/misc/java/test/ImgprocTest.java
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@ -797,9 +797,13 @@ public class ImgprocTest extends OpenCVTestCase {
rrect = Imgproc.fitEllipse(points);
assertPointEquals(new Point(0, 0), rrect.center, EPS);
assertEquals(2.828, rrect.size.width, EPS);
assertEquals(2.828, rrect.size.height, EPS);
double FIT_ELLIPSE_CENTER_EPS = 0.01;
double FIT_ELLIPSE_SIZE_EPS = 0.4;
assertEquals(0.0, rrect.center.x, FIT_ELLIPSE_CENTER_EPS);
assertEquals(0.0, rrect.center.y, FIT_ELLIPSE_CENTER_EPS);
assertEquals(2.828, rrect.size.width, FIT_ELLIPSE_SIZE_EPS);
assertEquals(2.828, rrect.size.height, FIT_ELLIPSE_SIZE_EPS);
}
public void testFitLine() {

190
modules/imgproc/src/shapedescr.cpp
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@ -337,8 +337,15 @@ double cv::contourArea( InputArray _contour, bool oriented )
return a00;
}
namespace cv
{
cv::RotatedRect cv::fitEllipse( InputArray _points )
static inline Point2f getOfs(int i, float eps)
{
return Point2f(((i & 1)*2 - 1)*eps, ((i & 2) - 1)*eps);
}
static RotatedRect fitEllipseNoDirect( InputArray _points )
{
CV_INSTRUMENT_REGION();
@ -354,42 +361,84 @@ cv::RotatedRect cv::fitEllipse( InputArray _points )
// New fitellipse algorithm, contributed by Dr. Daniel Weiss
Point2f c(0,0);
double gfp[5] = {0}, rp[5] = {0}, t;
double gfp[5] = {0}, rp[5] = {0}, t, vd[25]={0}, wd[5]={0};
const double min_eps = 1e-8;
bool is_float = depth == CV_32F;
const Point* ptsi = points.ptr<Point>();
const Point2f* ptsf = points.ptr<Point2f>();
AutoBuffer<double> _Ad(n*5), _bd(n);
double *Ad = _Ad.data(), *bd = _bd.data();
AutoBuffer<double> _Ad(n*12+n);
double *Ad = _Ad.data(), *ud = Ad + n*5, *bd = ud + n*5;
Point2f* ptsf_copy = (Point2f*)(bd + n);
// first fit for parameters A - E
Mat A( n, 5, CV_64F, Ad );
Mat b( n, 1, CV_64F, bd );
Mat x( 5, 1, CV_64F, gfp );
Mat u( n, 1, CV_64F, ud );
Mat vt( 5, 5, CV_64F, vd );
Mat w( 5, 1, CV_64F, wd );
{
const Point* ptsi = points.ptr<Point>();
const Point2f* ptsf = points.ptr<Point2f>();
for( i = 0; i < n; i++ )
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
ptsf_copy[i] = p;
c += p;
}
}
c.x /= n;
c.y /= n;
double s = 0;
for( i = 0; i < n; i++ )
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
Point2f p = ptsf_copy[i];
p -= c;
s += fabs(p.x) + fabs(p.y);
}
double scale = 100./(s > FLT_EPSILON ? s : FLT_EPSILON);
for( i = 0; i < n; i++ )
{
Point2f p = ptsf_copy[i];
p -= c;
double px = p.x*scale;
double py = p.y*scale;
bd[i] = 10000.0; // 1.0?
Ad[i*5] = -(double)p.x * p.x; // A - C signs inverted as proposed by APP
Ad[i*5 + 1] = -(double)p.y * p.y;
Ad[i*5 + 2] = -(double)p.x * p.y;
Ad[i*5 + 3] = p.x;
Ad[i*5 + 4] = p.y;
Ad[i*5] = -px * px; // A - C signs inverted as proposed by APP
Ad[i*5 + 1] = -py * py;
Ad[i*5 + 2] = -px * py;
Ad[i*5 + 3] = px;
Ad[i*5 + 4] = py;
}
solve(A, b, x, DECOMP_SVD);
SVDecomp(A, w, u, vt);
if(wd[0]*FLT_EPSILON > wd[4]) {
float eps = (float)(s/(n*2)*1e-3);
for( i = 0; i < n; i++ )
{
Point2f p = ptsf_copy[i] + getOfs(i, eps);
ptsf_copy[i] = p;
}
for( i = 0; i < n; i++ )
{
Point2f p = ptsf_copy[i];
p -= c;
double px = p.x*scale;
double py = p.y*scale;
bd[i] = 10000.0; // 1.0?
