参考：ORB特征描述原理、python实现及基于opencv实现
#include <iostream>
#include <opencv2/opencv.hpp>
#define _USE_MATH_DEFINES
#include <math.h>
#include <numeric>
int kBytes = 32;
int nfeatures = 500;
float scaleFactor = 1.2;
int nlevels = 8;
int edgeThreshold = 31;
int firstLevel = 0;
int wta_k = 2;
int scoreType = 0;
int patchSize = 31;
int fastThreshold = 20;
float harris_k = 0.04;
float getScale(int level, int firstLevel, float scaleFactor)
{
return pow(scaleFactor, level - firstLevel);
}
template <typename T>
std::vector<size_t> sort_indices(const std::vector<T>& v)
{
std::vector<size_t> idx(v.size());
std::iota(idx.begin(), idx.end(), 0);
std::sort(idx.begin(), idx.end(), [&v](size_t i1, size_t i2) {
return v[i1] < v[i2]; });
return idx;
}
std::vector<cv::KeyPoint> retainBest(std::vector<cv::KeyPoint> keypoints, int n_points)
{
if (n_points >= 0 && keypoints.size() > n_points)
{
std::vector<float> res;
for (auto kp : keypoints)
res.push_back(kp.response);
std::vector<size_t> index = sort_indices(res);
std::reverse(index.begin(), index.end());
std::vector<cv::KeyPoint> new_keypoints;
for (size_t i = 0; i < n_points; i++)
new_keypoints.push_back(keypoints[index[i]]);
return new_keypoints;
}
return keypoints;
}
void HarrisResponses(cv::Mat img, std::vector<std::vector<int>> layerinfo, std::vector<cv::KeyPoint>& pts, int blockSize)
{
int radius = int(blockSize / 2);
float scale = 1.0 / ((1 << 2) * blockSize * 255.0);
float scale_sq_sq = pow(scale, 4);
for (size_t i = 0; i < pts.size(); i++)
{
int x0 = int(round(pts[i].pt.x));
int y0 = int(round(pts[i].pt.y));
int z = int(pts[i].octave);
int center_c = layerinfo[z][0] + x0;
int center_r = layerinfo[z][1] + y0;
long long a = 0, b = 0, c = 0;
for (int index_r = - radius; index_r < blockSize - radius; index_r++)
{
for (int index_c = - radius; index_c < blockSize - radius; index_c++)
{
int rr = center_r + index_r;
int cc = center_c + index_c;
int Ix = (img.at<uchar>(rr, cc + 1) - img.at<uchar>(rr, cc - 1)) * 2 +
(img.at<uchar>(rr - 1, cc + 1) - img.at<uchar>(rr - 1, cc - 1)) +
(img.at<uchar>(rr + 1, cc + 1) - img.at<uchar>(rr + 1, cc - 1));
int Iy = (img.at<uchar>(rr + 1, cc ) - img.at<uchar>(rr - 1, cc )) * 2 +
(img.at<uchar>(rr + 1, cc - 1) - img.at<uchar>(rr - 1, cc - 1)) +
(img.at<uchar>(rr + 1, cc + 1) - img.at<uchar>(rr - 1, cc + 1));
a += Ix * Ix;
b += Iy * Iy;
c += Ix * Iy;
}
}
pts[i].response = (a * b - c * c - harris_k * (a + b) * (a + b)) * scale_sq_sq;
}
}
void ICAngles(cv::Mat img, std::vector<std::vector<int>> layerinfo, std::vector<cv::KeyPoint>& pts, std::vector<int> u_max, int half_k)
{
for (size_t i = 0; i < pts.size(); i++)
{
std::vector<int> layer = layerinfo[pts[i].octave];
int c = round(pts[i].pt.x) + layer[0], r = round(pts[i].pt.y) + layer[1];
int m_01 = 0, m_10 = 0;
for (int u = -half_k; u < half_k + 1; u++)
m_10 += u * img.at<uchar>(r, c + u);
for (int v = 1; v < half_k + 1; v++)
{
int v_sum = 0, d = u_max[v];
for (int u = - d; u < d + 1; u++)
{
int val_plus= img.at<uchar>(r + v, c + u);
int val_minus = img.at<uchar>(r - v, c + u);
v_sum += (val_plus - val_minus);
m_10 += u * (val_plus + val_minus);
}
m_01 += v * v_sum;
}
pts[i].angle = cv::fastAtan2(float(m_01), float(m_10));
}
}
