Merge pull request #8301 from tonyke1993:p3p_alg

New p3p algorithm (accepted by CVPR 2017) (#8301)

* add p3p source code

* indent 4

* update publication info

* fix filename

* interface done

* plug in done, test needed

* debugging

* for test

* a working version

* clean p3p code

* test

* test

* fix warning, blank line

* apply patch from @catree

* add reference info

* namespace, indent 4

* static solveQuartic

* put small functions to anonymous namespace

doc/opencv.bib

@@ -897,3 +897,10 @@
   year={2010},
   publisher={Springer}
 }
+@INPROCEEDINGS{Ke17,
+  author = {Ke, Tong and Roumeliotis, Stergios},
+  title = {An Efficient Algebraic Solution to the Perspective-Three-Point Problem},
+  booktitle = {Computer Vision and Pattern Recognition (CVPR), 2017 IEEE Conference on},
+  year = {2017},
+  organization = {IEEE}
+}

modules/calib3d/include/opencv2/calib3d.hpp

@@ -236,8 +236,8 @@ enum { SOLVEPNP_ITERATIVE = 0,
        SOLVEPNP_EPNP      = 1, //!< EPnP: Efficient Perspective-n-Point Camera Pose Estimation @cite lepetit2009epnp
        SOLVEPNP_P3P       = 2, //!< Complete Solution Classification for the Perspective-Three-Point Problem @cite gao2003complete
        SOLVEPNP_DLS       = 3, //!< A Direct Least-Squares (DLS) Method for PnP  @cite hesch2011direct
-       SOLVEPNP_UPNP      = 4  //!< Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation @cite penate2013exhaustive
-
+       SOLVEPNP_UPNP      = 4, //!< Exhaustive Linearization for Robust Camera Pose and Focal Length Estimation @cite penate2013exhaustive
+       SOLVEPNP_AP3P      = 5  //!< An Efficient Algebraic Solution to the Perspective-Three-Point Problem @cite Ke17
 };
 