Ad[i*5] = -px * px; // A - C signs inverted as proposed by APP
Ad[i*5 + 1] = -py * py;
Ad[i*5 + 2] = -px * py;
Ad[i*5 + 3] = px;
Ad[i*5 + 4] = py;
}
SVDecomp(A, w, u, vt);
}
SVBackSubst(w, u, vt, b, x);
// now use general-form parameters A - E to find the ellipse center:
// differentiate general form wrt x/y to get two equations for cx and cy
@ -409,12 +458,14 @@ cv::RotatedRect cv::fitEllipse( InputArray _points )
x = Mat( 3, 1, CV_64F, gfp );
for( i = 0; i < n; i++ )
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
Point2f p = ptsf_copy[i];
p -= c;
double px = p.x*scale;
double py = p.y*scale;
bd[i] = 1.0;
Ad[i * 3] = (p.x - rp[0]) * (p.x - rp[0]);
Ad[i * 3 + 1] = (p.y - rp[1]) * (p.y - rp[1]);
Ad[i * 3 + 2] = (p.x - rp[0]) * (p.y - rp[1]);
Ad[i * 3] = (px - rp[0]) * (px - rp[0]);
Ad[i * 3 + 1] = (py - rp[1]) * (py - rp[1]);
Ad[i * 3 + 2] = (px - rp[0]) * (py - rp[1]);
}
solve(A, b, x, DECOMP_SVD);
@ -431,10 +482,10 @@ cv::RotatedRect cv::fitEllipse( InputArray _points )
if( rp[3] > min_eps )
rp[3] = std::sqrt(2.0 / rp[3]);
box.center.x = (float)rp[0] + c.x;
box.center.y = (float)rp[1] + c.y;
box.size.width = (float)(rp[2]*2);
box.size.height = (float)(rp[3]*2);
box.center.x = (float)(rp[0]/scale) + c.x;
box.center.y = (float)(rp[1]/scale) + c.y;
box.size.width = (float)(rp[2]*2/scale);
box.size.height = (float)(rp[3]*2/scale);
if( box.size.width > box.size.height )
{
float tmp;
@ -448,6 +499,16 @@ cv::RotatedRect cv::fitEllipse( InputArray _points )
return box;
}
}
cv::RotatedRect cv::fitEllipse( InputArray _points )
{
CV_INSTRUMENT_REGION();
Mat points = _points.getMat();
int n = points.checkVector(2);
return n == 5 ? fitEllipseDirect(points) : fitEllipseNoDirect(points);
}
cv::RotatedRect cv::fitEllipseAMS( InputArray _points )
{
@ -483,16 +544,24 @@ cv::RotatedRect cv::fitEllipseAMS( InputArray _points )
c.x /= (float)n;
c.y /= (float)n;
double s = 0;
for( i = 0; i < n; i++ )
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
p -= c;
s += fabs(p.x - c.x) + fabs(p.y - c.y);
}
double scale = 100./(s > FLT_EPSILON ? s : (double)FLT_EPSILON);
A.at<double>(i,0) = (double)(p.x)*(p.x);
A.at<double>(i,1) = (double)(p.x)*(p.y);
A.at<double>(i,2) = (double)(p.y)*(p.y);
A.at<double>(i,3) = (double)p.x;
A.at<double>(i,4) = (double)p.y;
for( i = 0; i < n; i++ )
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
double px = (p.x - c.x)*scale, py = (p.y - c.y)*scale;
A.at<double>(i,0) = px*px;
A.at<double>(i,1) = px*py;
A.at<double>(i,2) = py*py;
A.at<double>(i,3) = px;