std::vector<cv::KeyPoint> computeKeyPoints(cv::Mat imagePyramid, std::vector<std::vector<int>> layerInfo, std::vector<float> layerScale)
{
int nlevels = layerInfo.size();
std::vector<int> nfeaturesPerLevel;
float factor = float(1.0 / scaleFactor);
float ndesiredFeaturesPerScale = nfeatures * (1 - factor) / (1 - pow(factor, nlevels));
int sumFeatures = 0;
for (size_t level = 0; level < nlevels - 1; level++)
{
nfeaturesPerLevel.push_back(int(round(ndesiredFeaturesPerScale)));
sumFeatures += nfeaturesPerLevel[level];
ndesiredFeaturesPerScale *= factor;
}
nfeaturesPerLevel.push_back(std::max(nfeatures - sumFeatures, 0));
int halfPatchSize = int(patchSize / 2);
std::vector<cv::KeyPoint> allKeypoints;
std::vector<int> counters;
for (size_t level = 0; level < nlevels; level++)
{
int featuresNum = int(nfeaturesPerLevel[level]);
std::vector<int> r = layerInfo[level];
cv::Mat img = imagePyramid(cv::Rect(r[0], r[1], r[2], r[3]));
cv::Ptr<cv::FastFeatureDetector> fast = cv::FastFeatureDetector::create(fastThreshold);
std::vector<cv::KeyPoint> keypoints;
fast->detect(img, keypoints);
cv::KeyPointsFilter::runByImageBorder(keypoints, img.size(), edgeThreshold);
keypoints = retainBest(keypoints, 2 * featuresNum);
int nkeypoints = keypoints.size();
counters.push_back(nkeypoints);
float sf = layerScale[level];
for (size_t i = 0; i < nkeypoints; i++)
{
keypoints[i].octave = level;
keypoints[i].size = patchSize * sf;
}
for (auto kp : keypoints)
allKeypoints.push_back(kp);
}
int nkeypoints = allKeypoints.size();
if (nkeypoints == 0)
return {
};
HarrisResponses(imagePyramid, layerInfo, allKeypoints, 7);
std::vector<cv::KeyPoint> newAllKeypoints;
int offset = 0;
for (size_t level = 0; level < nlevels; level++)
{
std::vector<cv::KeyPoint> keypoints;
int featuresNum = int(nfeaturesPerLevel[level]);
int nkeypoints = int(counters[level]);
for (size_t i = offset; i < offset + nkeypoints; i++)
keypoints.push_back(allKeypoints[i]);
offset += nkeypoints;
std::vector<cv::KeyPoint> keypoints2 = retainBest(keypoints, featuresNum);
for(auto kp: keypoints2)
newAllKeypoints.push_back(kp);
}
allKeypoints = newAllKeypoints;
nkeypoints = allKeypoints.size();
std::vector<int> umax(halfPatchSize + 2, 0);
int vmax = int(floor((halfPatchSize * sqrt(2.) / 2 + 1)));
for (int v = 0; v < vmax + 1; ++v)
umax[v] = round(sqrt(double(pow(halfPatchSize, 2) - pow(v, 2))));
int vmin = ceil(halfPatchSize * sqrt(2.0) / 2);
int v = halfPatchSize, v0 = 0;
while (v >= vmin)
{
while (umax[v0] == umax[v0 + 1])
v0 = v0 + 1;
umax[v] = v0;
v0 = v0 + 1;
v = v - 1;
}
ICAngles(imagePyramid, layerInfo, allKeypoints, umax, halfPatchSize);
for (size_t i = 0; i < nkeypoints; i++)
{
float scale = layerScale[allKeypoints[i].octave];
allKeypoints[i].pt = cv::Point(allKeypoints[i].pt.x * scale, allKeypoints[i].pt.y * scale);
}
return allKeypoints;
}
float GET_VALUE(int idx, std::vector<cv::Point> pattern, float a, float b, cv::Mat imagePyramid, int cx, int cy)
{
float x = pattern[idx].x * a - pattern[idx].y * b;
float y = pattern[idx].x * b + pattern[idx].y * a;
int ix = int(round(x));
int iy = int(round(y));
return imagePyramid.at<float>(cy + iy, cx + ix);
}
std::vector<std::vector<int>> computeOrbDescriptors(cv::Mat imagePyramid, std::vector<std::vector<int>> layerInfo,