 enum { CALIB_CB_ADAPTIVE_THRESH = 1,

modules/calib3d/src/ap3p.cpp

+#include "ap3p.h"
+
+#include <cmath>
+#include <complex>
+
+using namespace std;
+
+namespace {
+void solveQuartic(const double *factors, double *realRoots) {
+    const double &a4 = factors[0];
+    const double &a3 = factors[1];
+    const double &a2 = factors[2];
+    const double &a1 = factors[3];
+    const double &a0 = factors[4];
+
+    double a4_2 = a4 * a4;
+    double a3_2 = a3 * a3;
+    double a4_3 = a4_2 * a4;
+    double a2a4 = a2 * a4;
+
+    double p4 = (8 * a2a4 - 3 * a3_2) / (8 * a4_2);
+    double q4 = (a3_2 * a3 - 4 * a2a4 * a3 + 8 * a1 * a4_2) / (8 * a4_3);
+    double r4 = (256 * a0 * a4_3 - 3 * (a3_2 * a3_2) - 64 * a1 * a3 * a4_2 + 16 * a2a4 * a3_2) / (256 * (a4_3 * a4));
+
+    double p3 = ((p4 * p4) / 12 + r4) / 3; // /=-3
+    double q3 = (72 * r4 * p4 - 2 * p4 * p4 * p4 - 27 * q4 * q4) / 432; // /=2
+
+    double t; // *=2
+    complex<double> w;
+    if (q3 >= 0)
+        w = -sqrt(static_cast<complex<double> >(q3 * q3 - p3 * p3 * p3)) - q3;
+    else
+        w = sqrt(static_cast<complex<double> >(q3 * q3 - p3 * p3 * p3)) - q3;
+    if (w.imag() == 0.0) {
+        w.real(cbrt(w.real()));
+        t = 2.0 * (w.real() + p3 / w.real());
+    } else {
+        w = pow(w, 1.0 / 3);
+        t = 4.0 * w.real();
+    }
+
+    complex<double> sqrt_2m = sqrt(static_cast<complex<double> >(-2 * p4 / 3 + t));
+    double B_4A = -a3 / (4 * a4);
+    double complex1 = 4 * p4 / 3 + t;
+    complex<double> complex2 = 2 * q4 / sqrt_2m;
+    double sqrt_2m_rh = sqrt_2m.real() / 2;
+    double sqrt1 = sqrt(-(complex1 + complex2)).real() / 2;
+    realRoots[0] = B_4A + sqrt_2m_rh + sqrt1;
+    realRoots[1] = B_4A + sqrt_2m_rh - sqrt1;
+    double sqrt2 = sqrt(-(complex1 - complex2)).real() / 2;
+    realRoots[2] = B_4A - sqrt_2m_rh + sqrt2;
+    realRoots[3] = B_4A - sqrt_2m_rh - sqrt2;
+}
+
+void polishQuarticRoots(const double *coeffs, double *roots) {
+    const int iterations = 2;
+    for (int i = 0; i < iterations; ++i) {
+        for (int j = 0; j < 4; ++j) {
+            double error =
+                    (((coeffs[0] * roots[j] + coeffs[1]) * roots[j] + coeffs[2]) * roots[j] + coeffs[3]) * roots[j] +
+                    coeffs[4];
+            double
+                    derivative =
+                    ((4 * coeffs[0] * roots[j] + 3 * coeffs[1]) * roots[j] + 2 * coeffs[2]) * roots[j] + coeffs[3];
+            roots[j] -= error / derivative;
+        }
+    }
+}
+
+inline void vect_cross(const double *a, const double *b, double *result) {
+    result[0] = a[1] * b[2] - a[2] * b[1];
+    result[1] = -(a[0] * b[2] - a[2] * b[0]);
+    result[2] = a[0] * b[1] - a[1] * b[0];
+}
+
+inline double vect_dot(const double *a, const double *b) {
+    return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
+}
+
+inline double vect_norm(const double *a) {
+    return sqrt(a[0] * a[0] + a[1] * a[1] + a[2] * a[2]);
+}
+
+inline void vect_scale(const double s, const double *a, double *result) {
+    result[0] = a[0] * s;
+    result[1] = a[1] * s;
+    result[2] = a[2] * s;
+}
+
+inline void vect_sub(const double *a, const double *b, double *result) {
+    result[0] = a[0] - b[0];
+    result[1] = a[1] - b[1];
+    result[2] = a[2] - b[2];
+}
+
+inline void vect_divide(const double *a, const double d, double *result) {
+    result[0] = a[0] / d;
+    result[1] = a[1] / d;
+    result[2] = a[2] / d;