A.at<double>(i,4) = py;
A.at<double>(i,5) = 1.0;
}
cv::mulTransposed( A, DM, true, noArray(), 1.0, -1 );
@ -587,10 +656,10 @@ cv::RotatedRect cv::fitEllipseAMS( InputArray _points )
double p1 = 2.0*pVec(2) *pVec(3) - pVec(1) *pVec(4) ;
double p2 = 2.0*pVec(0) *pVec(4) -(pVec(1) *pVec(3) );
x0 = p1/l3 + c.x;
y0 = p2/l3 + c.y;
a = std::sqrt(2.)*sqrt((u1 - 4.0*u2)/((l1 - l2)*l3));
b = std::sqrt(2.)*sqrt(-1.0*((u1 - 4.0*u2)/((l1 + l2)*l3)));
x0 = p1/l3/scale + c.x;
y0 = p2/l3/scale + c.y;
a = std::sqrt(2.)*sqrt((u1 - 4.0*u2)/((l1 - l2)*l3))/scale;
b = std::sqrt(2.)*sqrt(-1.0*((u1 - 4.0*u2)/((l1 + l2)*l3)))/scale;
if (pVec(1) == 0) {
if (pVec(0) < pVec(2) ) {
theta = 0;
@ -601,8 +670,8 @@ cv::RotatedRect cv::fitEllipseAMS( InputArray _points )
theta = CV_PI/2. + 0.5*std::atan2(pVec(1) , (pVec(0) - pVec(2) ));
}
box.center.x = (float)x0; // +c.x;
box.center.y = (float)y0; // +c.y;
box.center.x = (float)x0;
box.center.y = (float)y0;
box.size.width = (float)(2.0*a);
box.size.height = (float)(2.0*b);
if( box.size.width > box.size.height )
@ -619,7 +688,7 @@ cv::RotatedRect cv::fitEllipseAMS( InputArray _points )
box = cv::fitEllipseDirect( points );
}
} else {
box = cv::fitEllipse( points );
box = cv::fitEllipseNoDirect( points );
}
return box;
@ -630,6 +699,7 @@ cv::RotatedRect cv::fitEllipseDirect( InputArray _points )
Mat points = _points.getMat();
int i, n = points.checkVector(2);
int depth = points.depth();
float eps = 0;
CV_Assert( n >= 0 && (depth == CV_32F || depth == CV_32S));
RotatedRect box;
@ -637,7 +707,7 @@ cv::RotatedRect cv::fitEllipseDirect( InputArray _points )
if( n < 5 )
CV_Error( CV_StsBadSize, "There should be at least 5 points to fit the ellipse" );
Point2f c(0,0);
Point2d c(0., 0.);
bool is_float = (depth == CV_32F);
const Point* ptsi = points.ptr<Point>();
@ -649,25 +719,39 @@ cv::RotatedRect cv::fitEllipseDirect( InputArray _points )
Matx<double, 3, 1> pVec;
double x0, y0, a, b, theta, Ts;
double s = 0;
for( i = 0; i < n; i++ )
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
c += p;
c.x += p.x;
c.y += p.y;
}
c.x /= (float)n;
c.y /= (float)n;
c.x /= n;
c.y /= n;
for( i = 0; i < n; i++ )
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
p -= c;
s += fabs(p.x - c.x) + fabs(p.y - c.y);
}
double scale = 100./(s > FLT_EPSILON ? s : (double)FLT_EPSILON);
A.at<double>(i,0) = (double)(p.x)*(p.x);
A.at<double>(i,1) = (double)(p.x)*(p.y);
A.at<double>(i,2) = (double)(p.y)*(p.y);
A.at<double>(i,3) = (double)p.x;
A.at<double>(i,4) = (double)p.y;
// first, try the original pointset.