std::vector<float> layerScale, std::vector<cv::KeyPoint> keypoints, std::vector<cv::Point> _pattern, int dsize)
{
std::vector<std::vector<int>> descriptors;
for (size_t i = 0; i < keypoints.size(); i++)
{
cv::KeyPoint kpt = keypoints[i];
std::vector<int> layer = layerInfo[int(kpt.octave)];
float scale = 1.0 / layerScale[int(kpt.octave)];
float angle = kpt.angle / 180.0 * M_PI;
float a = cos(angle), b = sin(angle);
int cx = round(kpt.pt.x * scale) + layer[0], cy = round(kpt.pt.y * scale) + layer[1];
int pattern_idx = 0;
std::vector<cv::Point> pattern;
pattern.assign(_pattern.begin()+ pattern_idx, _pattern.end());
std::vector<int> des;
for (size_t j = 0; j < dsize; j++)
{
int byte_v = 0;
for (size_t nn = 0; nn < 8; nn++)
{
float t0 = GET_VALUE(2 * nn, pattern, a, b, imagePyramid, cx, cy);
float t1 = GET_VALUE(2 * nn + 1, pattern, a, b, imagePyramid, cx, cy);
int bit_v = int(t0 < t1);
byte_v += (bit_v << nn);
}
des.push_back(byte_v);
pattern_idx += 16;
pattern.assign(_pattern.begin() + pattern_idx, _pattern.end());
}
descriptors.push_back(des);
}
return descriptors;
}
std::tuple<std::vector<cv::KeyPoint>, std::vector<std::vector<int>>> orb_detectAndCompute(cv::Mat img_src)
{
int HARRIS_BLOCK_SIZE = 9;
int halfPatchSize = int(patchSize / 2);
int descPatchSize = int(ceil(halfPatchSize * sqrt(2.0)));
std::vector<int> vec = {
edgeThreshold, descPatchSize, HARRIS_BLOCK_SIZE / 2 };
int border = int(*std::max_element(vec.begin(),vec.end()) + 1);
cv::Mat image = img_src.clone();
std::vector<float> layerScale;
std::vector<std::vector<int>> layerInfo;
int level_dy = (int)(image.cols + border * 2);
cv::Point level_ofs(0, 0);
int tmp = round(image.cols / getScale(0, firstLevel, scaleFactor)) + border * 2 + 15;
cv::Size bufSize(tmp / 16 * 16, 0);
for (size_t level = 0; level < nlevels; level++)
{
float scale = getScale(level, firstLevel, scaleFactor);
layerScale.push_back(scale);
cv::Size sz(int(round(image.cols / scale)), int(round(image.rows / scale)));
cv::Size wholeSize(sz.width + border * 2, sz.height + border * 2);
if (level_ofs.x + wholeSize.width > bufSize.width)
{
level_ofs = cv::Point(0, level_ofs.y + level_dy);
level_dy = wholeSize.height;
}
std::vector<int> linfo = {
level_ofs.x + border, level_ofs.y + border, sz.width, sz.height };
layerInfo.push_back(linfo);
level_ofs.x += wholeSize.width;
}
bufSize.height = level_ofs.y + level_dy;
cv::Mat imagePyramid(bufSize, CV_8UC1);
cv::Mat prevImg = image;
for (size_t level = 0; level < nlevels; level++)
{
std::vector<int> linfo = layerInfo[level];
cv::Size sz(linfo[2],linfo[3]);
cv::Size wholeSize(sz.width + border * 2, sz.height + border * 2);
std::vector<int> wholeLinfo = {
linfo[0] - border, linfo[1] - border, wholeSize.width, wholeSize.height };
cv::Mat extImg, currImg;
if (level == firstLevel)
{
cv::copyMakeBorder(image, extImg, border, border, border, border, cv::BORDER_REFLECT_101);
}
else
{
cv::resize(prevImg, currImg, sz, 0, 0, cv::INTER_LINEAR_EXACT);
cv::copyMakeBorder(currImg, extImg, border, border, border, border, cv::BORDER_REFLECT_101 + cv::BORDER_ISOLATED);
}
cv::Mat roi = imagePyramid(cv::Rect(wholeLinfo[0], wholeLinfo[1], wholeLinfo[2], wholeLinfo[3]));
extImg.copyTo(roi);
if (level > firstLevel)