+}
+
+inline void mat_mult(const double a[3][3], const double b[3][3], double result[3][3]) {
+    result[0][0] = a[0][0] * b[0][0] + a[0][1] * b[1][0] + a[0][2] * b[2][0];
+    result[0][1] = a[0][0] * b[0][1] + a[0][1] * b[1][1] + a[0][2] * b[2][1];
+    result[0][2] = a[0][0] * b[0][2] + a[0][1] * b[1][2] + a[0][2] * b[2][2];
+
+    result[1][0] = a[1][0] * b[0][0] + a[1][1] * b[1][0] + a[1][2] * b[2][0];
+    result[1][1] = a[1][0] * b[0][1] + a[1][1] * b[1][1] + a[1][2] * b[2][1];
+    result[1][2] = a[1][0] * b[0][2] + a[1][1] * b[1][2] + a[1][2] * b[2][2];
+
+    result[2][0] = a[2][0] * b[0][0] + a[2][1] * b[1][0] + a[2][2] * b[2][0];
+    result[2][1] = a[2][0] * b[0][1] + a[2][1] * b[1][1] + a[2][2] * b[2][1];
+    result[2][2] = a[2][0] * b[0][2] + a[2][1] * b[1][2] + a[2][2] * b[2][2];
+}
+}
+
+namespace cv {
+void ap3p::init_inverse_parameters() {
+    inv_fx = 1. / fx;
+    inv_fy = 1. / fy;
+    cx_fx = cx / fx;
+    cy_fy = cy / fy;
+}
+
+ap3p::ap3p(cv::Mat cameraMatrix) {
+    if (cameraMatrix.depth() == CV_32F)
+        init_camera_parameters<float>(cameraMatrix);
+    else
+        init_camera_parameters<double>(cameraMatrix);
+    init_inverse_parameters();
+}
+
+ap3p::ap3p(double _fx, double _fy, double _cx, double _cy) {
+    fx = _fx;
+    fy = _fy;
+    cx = _cx;
+    cy = _cy;
+    init_inverse_parameters();
+}
+
+// This algorithm is from "Tong Ke, Stergios Roumeliotis, An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (Accepted by CVPR 2017)
+// See https://arxiv.org/pdf/1701.08237.pdf
+// featureVectors: The 3 bearing measurements (normalized) stored as column vectors
+// worldPoints: The positions of the 3 feature points stored as column vectors
+// solutionsR: 4 possible solutions of rotation matrix of the world w.r.t the camera frame
+// solutionsT: 4 possible solutions of translation of the world origin w.r.t the camera frame
+int ap3p::computePoses(const double featureVectors[3][3],
+                       const double worldPoints[3][3],
+                       double solutionsR[4][3][3],
+                       double solutionsT[4][3]) {
+
+    //world point vectors
+    double w1[3] = {worldPoints[0][0], worldPoints[1][0], worldPoints[2][0]};
+    double w2[3] = {worldPoints[0][1], worldPoints[1][1], worldPoints[2][1]};
+    double w3[3] = {worldPoints[0][2], worldPoints[1][2], worldPoints[2][2]};
+    // k1
+    double u0[3];
+    vect_sub(w1, w2, u0);
+
+    double nu0 = vect_norm(u0);
+    double k1[3];
+    vect_divide(u0, nu0, k1);
+    // bi
+    double b1[3] = {featureVectors[0][0], featureVectors[1][0], featureVectors[2][0]};
+    double b2[3] = {featureVectors[0][1], featureVectors[1][1], featureVectors[2][1]};
+    double b3[3] = {featureVectors[0][2], featureVectors[1][2], featureVectors[2][2]};
+    // k3,tz
+    double k3[3];
+    vect_cross(b1, b2, k3);
+    double nk3 = vect_norm(k3);
+    vect_divide(k3, nk3, k3);
+
+    double tz[3];
+    vect_cross(b1, k3, tz);
+    // ui,vi
+    double v1[3];
+    vect_cross(b1, b3, v1);
+    double v2[3];
+    vect_cross(b2, b3, v2);
+
+    double u1[3];
+    vect_sub(w1, w3, u1);
+    // coefficients related terms
+    double u1k1 = vect_dot(u1, k1);
+    double k3b3 = vect_dot(k3, b3);
+    // f1i
+    double f11 = k3b3;
+    double f13 = vect_dot(k3, v1);
+    double f15 = -u1k1 * f11;
+    //delta
+    double nl[3];
+    vect_cross(u1, k1, nl);
+    double delta = vect_norm(nl);