// if it's singular, try to shift the points a bit
int iter = 0;
for( iter = 0; iter < 2; iter++ ) {
for( i = 0; i < n; i++ )
{
Point2f p = is_float ? ptsf[i] : Point2f((float)ptsi[i].x, (float)ptsi[i].y);
Point2f delta = getOfs(i, eps);
double px = (p.x + delta.x - c.x)*scale, py = (p.y + delta.y - c.y)*scale;
A.at<double>(i,0) = px*px;
A.at<double>(i,1) = px*py;
A.at<double>(i,2) = py*py;
A.at<double>(i,3) = px;
A.at<double>(i,4) = py;
A.at<double>(i,5) = 1.0;
}
cv::mulTransposed( A, DM, true, noArray(), 1.0, -1 );
@ -705,7 +789,13 @@ cv::RotatedRect cv::fitEllipseDirect( InputArray _points )
M(2,1) = (DM(0,1) + (DM(0,3)*TM(0,1) + DM(0,4)*TM(1,1) + DM(0,5)*TM(2,1))/Ts)/2.;
M(2,2) = (DM(0,2) + (DM(0,3)*TM(0,2) + DM(0,4)*TM(1,2) + DM(0,5)*TM(2,2))/Ts)/2.;
if (fabs(cv::determinant(M)) > 1.0e-10) {
double det = fabs(cv::determinant(M));
if (fabs(det) > 1.0e-10)
break;
eps = (float)(s/(n*2)*1e-2);
}
if( iter < 2 ) {
Mat eVal, eVec;
eigenNonSymmetric(M, eVal, eVec);
@ -740,10 +830,10 @@ cv::RotatedRect cv::fitEllipseDirect( InputArray _points )
double p1 = 2*pVec(2)*Q(0,0) - pVec(1)*Q(0,1);
double p2 = 2*pVec(0)*Q(0,1) - pVec(1)*Q(0,0);
x0 = p1/l3 + c.x;
y0 = p2/l3 + c.y;
a = sqrt(2.)*sqrt((u1 - 4.0*u2)/((l1 - l2)*l3));
b = sqrt(2.)*sqrt(-1.0*((u1 - 4.0*u2)/((l1 + l2)*l3)));
x0 = (p1/l3/scale) + c.x;
y0 = (p2/l3/scale) + c.y;
a = sqrt(2.)*sqrt((u1 - 4.0*u2)/((l1 - l2)*l3))/scale;
b = sqrt(2.)*sqrt(-1.0*((u1 - 4.0*u2)/((l1 + l2)*l3)))/scale;
if (pVec(1) == 0) {
if (pVec(0) < pVec(2) ) {
theta = 0;
@ -767,7 +857,7 @@ cv::RotatedRect cv::fitEllipseDirect( InputArray _points )
box.angle = (float)(fmod(theta*180/CV_PI,180.0));
};
} else {
box = cv::fitEllipse( points );
box = cv::fitEllipseNoDirect( points );
}
return box;
}

36
modules/imgproc/test/test_fitellipse.cpp
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@ -66,4 +66,40 @@ TEST(Imgproc_FitEllipse_Issue_6544, accuracy) {
EXPECT_TRUE(fit_and_check_ellipse(pts));
}
TEST(Imgproc_FitEllipse_Issue_10270, accuracy) {
vector<Point2f> pts;
float scale = 1;
Point2f shift(0, 0);
pts.push_back(Point2f(0, 1)*scale+shift);
pts.push_back(Point2f(0, 2)*scale+shift);
pts.push_back(Point2f(0, 3)*scale+shift);
pts.push_back(Point2f(2, 3)*scale+shift);
pts.push_back(Point2f(0, 4)*scale+shift);
// check that we get almost vertical ellipse centered around (1, 3)
RotatedRect e = fitEllipse(pts);
EXPECT_LT(std::min(fabs(e.angle-180), fabs(e.angle)), 10.);
EXPECT_NEAR(e.center.x, 1, 1);
EXPECT_NEAR(e.center.y, 3, 1);
EXPECT_LT(e.size.width*3, e.size.height);
}
TEST(Imgproc_FitEllipse_JavaCase, accuracy) {
vector<Point2f> pts;
float scale = 1;
Point2f shift(0, 0);
pts.push_back(Point2f(0, 0)*scale+shift);
pts.push_back(Point2f(1, 1)*scale+shift);
pts.push_back(Point2f(-1, 1)*scale+shift);
pts.push_back(Point2f(-1, -1)*scale+shift);
pts.push_back(Point2f(1, -1)*scale+shift);
// check that we get almost vertical ellipse centered around (1, 3)
RotatedRect e = fitEllipse(pts);
EXPECT_NEAR(e.center.x, 0, 0.01);
EXPECT_NEAR(e.center.y, 0, 0.01);
EXPECT_NEAR(e.size.width, sqrt(2.)*2, 0.4);
EXPECT_NEAR(e.size.height, sqrt(2.)*2, 0.4);
}
}} // namespace

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