prevImg = currImg.clone();
}
imagePyramid = cv::imread("imagePyramid.png", 0);
std::vector<cv::KeyPoint> keypoints = computeKeyPoints(imagePyramid, layerInfo, layerScale);
int dsize = kBytes;
int nkeypoints = keypoints.size();
int npoints = 512;
#include "bit_pattern_31.i"
std::vector<cv::Point> pattern;
for (size_t i = 0; i < npoints; i++)
pattern.push_back(cv::Point(bit_pattern_31_[2 * i], bit_pattern_31_[2 * i + 1]));
imagePyramid.convertTo(imagePyramid, CV_32F);
for (size_t level = 0; level < nlevels; level++)
{
int x = layerInfo[level][0], y = layerInfo[level][1], w = layerInfo[level][2], h = layerInfo[level][3];
cv::Mat workingMat = imagePyramid(cv::Rect(x, y, w, h));
workingMat.convertTo(workingMat, CV_32F);
cv::GaussianBlur(workingMat, workingMat, cv::Size(7, 7), 2, 2, cv::BORDER_REFLECT_101);
}
//cv::imwrite("imagePyramid.png", imagePyramid);
std::vector<std::vector<int>> descriptors = computeOrbDescriptors(imagePyramid, layerInfo, layerScale, keypoints, pattern, dsize);
return {
keypoints, descriptors };
}
int main()
{
cv::Mat img = cv::imread("1.png", 0);
auto [kp, des] = orb_detectAndCompute(img);
return 0;
}
其中bit_pattern_31.i来自OpenCV源码，其内容为：
static int bit_pattern_31_[256 * 4] =
{
8, -3, 9, 5/*mean (0), correlation (0)*/,
4, 2, 7, -12/*mean (1.12461e-05), correlation (0.0437584)*/,
-11, 9, -8, 2/*mean (3.37382e-05), correlation (0.0617409)*/,
7, -12, 12, -13/*mean (5.62303e-05), correlation (0.0636977)*/,
2, -13, 2, 12/*mean (0.000134953), correlation (0.085099)*/,
1, -7, 1, 6/*mean (0.000528565), correlation (0.0857175)*/,
-2, -10, -2, -4/*mean (0.0188821), correlation (0.0985774)*/,
-13, -13, -11, -8/*mean (0.0363135), correlation (0.0899616)*/,
-13, -3, -12, -9/*mean (0.121806), correlation (0.099849)*/,
10, 4, 11, 9/*mean (0.122065), correlation (0.093285)*/,
-13, -8, -8, -9/*mean (0.162787), correlation (0.0942748)*/,
-11, 7, -9, 12/*mean (0.21561), correlation (0.0974438)*/,
7, 7, 12, 6/*mean (0.160583), correlation (0.130064)*/,
-4, -5, -3, 0/*mean (0.228171), correlation (0.132998)*/,
-13, 2, -12, -3/*mean (0.00997526), correlation (0.145926)*/,
-9, 0, -7, 5/*mean (0.198234), correlation (0.143636)*/,
12, -6, 12, -1/*mean (0.0676226), correlation (0.16689)*/,
-3, 6, -2, 12/*mean (0.166847), correlation (0.171682)*/,
-6, -13, -4, -8/*mean (0.101215), correlation (0.179716)*/,
11, -13, 12, -8/*mean (0.200641), correlation (0.192279)*/,
4, 7, 5, 1/*mean (0.205106), correlation (0.186848)*/,
5, -3, 10, -3/*mean (0.234908), correlation (0.192319)*/,
3, -7, 6, 12/*mean (0.0709964), correlation (0.210872)*/,
-8, -7, -6, -2/*mean (0.0939834), correlation (0.212589)*/,
-2, 11, -1, -10/*mean (0.127778), correlation (0.20866)*/,
-13, 12, -8, 10/*mean (0.14783), correlation (0.206356)*/,
-7, 3, -5, -3/*mean (0.182141), correlation (0.198942)*/,
-4, 2, -3, 7/*mean (0.188237), correlation (0.21384)*/,
-10, -12, -6, 11/*mean (0.14865), correlation (0.23571)*/,
5, -12, 6, -7/*mean (0.222312), correlation (0.23324)*/,
5, -6, 7, -1/*mean (0.229082), correlation (0.23389)*/,
1, 0, 4, -5/*mean (0.241577), correlation (0.215286)*/,
9, 11, 11, -13/*mean (0.00338507), correlation (0.251373)*/,
4, 7, 4, 12/*mean (0.131005), correlation (0.257622)*/,
2, -1, 4, 4/*mean (0.152755), correlation (0.255205)*/,