+    vect_divide(nl, delta, nl);
+    f11 *= delta;
+    f13 *= delta;
+    // f2i
+    double u2k1 = u1k1 - nu0;
+    double f21 = vect_dot(tz, v2);
+    double f22 = nk3 * k3b3;
+    double f23 = vect_dot(k3, v2);
+    double f24 = u2k1 * f22;
+    double f25 = -u2k1 * f21;
+    f21 *= delta;
+    f22 *= delta;
+    f23 *= delta;
+    double g1 = f13 * f22;
+    double g2 = f13 * f25 - f15 * f23;
+    double g3 = f11 * f23 - f13 * f21;
+    double g4 = -f13 * f24;
+    double g5 = f11 * f22;
+    double g6 = f11 * f25 - f15 * f21;
+    double g7 = -f15 * f24;
+    double coeffs[5] = {g5 * g5 + g1 * g1 + g3 * g3,
+                        2 * (g5 * g6 + g1 * g2 + g3 * g4),
+                        g6 * g6 + 2 * g5 * g7 + g2 * g2 + g4 * g4 - g1 * g1 - g3 * g3,
+                        2 * (g6 * g7 - g1 * g2 - g3 * g4),
+                        g7 * g7 - g2 * g2 - g4 * g4};
+    double s[4];
+    solveQuartic(coeffs, s);
+    polishQuarticRoots(coeffs, s);
+
+    double temp[3];
+    vect_cross(k1, nl, temp);
+
+    double Ck1nl[3][3] =
+            {{k1[0], nl[0], temp[0]},
+             {k1[1], nl[1], temp[1]},
+             {k1[2], nl[2], temp[2]}};
+
+    double Cb1k3tzT[3][3] =
+            {{b1[0], b1[1], b1[2]},
+             {k3[0], k3[1], k3[2]},
+             {tz[0], tz[1], tz[2]}};
+
+    double b3p[3];
+    vect_scale((delta / k3b3), b3, b3p);
+
+    int nb_solutions = 0;
+    for (int i = 0; i < 4; ++i) {
+        double ctheta1p = s[i];
+        if (abs(ctheta1p) > 1)
+            continue;
+        double stheta1p = sqrt(1 - ctheta1p * ctheta1p);
+        stheta1p = (k3b3 > 0) ? stheta1p : -stheta1p;
+        double ctheta3 = g1 * ctheta1p + g2;
+        double stheta3 = g3 * ctheta1p + g4;
+        double ntheta3 = stheta1p / ((g5 * ctheta1p + g6) * ctheta1p + g7);
+        ctheta3 *= ntheta3;
+        stheta3 *= ntheta3;
+
+        double C13[3][3] =
+                {{ctheta3,            0,         -stheta3},
+                 {stheta1p * stheta3, ctheta1p,  stheta1p * ctheta3},
+                 {ctheta1p * stheta3, -stheta1p, ctheta1p * ctheta3}};
+
+        double temp_matrix[3][3];
+        double R[3][3];
+        mat_mult(Ck1nl, C13, temp_matrix);
+        mat_mult(temp_matrix, Cb1k3tzT, R);
+
+        // R' * p3
+        double rp3[3] =
+                {w3[0] * R[0][0] + w3[1] * R[1][0] + w3[2] * R[2][0],
+                 w3[0] * R[0][1] + w3[1] * R[1][1] + w3[2] * R[2][1],
+                 w3[0] * R[0][2] + w3[1] * R[1][2] + w3[2] * R[2][2]};
+
+        double pxstheta1p[3];
+        vect_scale(stheta1p, b3p, pxstheta1p);
+
+        vect_sub(pxstheta1p, rp3, solutionsT[nb_solutions]);
+
+        solutionsR[nb_solutions][0][0] = R[0][0];
+        solutionsR[nb_solutions][1][0] = R[0][1];
+        solutionsR[nb_solutions][2][0] = R[0][2];
+        solutionsR[nb_solutions][0][1] = R[1][0];
+        solutionsR[nb_solutions][1][1] = R[1][1];
+        solutionsR[nb_solutions][2][1] = R[1][2];
+        solutionsR[nb_solutions][0][2] = R[2][0];
+        solutionsR[nb_solutions][1][2] = R[2][1];
+        solutionsR[nb_solutions][2][2] = R[2][2];
+
+        nb_solutions++;
+    }
+
+    return nb_solutions;
+}
+
+bool ap3p::solve(cv::Mat &R, cv::Mat &tvec, const cv::Mat &opoints, const cv::Mat &ipoints) {
+    CV_INSTRUMENT_REGION()
+
+    double rotation_matrix[3][3], translation[3];
+    std::vector<double> points;
+    if (opoints.depth() == ipoints.depth()) {
