相关 :
Fast原理与源码解析
Brief描述子原理与源码解析
Harris原理与源码解析
- http://blog.csdn.net/luoshixian099/article/details/48523267
ORB特征提取详解
ORB特征点检测
为了满足实时性的要求，前面文章中介绍过快速提取特征点算法Fast,以及特征描述子Brief。本篇文章介绍的ORB算法结合了Fast和Brief的速度优势，并做了改进，且ORB是免费。
Ethan Rublee等人2011年在《ORB：An Efficient Alternative to SIFT or SURF》文章中提出了ORB算法。结合Fast与Brief算法，并给Fast特征点增加了方向性，使得特征点具有旋转不变性，并提出了构造金字塔方法，解决尺度不变性，但文章中没有具体详述。实验证明，ORB远优于之前的SIFT与SURF算法。
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论文核心内容概述：
1.构造金字塔，在每层金字塔上采用Fast算法提取特征点，采用Harris角点响应函数，按角点响应值排序，选取前N个特征点。
2. oFast:计算每个特征点的主方向，灰度质心法，计算特征点半径为r的圆形邻域范围内的灰度质心位置。从中心位置到质心位置的向量，定义为该特 征点的主方向。
定义矩的计算公式，x,y∈[-r,r]：
质心位置：
主方向：
3.rBrief:为了解决旋转不变性，把特征点的Patch旋转到主方向上(steered Brief)。通过实验得到，描述子在各个维度上的均值比较离散(偏离0.5)，同时维度间相关性很强，说明特征点描述子区分性不好，影响匹配的效果。论文中提出采取学习的方法，采用300K个训练样本点。每一个特征点，选取Patch大小为wp=31，Patch内每对点都采用wt=5大小的子窗口灰度均值做比较，子窗口的个数即为N=(wp-wt)*(wp-wt),从N个窗口中随机选两个做比较即构成描述子的一个bit,论文中采用M=205590种可能的情况：
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1.对所有样本点，做M种测试，构成M维的描述子，每个维度上非1即0；
2.按均值对M个维度排序（以0.5为中心），组成向量T；
3.贪婪搜索：把向量T中第一个元素移动到R中，然后继续取T的第二个元素，与R中的所有元素做相关性比较，如果相关性大于指定的阈值Threshold, 抛弃T的这个元素，否则加入到R中；
4.重复第3个步骤，直到R中有256个元素，若检测完毕,少于256个元素，则降低阈值，重复上述步骤；
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rBrief:通过上面的步骤取到的256对点，构成的描述子各维度间相关性很低，区分性好；
训练前 训练后
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ORB算法步骤,参考opencv源码:
1.首先构造尺度金字塔；
金字塔共n层，与SIFT不同，每层仅有一副图像；
第s层的尺度为
第s层图像大小:
2.在不同尺度上采用Fast检测特征点；在每一层上按公式计算需要提取的特征点数n,在本层上按Fast角点响应值排序，提取前2n个特征点，然后根据Harris 角点响应值排序， 取前n个特征点，作为本层的特征点；
3.计算每个特征点的主方向（质心法）；
4.旋转每个特征点的Patch到主方向，采用上述步骤3的选取的最优的256对特征点做τ测试，构成256维描述子，占32个字节；
4.采用汉明距离做特征点匹配；
----------OpenCV源码解析-------------------------------------------------------
ORB类定义：位置..\features2d.hpp
nfeatures:需要的特征点总数；
scaleFactor:尺度因子；
nlevels:金字塔层数；
edgeThreshold:边界阈值；
firstLevel:起始层；
WTA_K：描述子形成方法,WTA_K=2表示，采用两两比较；
scoreType:角点响应函数，可以选择Harris或者Fast的方法；
patchSize:特征点邻域大小；
/*!ORB implementation.*/class CV_EXPORTS_W ORB : public Feature2D{public:// the size of the signature in bytesenum { kBytes = 32, HARRIS_SCORE=0, FAST_SCORE=1 };CV_WRAP explicit ORB(int nfeatures = 500, float scaleFactor = 1.2f, int nlevels = 8, int edgeThreshold = 31,//构造函数int firstLevel = 0, int WTA_K=2, int scoreType=ORB::HARRIS_SCORE, int patchSize=31 );// returns the descriptor size in bytesint descriptorSize() const; //描述子占用的字节数，默认32字节// returns the descriptor typeint descriptorType() const;//描述子类型，8位整形数// Compute the ORB features and descriptors on an imagevoid operator()(InputArray image, InputArray mask, vector<KeyPoint>& keypoints) const;// Compute the ORB features and descriptors on an imagevoid operator()( InputArray image, InputArray mask, vector<KeyPoint>& keypoints, //提取特征点与形成描述子OutputArray descriptors, bool useProvidedKeypoints=false ) const;AlgorithmInfo* info() const;protected:void computeImpl( const Mat& image, vector<KeyPoint>& keypoints, Mat& descriptors ) const;//计算描述子void detectImpl( const Mat& image, vector<KeyPoint>& keypoints, const Mat& mask=Mat() ) const;//检测特征点 CV_PROP_RW int nfeatures;//特征点总数CV_PROP_RW double scaleFactor;//尺度因子CV_PROP_RW int nlevels;//金字塔内层数CV_PROP_RW int edgeThreshold;//边界阈值CV_PROP_RW int firstLevel;//开始层数CV_PROP_RW int WTA_K;//描述子形成方法，默认WTA_K=2，两两比较CV_PROP_RW int scoreType;//角点响应函数CV_PROP_RW int patchSize;//邻域Patch大小};