-4, -12, -2, 7/*mean (0.182771), correlation (0.244867)*/,
-8, -5, -7, -10/*mean (0.186898), correlation (0.23901)*/,
4, 11, 9, 12/*mean (0.226226), correlation (0.258255)*/,
0, -8, 1, -13/*mean (0.0897886), correlation (0.274827)*/,
-13, -2, -8, 2/*mean (0.148774), correlation (0.28065)*/,
-3, -2, -2, 3/*mean (0.153048), correlation (0.283063)*/,
-6, 9, -4, -9/*mean (0.169523), correlation (0.278248)*/,
8, 12, 10, 7/*mean (0.225337), correlation (0.282851)*/,
0, 9, 1, 3/*mean (0.226687), correlation (0.278734)*/,
7, -5, 11, -10/*mean (0.00693882), correlation (0.305161)*/,
-13, -6, -11, 0/*mean (0.0227283), correlation (0.300181)*/,
10, 7, 12, 1/*mean (0.125517), correlation (0.31089)*/,
-6, -3, -6, 12/*mean (0.131748), correlation (0.312779)*/,
10, -9, 12, -4/*mean (0.144827), correlation (0.292797)*/,
-13, 8, -8, -12/*mean (0.149202), correlation (0.308918)*/,
-13, 0, -8, -4/*mean (0.160909), correlation (0.310013)*/,
3, 3, 7, 8/*mean (0.177755), correlation (0.309394)*/,
5, 7, 10, -7/*mean (0.212337), correlation (0.310315)*/,
-1, 7, 1, -12/*mean (0.214429), correlation (0.311933)*/,
3, -10, 5, 6/*mean (0.235807), correlation (0.313104)*/,
2, -4, 3, -10/*mean (0.00494827), correlation (0.344948)*/,
-13, 0, -13, 5/*mean (0.0549145), correlation (0.344675)*/,
-13, -7, -12, 12/*mean (0.103385), correlation (0.342715)*/,
-13, 3, -11, 8/*mean (0.134222), correlation (0.322922)*/,
-7, 12, -4, 7/*mean (0.153284), correlation (0.337061)*/,
6, -10, 12, 8/*mean (0.154881), correlation (0.329257)*/,
-9, -1, -7, -6/*mean (0.200967), correlation (0.33312)*/,
-2, -5, 0, 12/*mean (0.201518), correlation (0.340635)*/,
-12, 5, -7, 5/*mean (0.207805), correlation (0.335631)*/,
3, -10, 8, -13/*mean (0.224438), correlation (0.34504)*/,
-7, -7, -4, 5/*mean (0.239361), correlation (0.338053)*/,
-3, -2, -1, -7/*mean (0.240744), correlation (0.344322)*/,
2, 9, 5, -11/*mean (0.242949), correlation (0.34145)*/,
-11, -13, -5, -13/*mean (0.244028), correlation (0.336861)*/,
-1, 6, 0, -1/*mean (0.247571), correlation (0.343684)*/,
5, -3, 5, 2/*mean (0.000697256), correlation (0.357265)*/,
-4, -13, -4, 12/*mean (0.00213675), correlation (0.373827)*/,
-9, -6, -9, 6/*mean (0.0126856), correlation (0.373938)*/,
-12, -10, -8, -4/*mean (0.0152497), correlation (0.364237)*/,
10, 2, 12, -3/*mean (0.0299933), correlation (0.345292)*/,
7, 12, 12, 12/*mean (0.0307242), correlation (0.366299)*/,
-7, -13, -6, 5/*mean (0.0534975), correlation (0.368357)*/,
-4, 9, -3, 4/*mean (0.099865), correlation (0.372276)*/,
7, -1, 12, 2/*mean (0.117083), correlation (0.364529)*/,
-7, 6, -5, 1/*mean (0.126125), correlation (0.369606)*/,
-13, 11, -12, 5/*mean (0.130364), correlation (0.358502)*/,
-3, 7, -2, -6/*mean (0.131691), correlation (0.375531)*/,
7, -8, 12, -7/*mean (0.160166), correlation (0.379508)*/,
-13, -7, -11, -12/*mean (0.167848), correlation (0.353343)*/,
1, -3, 12, 12/*mean (0.183378), correlation (0.371916)*/,
2, -6, 3, 0/*mean (0.228711), correlation (0.371761)*/,
-4, 3, -2, -13/*mean (0.247211), correlation (0.364063)*/,
-1, -13, 1, 9/*mean (0.249325), correlation (0.378139)*/,
7, 1, 8, -6/*mean (0.000652272), correlation (0.411682)*/,
1, -1, 3, 12/*mean (0.00248538), correlation (0.392988)*/,