+        if (opoints.depth() == CV_32F)
+            extract_points<cv::Point3f, cv::Point2f>(opoints, ipoints, points);
+        else
+            extract_points<cv::Point3d, cv::Point2d>(opoints, ipoints, points);
+    } else if (opoints.depth() == CV_32F)
+        extract_points<cv::Point3f, cv::Point2d>(opoints, ipoints, points);
+    else
+        extract_points<cv::Point3d, cv::Point2f>(opoints, ipoints, points);
+
+    bool result = solve(rotation_matrix, translation, points[0], points[1], points[2], points[3], points[4], points[5],
+                        points[6], points[7], points[8], points[9], points[10], points[11], points[12], points[13],
+                        points[14],
+                        points[15], points[16], points[17], points[18], points[19]);
+    cv::Mat(3, 1, CV_64F, translation).copyTo(tvec);
+    cv::Mat(3, 3, CV_64F, rotation_matrix).copyTo(R);
+    return result;
+}
+
+bool
+ap3p::solve(double R[3][3], double t[3], double mu0, double mv0, double X0, double Y0, double Z0, double mu1,
+            double mv1,
+            double X1, double Y1, double Z1, double mu2, double mv2, double X2, double Y2, double Z2, double mu3,
+            double mv3, double X3, double Y3, double Z3) {
+    double Rs[4][3][3], ts[4][3];
+
+    int n = solve(Rs, ts, mu0, mv0, X0, Y0, Z0, mu1, mv1, X1, Y1, Z1, mu2, mv2, X2, Y2, Z2);
+    if (n == 0)
+        return false;
+
+    int ns = 0;
+    double min_reproj = 0;
+    for (int i = 0; i < n; i++) {
+        double X3p = Rs[i][0][0] * X3 + Rs[i][0][1] * Y3 + Rs[i][0][2] * Z3 + ts[i][0];
+        double Y3p = Rs[i][1][0] * X3 + Rs[i][1][1] * Y3 + Rs[i][1][2] * Z3 + ts[i][1];
+        double Z3p = Rs[i][2][0] * X3 + Rs[i][2][1] * Y3 + Rs[i][2][2] * Z3 + ts[i][2];
+        double mu3p = cx + fx * X3p / Z3p;
+        double mv3p = cy + fy * Y3p / Z3p;
+        double reproj = (mu3p - mu3) * (mu3p - mu3) + (mv3p - mv3) * (mv3p - mv3);
+        if (i == 0 || min_reproj > reproj) {
+            ns = i;
+            min_reproj = reproj;
+        }
+    }
+
+    for (int i = 0; i < 3; i++) {
+        for (int j = 0; j < 3; j++)
+            R[i][j] = Rs[ns][i][j];
+        t[i] = ts[ns][i];
+    }
+
+    return true;
+}
+
+int ap3p::solve(double R[4][3][3], double t[4][3], double mu0, double mv0, double X0, double Y0, double Z0, double mu1,
+                double mv1, double X1, double Y1, double Z1, double mu2, double mv2, double X2, double Y2, double Z2) {
+    double mk0, mk1, mk2;
+    double norm;
+
+    mu0 = inv_fx * mu0 - cx_fx;
+    mv0 = inv_fy * mv0 - cy_fy;
+    norm = sqrt(mu0 * mu0 + mv0 * mv0 + 1);
+    mk0 = 1. / norm;
+    mu0 *= mk0;
+    mv0 *= mk0;
+
+    mu1 = inv_fx * mu1 - cx_fx;
+    mv1 = inv_fy * mv1 - cy_fy;
+    norm = sqrt(mu1 * mu1 + mv1 * mv1 + 1);
+    mk1 = 1. / norm;
+    mu1 *= mk1;
+    mv1 *= mk1;
+
+    mu2 = inv_fx * mu2 - cx_fx;
+    mv2 = inv_fy * mv2 - cy_fy;
+    norm = sqrt(mu2 * mu2 + mv2 * mv2 + 1);
+    mk2 = 1. / norm;
+    mu2 *= mk2;
+    mv2 *= mk2;
+
+    double featureVectors[3][3] = {{mu0, mu1, mu2},
+                                   {mv0, mv1, mv2},
+                                   {mk0, mk1, mk2}};
+    double worldPoints[3][3] = {{X0, X1, X2},
+                                {Y0, Y1, Y2},
+                                {Z0, Z1, Z2}};
+
+    return computePoses(featureVectors, worldPoints, R, t);
+}
+}
\ No newline at end of file