特征提取及形成描述子：通过这个函数对图像提取Fast特征点或者计算特征描述子
_image:输入图像；
_mask:掩码图像;
_keypoints:输入角点；
_descriptors:如果为空，只寻找特征点，不计算特征描述子；
_useProvidedKeypoints:如果为true,函数只计算特征描述子；
/** Compute the ORB features and descriptors on an image* @param img the image to compute the features and descriptors on* @param mask the mask to apply* @param keypoints the resulting keypoints* @param descriptors the resulting descriptors* @param do_keypoints if true, the keypoints are computed, otherwise used as an input* @param do_descriptors if true, also computes the descriptors*/void ORB::operator()( InputArray _image, InputArray _mask, vector<KeyPoint>& _keypoints,OutputArray _descriptors, bool useProvidedKeypoints) const{CV_Assert(patchSize >= 2);bool do_keypoints = !useProvidedKeypoints;bool do_descriptors = _descriptors.needed();if( (!do_keypoints && !do_descriptors) || _image.empty() )return;//ROI handlingconst int HARRIS_BLOCK_SIZE = 9;//Harris角点响应需要的边界大小int halfPatchSize = patchSize / 2;.//邻域半径int border = std::max(edgeThreshold, std::max(halfPatchSize, HARRIS_BLOCK_SIZE/2))+1;//采用最大的边界 Mat image = _image.getMat(), mask = _mask.getMat();if( image.type() != CV_8UC1 )cvtColor(_image, image, CV_BGR2GRAY);//转灰度图int levelsNum = this->nlevels;//金字塔层数if( !do_keypoints ) //不做特征点检测 {// if we have pre-computed keypoints, they may use more levels than it is set in parameters// !!!TODO!!! implement more correct method, independent from the used keypoint detector.// Namely, the detector should provide correct size of each keypoint. Based on the keypoint size// and the algorithm used (i.e. BRIEF, running on 31x31 patches) we should compute the approximate// scale-factor that we need to apply. Then we should cluster all the computed scale-factors and// for each cluster compute the corresponding image.//// In short, ultimately the descriptor should// ignore octave parameter and deal only with the keypoint size.levelsNum = 0;for( size_t i = 0; i < _keypoints.size(); i++ )levelsNum = std::max(levelsNum, std::max(_keypoints[i].octave, 0));//提取特征点的最大层数levelsNum++;}// Pre-compute the scale pyramidsvector<Mat> imagePyramid(levelsNum), maskPyramid(levelsNum);//创建尺度金字塔图像for (int level = 0; level < levelsNum; ++level){float scale = 1/getScale(level, firstLevel, scaleFactor); //每层对应的尺度/*static inline float getScale(int level, int firstLevel, double scaleFactor){return (float)std::pow(scaleFactor, (double)(level - firstLevel));}*/Size sz(cvRound(image.cols*scale), cvRound(image.rows*scale));//每层对应的图像大小Size wholeSize(sz.width + border*2, sz.height + border*2);Mat temp(wholeSize, image.type()), masktemp;imagePyramid[level] = temp(Rect(border, border, sz.width, sz.height));if( !mask.empty() ){masktemp = Mat(wholeSize, mask.type());maskPyramid[level] = masktemp(Rect(border, border, sz.width, sz.height));}// Compute the resized imageif( level != firstLevel ) //得到金字塔每层的图像 {if( level < firstLevel ){resize(image, imagePyramid[level], sz, 0, 0, INTER_LINEAR);if (!mask.empty())resize(mask, maskPyramid[level], sz, 0, 0, INTER_LINEAR);}else{resize(imagePyramid[level-1], imagePyramid[level], sz, 0, 0, INTER_LINEAR);if (!mask.empty()){resize(maskPyramid[level-1], maskPyramid[level], sz, 0, 0, INTER_LINEAR);threshold(maskPyramid[level], maskPyramid[level], 254, 0, THRESH_TOZERO);}}copyMakeBorder(imagePyramid[level], temp, border, border, border, border,//扩大图像的边界BORDER_REFLECT_101+BORDER_ISOLATED);if (!mask.empty())copyMakeBorder(maskPyramid[level], masktemp, border, border, border, border,BORDER_CONSTANT+BORDER_ISOLATED);}else{copyMakeBorder(image, temp, border, border, border, border,//扩大图像的四个边界 BORDER_REFLECT_101);if( !mask.empty() )copyMakeBorder(mask, masktemp, border, border, border, border,BORDER_CONSTANT+BORDER_ISOLATED);}}// Pre-compute the keypoints (we keep the best over all scales, so this has to be done beforehandvector < vector<KeyPoint> > allKeypoints;if( do_keypoints )//提取角点 {// Get keypoints, those will be far enough from the border that no check will be required for the descriptorcomputeKeyPoints(imagePyramid, maskPyramid, allKeypoints, //对每一层图像提取角点，见下面(1)的分析 nfeatures, firstLevel, scaleFactor,edgeThreshold, patchSize, scoreType);// make sure we have the right number of keypoints keypoints/*vector<KeyPoint> temp;for (int level = 0; level < n_levels; ++level){vector<KeyPoint>& keypoints = all_keypoints[level];temp.insert(temp.end(), keypoints.begin(), keypoints.end());keypoints.clear();}KeyPoint::retainBest(temp, n_features_);for (vector<KeyPoint>::iterator keypoint = temp.begin(),keypoint_end = temp.end(); keypoint != keypoint_end; ++keypoint)all_keypoints[keypoint->octave].push_back(*keypoint);*/}else //不提取角点 {// Remove keypoints very close to the border KeyPointsFilter::runByImageBorder(_keypoints, image.size(), edgeThreshold);// Cluster the input keypoints depending on the level they were computed at allKeypoints.resize(levelsNum);for (vector<KeyPoint>::iterator keypoint = _keypoints.begin(),keypointEnd = _keypoints.end(); keypoint != keypointEnd; ++keypoint)allKeypoints[keypoint->octave].push_back(*keypoint); //把角点信息存入allKeypoints内// Make sure we rescale the coordinatesfor (int level = 0; level < levelsNum; ++level) //把角点位置信息缩放到指定层位置上 {if (level == firstLevel)continue;vector<KeyPoint> & keypoints = allKeypoints[level];float scale = 1/getScale(level, firstLevel, scaleFactor);for (vector<KeyPoint>::iterator keypoint = keypoints.begin(),keypointEnd = keypoints.end(); keypoint != keypointEnd; ++keypoint)keypoint->pt *= scale; //缩放 }}Mat descriptors;vector<Point> pattern;if( do_descriptors ) //计算特征描述子 {int nkeypoints = 0;for (int level = 0; level < levelsNum; ++level)nkeypoints += (int)allKeypoints[level].size();//得到所有层的角点总数if( nkeypoints == 0 )_descriptors.release();else{_descriptors.create(nkeypoints, descriptorSize(), CV_8U);//创建一个矩阵存放描述子,每一行表示一个角点信息descriptors = _descriptors.getMat();}const int npoints = 512;//取512个点,共256对,产生256维描述子,32个字节 Point patternbuf[npoints];const Point* pattern0 = (const Point*)bit_pattern_31_;//训练好的256对数据点位置if( patchSize != 31 ){pattern0 = patternbuf;makeRandomPattern(patchSize, patternbuf, npoints);}CV_Assert( WTA_K == 2 || WTA_K == 3 || WTA_K == 4 );if( WTA_K == 2 ) //WTA_K=2使用两个点之间作比较std::copy(pattern0, pattern0 + npoints, std::back_inserter(pattern));else{int ntuples = descriptorSize()*4;initializeOrbPattern(pattern0, pattern, ntuples, WTA_K, npoints);}}_keypoints.clear();int offset = 0;for (int level = 0; level < levelsNum; ++level)//依次计算每一层的角点描述子 {// Get the features and compute their orientationvector<KeyPoint>& keypoints = allKeypoints[level];int nkeypoints = (int)keypoints.size();//本层内角点个数// Compute the descriptorsif (do_descriptors){Mat desc;if (!descriptors.empty()){desc = descriptors.rowRange(offset, offset + nkeypoints);}offset += nkeypoints; //偏移量// preprocess the resized imageMat& workingMat = imagePyramid[level];//boxFilter(working_mat, working_mat, working_mat.depth(), Size(5,5), Point(-1,-1), true, BORDER_REFLECT_101);GaussianBlur(workingMat, workingMat, Size(7, 7), 2, 2, BORDER_REFLECT_101);//高斯平滑图像computeDescriptors(workingMat, keypoints, desc, pattern, descriptorSize(), WTA_K);//计算本层内角点的描述子,（3） }// Copy to the output dataif (level != firstLevel) //角点位置信息返回到原图上 {float scale = getScale(level, firstLevel, scaleFactor);for (vector<KeyPoint>::iterator keypoint = keypoints.begin(),keypointEnd = keypoints.end(); keypoint != keypointEnd; ++keypoint)keypoint->pt *= scale;}// And add the keypoints to the output_keypoints.insert(_keypoints.end(), keypoints.begin(), keypoints.end());//存入描述子信息，返回 }}
（1）提取角点：computeKeyPoints
imagePyramid:即构造好的金字塔
/** Compute the ORB keypoints on an image* @param image_pyramid the image pyramid to compute the features and descriptors on* @param mask_pyramid the masks to apply at every level* @param keypoints the resulting keypoints, clustered per level*/static void computeKeyPoints(const vector<Mat>& imagePyramid,const vector<Mat>& maskPyramid,vector<vector<KeyPoint> >& allKeypoints,int nfeatures, int firstLevel, double scaleFactor,int edgeThreshold, int patchSize, int scoreType ){int nlevels = (int)imagePyramid.size(); //金字塔层数vector<int> nfeaturesPerLevel(nlevels);// fill the extractors and descriptors for the corresponding scalesfloat factor = (float)(1.0 / scaleFactor);float ndesiredFeaturesPerScale = nfeatures*(1 - factor)/(1 - (float)pow((double)factor, (double)nlevels));// int sumFeatures = 0;for( int level = 0; level < nlevels-1; level++ ) //对每层图像上分配相应角点数 {nfeaturesPerLevel[level] = cvRound(ndesiredFeaturesPerScale);sumFeatures += nfeaturesPerLevel[level];ndesiredFeaturesPerScale *= factor;}nfeaturesPerLevel[nlevels-1] = std::max(nfeatures - sumFeatures, 0);//剩下角点数，由最上层图像提取// Make sure we forget about what is too close to the boundary//edge_threshold_ = std::max(edge_threshold_, patch_size_/2 + kKernelWidth / 2 + 2);// pre-compute the end of a row in a circular patchint halfPatchSize = patchSize / 2; //计算每个特征点圆邻域的位置信息vector<int> umax(halfPatchSize + 2);int v, v0, vmax = cvFloor(halfPatchSize * sqrt(2.f) / 2 + 1);int vmin = cvCeil(halfPatchSize * sqrt(2.f) / 2);for (v = 0; v <= vmax; ++v) // umax[v] = cvRound(sqrt((double)halfPatchSize * halfPatchSize - v * v));// Make sure we are symmetricfor (v = halfPatchSize, v0 = 0; v >= vmin; --v){while (umax[v0] == umax[v0 + 1])++v0;umax[v] = v0;++v0;}allKeypoints.resize(nlevels);for (int level = 0; level < nlevels; ++level){int featuresNum = nfeaturesPerLevel[level];allKeypoints[level].reserve(featuresNum*2);vector<KeyPoint> & keypoints = allKeypoints[level];// Detect FAST features, 20 is a good thresholdFastFeatureDetector fd(20, true);fd.detect(imagePyramid[level], keypoints, maskPyramid[level]);//Fast角点检测// Remove keypoints very close to the borderKeyPointsFilter::runByImageBorder(keypoints, imagePyramid[level].size(), edgeThreshold);//去除邻近边界的点if( scoreType == ORB::HARRIS_SCORE ){// Keep more points than necessary as FAST does not give amazing cornersKeyPointsFilter::retainBest(keypoints, 2 * featuresNum);//按Fast强度排序,保留前2*featuresNum个特征点// Compute the Harris cornerness (better scoring than FAST)HarrisResponses(imagePyramid[level], keypoints, 7, HARRIS_K); //计算每个角点的Harris强度响应 }//cull to the final desired level, using the new Harris scores or the original FAST scores.KeyPointsFilter::retainBest(keypoints, featuresNum);//按Harris强度排序，保留前featuresNum个float sf = getScale(level, firstLevel, scaleFactor);// Set the level of the coordinatesfor (vector<KeyPoint>::iterator keypoint = keypoints.begin(),keypointEnd = keypoints.end(); keypoint != keypointEnd; ++keypoint){keypoint->octave = level; //层信息keypoint->size = patchSize*sf; // }computeOrientation(imagePyramid[level], keypoints, halfPatchSize, umax); //计算角点的方向，（2）分析 }}
（2）为每个角点计算主方向，质心法；
static void computeOrientation(const Mat& image, vector<KeyPoint>& keypoints,int halfPatchSize, const vector<int>& umax){// Process each keypointfor (vector<KeyPoint>::iterator keypoint = keypoints.begin(), //为每个角点计算主方向keypointEnd = keypoints.end(); keypoint != keypointEnd; ++keypoint){keypoint->angle = IC_Angle(image, halfPatchSize, keypoint->pt, umax);//计算质心方向 }}
static float IC_Angle(const Mat& image, const int half_k, Point2f pt,const vector<int> & u_max){int m_01 = 0, m_10 = 0;const uchar* center = &image.at<uchar> (cvRound(pt.y), cvRound(pt.x));// Treat the center line differently, v=0for (int u = -half_k; u <= half_k; ++u)m_10 += u * center[u];// Go line by line in the circular patchint step = (int)image.step1();for (int v = 1; v <= half_k; ++v) //每次处理对称的两行v {// Proceed over the two linesint v_sum = 0;int d = u_max[v];for (int u = -d; u <= d; ++u){int val_plus = center[u + v*step], val_minus = center[u - v*step];v_sum += (val_plus - val_minus); //计算m_01时,位置上差一个符号m_10 += u * (val_plus + val_minus);}m_01 += v * v_sum;//计算上下两行的m_01 }return fastAtan2((float)m_01, (float)m_10);//计算角度}
(3)计算特征点描述子
static void computeDescriptors(const Mat& image, vector<KeyPoint>& keypoints, Mat& descriptors,const vector<Point>& pattern, int dsize, int WTA_K){//convert to grayscale if more than one colorCV_Assert(image.type() == CV_8UC1);//create the descriptor mat, keypoints.size() rows, BYTES colsdescriptors = Mat::zeros((int)keypoints.size(), dsize, CV_8UC1);for (size_t i = 0; i < keypoints.size(); i++)computeOrbDescriptor(keypoints[i], image, &pattern[0], descriptors.ptr((int)i), dsize, WTA_K);}