9, 1, 12, 6/*mean (0.0206815), correlation (0.386106)*/,
-1, -9, -1, 3/*mean (0.0364485), correlation (0.410752)*/,
-13, -13, -10, 5/*mean (0.0376068), correlation (0.398374)*/,
7, 7, 10, 12/*mean (0.0424202), correlation (0.405663)*/,
12, -5, 12, 9/*mean (0.0942645), correlation (0.410422)*/,
6, 3, 7, 11/*mean (0.1074), correlation (0.413224)*/,
5, -13, 6, 10/*mean (0.109256), correlation (0.408646)*/,
2, -12, 2, 3/*mean (0.131691), correlation (0.416076)*/,
3, 8, 4, -6/*mean (0.165081), correlation (0.417569)*/,
2, 6, 12, -13/*mean (0.171874), correlation (0.408471)*/,
9, -12, 10, 3/*mean (0.175146), correlation (0.41296)*/,
-8, 4, -7, 9/*mean (0.183682), correlation (0.402956)*/,
-11, 12, -4, -6/*mean (0.184672), correlation (0.416125)*/,
1, 12, 2, -8/*mean (0.191487), correlation (0.386696)*/,
6, -9, 7, -4/*mean (0.192668), correlation (0.394771)*/,
2, 3, 3, -2/*mean (0.200157), correlation (0.408303)*/,
6, 3, 11, 0/*mean (0.204588), correlation (0.411762)*/,
3, -3, 8, -8/*mean (0.205904), correlation (0.416294)*/,
7, 8, 9, 3/*mean (0.213237), correlation (0.409306)*/,
-11, -5, -6, -4/*mean (0.243444), correlation (0.395069)*/,
-10, 11, -5, 10/*mean (0.247672), correlation (0.413392)*/,
-5, -8, -3, 12/*mean (0.24774), correlation (0.411416)*/,
-10, 5, -9, 0/*mean (0.00213675), correlation (0.454003)*/,
8, -1, 12, -6/*mean (0.0293635), correlation (0.455368)*/,
4, -6, 6, -11/*mean (0.0404971), correlation (0.457393)*/,
-10, 12, -8, 7/*mean (0.0481107), correlation (0.448364)*/,
4, -2, 6, 7/*mean (0.050641), correlation (0.455019)*/,
-2, 0, -2, 12/*mean (0.0525978), correlation (0.44338)*/,
-5, -8, -5, 2/*mean (0.0629667), correlation (0.457096)*/,
7, -6, 10, 12/*mean (0.0653846), correlation (0.445623)*/,
-9, -13, -8, -8/*mean (0.0858749), correlation (0.449789)*/,
-5, -13, -5, -2/*mean (0.122402), correlation (0.450201)*/,
8, -8, 9, -13/*mean (0.125416), correlation (0.453224)*/,
-9, -11, -9, 0/*mean (0.130128), correlation (0.458724)*/,
1, -8, 1, -2/*mean (0.132467), correlation (0.440133)*/,
7, -4, 9, 1/*mean (0.132692), correlation (0.454)*/,
-2, 1, -1, -4/*mean (0.135695), correlation (0.455739)*/,
11, -6, 12, -11/*mean (0.142904), correlation (0.446114)*/,
-12, -9, -6, 4/*mean (0.146165), correlation (0.451473)*/,
3, 7, 7, 12/*mean (0.147627), correlation (0.456643)*/,
5, 5, 10, 8/*mean (0.152901), correlation (0.455036)*/,
0, -4, 2, 8/*mean (0.167083), correlation (0.459315)*/,
-9, 12, -5, -13/*mean (0.173234), correlation (0.454706)*/,
0, 7, 2, 12/*mean (0.18312), correlation (0.433855)*/,
-1, 2, 1, 7/*mean (0.185504), correlation (0.443838)*/,
5, 11, 7, -9/*mean (0.185706), correlation (0.451123)*/,
3, 5, 6, -8/*mean (0.188968), correlation (0.455808)*/,
-13, -4, -8, 9/*mean (0.191667), correlation (0.459128)*/,
-5, 9, -3, -3/*mean (0.193196), correlation (0.458364)*/,
-4, -7, -3, -12/*mean (0.196536), correlation (0.455782)*/,
6, 5, 8, 0/*mean (0.1972), correlation (0.450481)*/,
-7, 6, -6, 12/*mean (0.199438), correlation (0.458156)*/,
-13, 6, -5, -2/*mean (0.211224), correlation (0.449548)*/,
1, -10, 3, 10/*mean (0.211718), correlation (0.440606)*/,
4, 1, 8, -4/*mean (0.213034), correlation (0.443177)*/,