modules/calib3d/src/ap3p.h

+#ifndef P3P_P3P_H
+#define P3P_P3P_H
+
+#include "precomp.hpp"
+
+namespace cv {
+class ap3p {
+private:
+    template<typename T>
+    void init_camera_parameters(const cv::Mat &cameraMatrix) {
+        cx = cameraMatrix.at<T>(0, 2);
+        cy = cameraMatrix.at<T>(1, 2);
+        fx = cameraMatrix.at<T>(0, 0);
+        fy = cameraMatrix.at<T>(1, 1);
+    }
+
+    template<typename OpointType, typename IpointType>
+    void extract_points(const cv::Mat &opoints, const cv::Mat &ipoints, std::vector<double> &points) {
+        points.clear();
+        points.resize(20);
+        for (int i = 0; i < 4; i++) {
+            points[i * 5] = ipoints.at<IpointType>(i).x * fx + cx;
+            points[i * 5 + 1] = ipoints.at<IpointType>(i).y * fy + cy;
+            points[i * 5 + 2] = opoints.at<OpointType>(i).x;
+            points[i * 5 + 3] = opoints.at<OpointType>(i).y;
+            points[i * 5 + 4] = opoints.at<OpointType>(i).z;
+        }
+    }
+
+    void init_inverse_parameters();
+
+    double fx, fy, cx, cy;
+    double inv_fx, inv_fy, cx_fx, cy_fy;
+public:
+    ap3p() {}
+
+    ap3p(double fx, double fy, double cx, double cy);
+
+    ap3p(cv::Mat cameraMatrix);
+
+    bool solve(cv::Mat &R, cv::Mat &tvec, const cv::Mat &opoints, const cv::Mat &ipoints);
+
+    int solve(double R[4][3][3], double t[4][3],
+              double mu0, double mv0, double X0, double Y0, double Z0,
+              double mu1, double mv1, double X1, double Y1, double Z1,
+              double mu2, double mv2, double X2, double Y2, double Z2);
+
+    bool solve(double R[3][3], double t[3],
+               double mu0, double mv0, double X0, double Y0, double Z0,
+               double mu1, double mv1, double X1, double Y1, double Z1,
+               double mu2, double mv2, double X2, double Y2, double Z2,
+               double mu3, double mv3, double X3, double Y3, double Z3);
+
+    // This algorithm is from "Tong Ke, Stergios Roumeliotis, An Efficient Algebraic Solution to the Perspective-Three-Point Problem" (Accepted by CVPR 2017)
+    // See https://arxiv.org/pdf/1701.08237.pdf
+    // featureVectors: 3 bearing measurements (normalized) stored as column vectors
+    // worldPoints: Positions of the 3 feature points stored as column vectors
+    // solutionsR: 4 possible solutions of rotation matrix of the world w.r.t the camera frame
+    // solutionsT: 4 possible solutions of translation of the world origin w.r.t the camera frame
+    int computePoses(const double featureVectors[3][3], const double worldPoints[3][3], double solutionsR[4][3][3],
+                     double solutionsT[4][3]);
+
+};
+}
+#endif //P3P_P3P_H

modules/calib3d/src/solvepnp.cpp

@@ -45,6 +45,7 @@
 #include "dls.h"
 #include "epnp.h"
 #include "p3p.h"
+#include "ap3p.h"
 #include "opencv2/calib3d/calib3d_c.h"
 