static void computeOrbDescriptor(const KeyPoint& kpt,const Mat& img, const Point* pattern,uchar* desc, int dsize, int WTA_K){float angle = kpt.angle;//angle = cvFloor(angle/12)*12.f;angle *= (float)(CV_PI/180.f);float a = (float)cos(angle), b = (float)sin(angle);const uchar* center = &img.at<uchar>(cvRound(kpt.pt.y), cvRound(kpt.pt.x));int step = (int)img.step;#if 1#define GET_VALUE(idx) \ //取旋转后一个像素点的值center[cvRound(pattern[idx].x*b + pattern[idx].y*a)*step + \cvRound(pattern[idx].x*a - pattern[idx].y*b)]#elsefloat x, y;int ix, iy;#define GET_VALUE(idx) \ //取旋转后一个像素点，插值法(x = pattern[idx].x*a - pattern[idx].y*b, \y = pattern[idx].x*b + pattern[idx].y*a, \ix = cvFloor(x), iy = cvFloor(y), \x -= ix, y -= iy, \cvRound(center[iy*step + ix]*(1-x)*(1-y) + center[(iy+1)*step + ix]*(1-x)*y + \center[iy*step + ix+1]*x*(1-y) + center[(iy+1)*step + ix+1]*x*y))#endifif( WTA_K == 2 ){for (int i = 0; i < dsize; ++i, pattern += 16)//每个特征描述子长度为32个字节 {int t0, t1, val;t0 = GET_VALUE(0); t1 = GET_VALUE(1);val = t0 < t1;t0 = GET_VALUE(2); t1 = GET_VALUE(3);val |= (t0 < t1) << 1;t0 = GET_VALUE(4); t1 = GET_VALUE(5);val |= (t0 < t1) << 2;t0 = GET_VALUE(6); t1 = GET_VALUE(7);val |= (t0 < t1) << 3;t0 = GET_VALUE(8); t1 = GET_VALUE(9);val |= (t0 < t1) << 4;t0 = GET_VALUE(10); t1 = GET_VALUE(11);val |= (t0 < t1) << 5;t0 = GET_VALUE(12); t1 = GET_VALUE(13);val |= (t0 < t1) << 6;t0 = GET_VALUE(14); t1 = GET_VALUE(15);val |= (t0 < t1) << 7;desc[i] = (uchar)val;}}else if( WTA_K == 3 ){for (int i = 0; i < dsize; ++i, pattern += 12){int t0, t1, t2, val;t0 = GET_VALUE(0); t1 = GET_VALUE(1); t2 = GET_VALUE(2);val = t2 > t1 ? (t2 > t0 ? 2 : 0) : (t1 > t0);t0 = GET_VALUE(3); t1 = GET_VALUE(4); t2 = GET_VALUE(5);val |= (t2 > t1 ? (t2 > t0 ? 2 : 0) : (t1 > t0)) << 2;t0 = GET_VALUE(6); t1 = GET_VALUE(7); t2 = GET_VALUE(8);val |= (t2 > t1 ? (t2 > t0 ? 2 : 0) : (t1 > t0)) << 4;t0 = GET_VALUE(9); t1 = GET_VALUE(10); t2 = GET_VALUE(11);val |= (t2 > t1 ? (t2 > t0 ? 2 : 0) : (t1 > t0)) << 6;desc[i] = (uchar)val;}}else if( WTA_K == 4 ){for (int i = 0; i < dsize; ++i, pattern += 16){int t0, t1, t2, t3, u, v, k, val;t0 = GET_VALUE(0); t1 = GET_VALUE(1);t2 = GET_VALUE(2); t3 = GET_VALUE(3);u = 0, v = 2;if( t1 > t0 ) t0 = t1, u = 1;if( t3 > t2 ) t2 = t3, v = 3;k = t0 > t2 ? u : v;val = k;t0 = GET_VALUE(4); t1 = GET_VALUE(5);t2 = GET_VALUE(6); t3 = GET_VALUE(7);u = 0, v = 2;if( t1 > t0 ) t0 = t1, u = 1;if( t3 > t2 ) t2 = t3, v = 3;k = t0 > t2 ? u : v;val |= k << 2;t0 = GET_VALUE(8); t1 = GET_VALUE(9);t2 = GET_VALUE(10); t3 = GET_VALUE(11);u = 0, v = 2;if( t1 > t0 ) t0 = t1, u = 1;if( t3 > t2 ) t2 = t3, v = 3;k = t0 > t2 ? u : v;val |= k << 4;t0 = GET_VALUE(12); t1 = GET_VALUE(13);t2 = GET_VALUE(14); t3 = GET_VALUE(15);u = 0, v = 2;if( t1 > t0 ) t0 = t1, u = 1;if( t3 > t2 ) t2 = t3, v = 3;k = t0 > t2 ? u : v;val |= k << 6;desc[i] = (uchar)val;}}elseCV_Error( CV_StsBadSize, "Wrong WTA_K. It can be only 2, 3 or 4." );#undef GET_VALUE}