-2, -2, 2, -13/*mean (0.234334), correlation (0.455304)*/,
2, -12, 12, 12/*mean (0.235684), correlation (0.443436)*/,
-2, -13, 0, -6/*mean (0.237674), correlation (0.452525)*/,
4, 1, 9, 3/*mean (0.23962), correlation (0.444824)*/,
-6, -10, -3, -5/*mean (0.248459), correlation (0.439621)*/,
-3, -13, -1, 1/*mean (0.249505), correlation (0.456666)*/,
7, 5, 12, -11/*mean (0.00119208), correlation (0.495466)*/,
4, -2, 5, -7/*mean (0.00372245), correlation (0.484214)*/,
-13, 9, -9, -5/*mean (0.00741116), correlation (0.499854)*/,
7, 1, 8, 6/*mean (0.0208952), correlation (0.499773)*/,
7, -8, 7, 6/*mean (0.0220085), correlation (0.501609)*/,
-7, -4, -7, 1/*mean (0.0233806), correlation (0.496568)*/,
-8, 11, -7, -8/*mean (0.0236505), correlation (0.489719)*/,
-13, 6, -12, -8/*mean (0.0268781), correlation (0.503487)*/,
2, 4, 3, 9/*mean (0.0323324), correlation (0.501938)*/,
10, -5, 12, 3/*mean (0.0399235), correlation (0.494029)*/,
-6, -5, -6, 7/*mean (0.0420153), correlation (0.486579)*/,
8, -3, 9, -8/*mean (0.0548021), correlation (0.484237)*/,
2, -12, 2, 8/*mean (0.0616622), correlation (0.496642)*/,
-11, -2, -10, 3/*mean (0.0627755), correlation (0.498563)*/,
-12, -13, -7, -9/*mean (0.0829622), correlation (0.495491)*/,
-11, 0, -10, -5/*mean (0.0843342), correlation (0.487146)*/,
5, -3, 11, 8/*mean (0.0929937), correlation (0.502315)*/,
-2, -13, -1, 12/*mean (0.113327), correlation (0.48941)*/,
-1, -8, 0, 9/*mean (0.132119), correlation (0.467268)*/,
-13, -11, -12, -5/*mean (0.136269), correlation (0.498771)*/,
-10, -2, -10, 11/*mean (0.142173), correlation (0.498714)*/,
-3, 9, -2, -13/*mean (0.144141), correlation (0.491973)*/,
2, -3, 3, 2/*mean (0.14892), correlation (0.500782)*/,
-9, -13, -4, 0/*mean (0.150371), correlation (0.498211)*/,
-4, 6, -3, -10/*mean (0.152159), correlation (0.495547)*/,
-4, 12, -2, -7/*mean (0.156152), correlation (0.496925)*/,
-6, -11, -4, 9/*mean (0.15749), correlation (0.499222)*/,
6, -3, 6, 11/*mean (0.159211), correlation (0.503821)*/,
-13, 11, -5, 5/*mean (0.162427), correlation (0.501907)*/,
11, 11, 12, 6/*mean (0.16652), correlation (0.497632)*/,
7, -5, 12, -2/*mean (0.169141), correlation (0.484474)*/,
-1, 12, 0, 7/*mean (0.169456), correlation (0.495339)*/,
-4, -8, -3, -2/*mean (0.171457), correlation (0.487251)*/,
-7, 1, -6, 7/*mean (0.175), correlation (0.500024)*/,
-13, -12, -8, -13/*mean (0.175866), correlation (0.497523)*/,
-7, -2, -6, -8/*mean (0.178273), correlation (0.501854)*/,
-8, 5, -6, -9/*mean (0.181107), correlation (0.494888)*/,
-5, -1, -4, 5/*mean (0.190227), correlation (0.482557)*/,
-13, 7, -8, 10/*mean (0.196739), correlation (0.496503)*/,
1, 5, 5, -13/*mean (0.19973), correlation (0.499759)*/,
1, 0, 10, -13/*mean (0.204465), correlation (0.49873)*/,
9, 12, 10, -1/*mean (0.209334), correlation (0.49063)*/,
5, -8, 10, -9/*mean (0.211134), correlation (0.503011)*/,
-1, 11, 1, -13/*mean (0.212), correlation (0.499414)*/,
-9, -3, -6, 2/*mean (0.212168), correlation (0.480739)*/,
-1, -10, 1, 12/*mean (0.212731), correlation (0.502523)*/,
-13, 1, -8, -10/*mean (0.21327), correlation (0.489786)*/,
8, -11, 10, -6/*mean (0.214159), correlation (0.488246)*/,
2, -13, 3, -6/*mean (0.216993), correlation (0.50287)*/,
7, -13, 12, -9/*mean (0.223639), correlation (0.470502)*/,