 #include <iostream>
@@ -118,6 +119,18 @@ bool solvePnP( InputArray _opoints, InputArray _ipoints,
         if (result)
             Rodrigues(R, rvec);
     }
+    else if (flags == SOLVEPNP_AP3P)
+    {
+        CV_Assert( npoints == 4);
+        Mat undistortedPoints;
+        undistortPoints(ipoints, undistortedPoints, cameraMatrix, distCoeffs);
+        ap3p P3Psolver(cameraMatrix);
+
+        Mat R;
+        result = P3Psolver.solve(R, tvec, opoints, undistortedPoints);
+        if (result)
+            Rodrigues(R, rvec);
+    }
     else if (flags == SOLVEPNP_ITERATIVE)
     {
         CvMat c_objectPoints = opoints, c_imagePoints = ipoints;
@@ -291,7 +304,8 @@ bool solvePnPRansac(InputArray _opoints, InputArray _ipoints,
         opoints_inliers.resize(npoints1);
         ipoints_inliers.resize(npoints1);
         result = solvePnP(opoints_inliers, ipoints_inliers, cameraMatrix,
-                          distCoeffs, rvec, tvec, false, flags == SOLVEPNP_P3P ? SOLVEPNP_EPNP : flags) ? 1 : -1;
+                          distCoeffs, rvec, tvec, false,
+                          (flags == SOLVEPNP_P3P || flags == SOLVEPNP_AP3P) ? SOLVEPNP_EPNP : flags) ? 1 : -1;
     }
 
     if( result <= 0 || _local_model.rows <= 0)

modules/calib3d/test/test_solvepnp_ransac.cpp

@@ -57,6 +57,7 @@ public:
         eps[SOLVEPNP_ITERATIVE] = 1.0e-2;
         eps[SOLVEPNP_EPNP] = 1.0e-2;
         eps[SOLVEPNP_P3P] = 1.0e-2;
+        eps[SOLVEPNP_AP3P] = 1.0e-2;
         eps[SOLVEPNP_DLS] = 1.0e-2;
         eps[SOLVEPNP_UPNP] = 1.0e-2;
         totalTestsCount = 10;
@@ -161,7 +162,7 @@ protected:
         points.resize(pointsCount);
         generate3DPointCloud(points);
 
-        const int methodsCount = 5;
+        const int methodsCount = 6;
         RNG rng = ts->get_rng();
 
 
@@ -189,7 +190,7 @@ protected:
             }
         }
     }
-    double eps[5];
+    double eps[6];
     int totalTestsCount;
 };
 
@@ -201,6 +202,7 @@ public:
         eps[SOLVEPNP_ITERATIVE] = 1.0e-6;
         eps[SOLVEPNP_EPNP] = 1.0e-6;
         eps[SOLVEPNP_P3P] = 1.0e-4;
+        eps[SOLVEPNP_AP3P] = 1.0e-4;
         eps[SOLVEPNP_DLS] = 1.0e-4;
         eps[SOLVEPNP_UPNP] = 1.0e-4;
         totalTestsCount = 1000;
@@ -222,7 +224,7 @@ protected:
         generatePose(trueRvec, trueTvec, rng);
 
         std::vector<Point3f> opoints;
-        if (method == 2)
+        if (method == 2 || method == 5)
         {
             opoints = std::vector<Point3f>(points.begin(), points.begin()+4);
         }