-10, -10, -5, -7/*mean (0.224089), correlation (0.500852)*/,
-10, -8, -8, -13/*mean (0.228666), correlation (0.502629)*/,
4, -6, 8, 5/*mean (0.22906), correlation (0.498305)*/,
3, 12, 8, -13/*mean (0.233378), correlation (0.503825)*/,
-4, 2, -3, -3/*mean (0.234323), correlation (0.476692)*/,
5, -13, 10, -12/*mean (0.236392), correlation (0.475462)*/,
4, -13, 5, -1/*mean (0.236842), correlation (0.504132)*/,
-9, 9, -4, 3/*mean (0.236977), correlation (0.497739)*/,
0, 3, 3, -9/*mean (0.24314), correlation (0.499398)*/,
-12, 1, -6, 1/*mean (0.243297), correlation (0.489447)*/,
3, 2, 4, -8/*mean (0.00155196), correlation (0.553496)*/,
-10, -10, -10, 9/*mean (0.00239541), correlation (0.54297)*/,
8, -13, 12, 12/*mean (0.0034413), correlation (0.544361)*/,
-8, -12, -6, -5/*mean (0.003565), correlation (0.551225)*/,
2, 2, 3, 7/*mean (0.00835583), correlation (0.55285)*/,
10, 6, 11, -8/*mean (0.00885065), correlation (0.540913)*/,
6, 8, 8, -12/*mean (0.0101552), correlation (0.551085)*/,
-7, 10, -6, 5/*mean (0.0102227), correlation (0.533635)*/,
-3, -9, -3, 9/*mean (0.0110211), correlation (0.543121)*/,
-1, -13, -1, 5/*mean (0.0113473), correlation (0.550173)*/,
-3, -7, -3, 4/*mean (0.0140913), correlation (0.554774)*/,
-8, -2, -8, 3/*mean (0.017049), correlation (0.55461)*/,
4, 2, 12, 12/*mean (0.01778), correlation (0.546921)*/,
2, -5, 3, 11/*mean (0.0224022), correlation (0.549667)*/,
6, -9, 11, -13/*mean (0.029161), correlation (0.546295)*/,
3, -1, 7, 12/*mean (0.0303081), correlation (0.548599)*/,
11, -1, 12, 4/*mean (0.0355151), correlation (0.523943)*/,
-3, 0, -3, 6/*mean (0.0417904), correlation (0.543395)*/,
4, -11, 4, 12/*mean (0.0487292), correlation (0.542818)*/,
2, -4, 2, 1/*mean (0.0575124), correlation (0.554888)*/,
-10, -6, -8, 1/*mean (0.0594242), correlation (0.544026)*/,
-13, 7, -11, 1/*mean (0.0597391), correlation (0.550524)*/,
-13, 12, -11, -13/*mean (0.0608974), correlation (0.55383)*/,
6, 0, 11, -13/*mean (0.065126), correlation (0.552006)*/,
0, -1, 1, 4/*mean (0.074224), correlation (0.546372)*/,
-13, 3, -9, -2/*mean (0.0808592), correlation (0.554875)*/,
-9, 8, -6, -3/*mean (0.0883378), correlation (0.551178)*/,
-13, -6, -8, -2/*mean (0.0901035), correlation (0.548446)*/,
5, -9, 8, 10/*mean (0.0949843), correlation (0.554694)*/,
2, 7, 3, -9/*mean (0.0994152), correlation (0.550979)*/,
-1, -6, -1, -1/*mean (0.10045), correlation (0.552714)*/,
9, 5, 11, -2/*mean (0.100686), correlation (0.552594)*/,
11, -3, 12, -8/*mean (0.101091), correlation (0.532394)*/,
3, 0, 3, 5/*mean (0.101147), correlation (0.525576)*/,
-1, 4, 0, 10/*mean (0.105263), correlation (0.531498)*/,
3, -6, 4, 5/*mean (0.110785), correlation (0.540491)*/,
-13, 0, -10, 5/*mean (0.112798), correlation (0.536582)*/,
5, 8, 12, 11/*mean (0.114181), correlation (0.555793)*/,
8, 9, 9, -6/*mean (0.117431), correlation (0.553763)*/,
7, -4, 8, -12/*mean (0.118522), correlation (0.553452)*/,
-10, 4, -10, 9/*mean (0.12094), correlation (0.554785)*/,
7, 3, 12, 4/*mean (0.122582), correlation (0.555825)*/,
9, -7, 10, -2/*mean (0.124978), correlation (0.549846)*/,
7, 0, 12, -2/*mean (0.127002), correlation (0.537452)*/,
-1, -6, 0, -11/*mean (0.127148), correlation (0.547401)*/
};