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转载请注明出处：http://blog.csdn.net/luoshixian099/article/details/50217655
随机抽样一致性（RANSAC）算法，可以在一组包含“外点”的数据集中，采用不断迭代的方法，寻找最优参数模型，不符合最优模型的点，被定义为“外点”。在图像配准以及拼接上得到广泛的应用，本文将对RANSAC算法在OpenCV中角点误匹配对的检测中进行解析。
1.RANSAC原理
OpenCV中滤除误匹配对采用RANSAC算法寻找一个最佳单应性矩阵H，矩阵大小为3×3。RANSAC目的是找到最优的参数矩阵使得满足该矩阵的数据点个数最多，通常令h33=1来归一化矩阵。由于单应性矩阵有8个未知参数，至少需要8个线性方程求解，对应到点位置信息上，一组点对可以列出两个方程，则至少包含4组匹配点对。
其中(x,y)表示目标图像角点位置,(x‘,y‘)为场景图像角点位置，s为尺度参数。
RANSAC算法从匹配数据集中随机抽出4个样本并保证这4个样本之间不共线，计算出单应性矩阵，然后利用这个模型测试所有数据，并计算满足这个模型数据点的个数与投影误差(即代价函数)，若此模型为最优模型，则对应的代价函数最小。
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RANSAC算法步骤：
1. 随机从数据集中随机抽出4个样本数据 (此4个样本之间不能共线)，计算出变换矩阵H，记为模型M；
2. 计算数据集中所有数据与模型M的投影误差，若误差小于阈值，加入内点集 I ；
3. 如果当前内点集 I 元素个数大于最优内点集 I_best , 则更新 I_best = I，同时更新迭代次数k ;
4. 如果迭代次数大于k,则退出 ; 否则迭代次数加1，并重复上述步骤；
注：迭代次数k在不大于最大迭代次数的情况下，是在不断更新而不是固定的；
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2.例程
OpenCV中此功能通过调用findHomography函数调用，下面是个例程：
#include <iostream>
#include "opencv2/opencv.hpp"
#include "opencv2/core/core.hpp"
#include "opencv2/features2d/features2d.hpp"
#include "opencv2/highgui/highgui.hpp"
using namespace cv;
using namespace std;
int main(int argc, char** argv)
{
Mat obj=imread("F:\\Picture\\obj.jpg"); //载入目标图像
Mat scene=imread("F:\\Picture\\scene.jpg"); //载入场景图像
if (obj.empty() || scene.empty() )
{
cout<<"Can't open the picture!\n";
return 0;
}
vector<KeyPoint> obj_keypoints,scene_keypoints;
Mat obj_descriptors,scene_descriptors;
ORB detector; //采用ORB算法提取特征点
detector.detect(obj,obj_keypoints);
detector.detect(scene,scene_keypoints);
detector.compute(obj,obj_keypoints,obj_descriptors);
detector.compute(scene,scene_keypoints,scene_descriptors);
BFMatcher matcher(NORM_HAMMING,true); //汉明距离做为相似度度量
vector<DMatch> matches;
matcher.match(obj_descriptors, scene_descriptors, matches);
Mat match_img;
drawMatches(obj,obj_keypoints,scene,scene_keypoints,matches,match_img);
imshow("滤除误匹配前",match_img);
//保存匹配对序号
vector<int> queryIdxs( matches.size() ), trainIdxs( matches.size() );
for( size_t i = 0; i < matches.size(); i++ )
{
queryIdxs[i] = matches[i].queryIdx;
trainIdxs[i] = matches[i].trainIdx;
}
Mat H12; //变换矩阵
vector<Point2f> points1; KeyPoint::convert(obj_keypoints, points1, queryIdxs);
vector<Point2f> points2; KeyPoint::convert(scene_keypoints, points2, trainIdxs);
int ransacReprojThreshold = 5; //拒绝阈值
H12 = findHomography( Mat(points1), Mat(points2), CV_RANSAC, ransacReprojThreshold );
vector<char> matchesMask( matches.size(), 0 );
Mat points1t;
perspectiveTransform(Mat(points1), points1t, H12);
for( size_t i1 = 0; i1 < points1.size(); i1++ ) //保存‘内点’
{
if( norm(points2[i1] - points1t.at<Point2f>((int)i1,0)) <= ransacReprojThreshold ) //给内点做标记
{
matchesMask[i1] = 1;
}
}
Mat match_img2; //滤除‘外点’后
drawMatches(obj,obj_keypoints,scene,scene_keypoints,matches,match_img2,Scalar(0,0,255),Scalar::all(-1),matchesMask);
//画出目标位置
std::vector<Point2f> obj_corners(4);
obj_corners[0] = cvPoint(0,0); obj_corners[1] = cvPoint( obj.cols, 0 );
obj_corners[2] = cvPoint( obj.cols, obj.rows ); obj_corners[3] = cvPoint( 0, obj.rows );
std::vector<Point2f> scene_corners(4);
perspectiveTransform( obj_corners, scene_corners, H12);
line( match_img2, scene_corners[0] + Point2f(static_cast<float>(obj.cols), 0),
scene_corners[1] + Point2f(static_cast<float>(obj.cols), 0),Scalar(0,0,255),2);
line( match_img2, scene_corners[1] + Point2f(static_cast<float>(obj.cols), 0),
scene_corners[2] + Point2f(static_cast<float>(obj.cols), 0),Scalar(0,0,255),2);
line( match_img2, scene_corners[2] + Point2f(static_cast<float>(obj.cols), 0),
scene_corners[3] + Point2f(static_cast<float>(obj.cols), 0),Scalar(0,0,255),2);
line( match_img2, scene_corners[3] + Point2f(static_cast<float>(obj.cols), 0),
scene_corners[0] + Point2f(static_cast<float>(obj.cols), 0),Scalar(0,0,255),2);
imshow("滤除误匹配后",match_img2);
waitKey(0);
return 0;
}
(1)findHomography内部调用cvFindHomography函数
srcPoints:目标图像点集
dstPoints:场景图像点集
method: 最小中值法、RANSAC方法、最小二乘法
ransacReprojTheshold:投影误差阈值
mask:掩码
cvFindHomography( const CvMat* objectPoints, const CvMat* imagePoints,
CvMat* __H, int method, double ransacReprojThreshold,
CvMat* mask )
{
const double confidence = 0.995; //置信度
const int maxIters = 2000; //迭代最大次数
const double defaultRANSACReprojThreshold = 3; //默认拒绝阈值
bool result = false;
Ptr<CvMat> m, M, tempMask;
double H[9];
CvMat matH = cvMat( 3, 3, CV_64FC1, H ); //变换矩阵
int count;
CV_Assert( CV_IS_MAT(imagePoints) && CV_IS_MAT(objectPoints) );
count = MAX(imagePoints->cols, imagePoints->rows);
CV_Assert( count >= 4 ); //至少有4个样本
if( ransacReprojThreshold <= 0 )
ransacReprojThreshold = defaultRANSACReprojThreshold;
m = cvCreateMat( 1, count, CV_64FC2 ); //转换为齐次坐标
cvConvertPointsHomogeneous( imagePoints, m );
M = cvCreateMat( 1, count, CV_64FC2 );//转换为齐次坐标
cvConvertPointsHomogeneous( objectPoints, M );
if( mask )
{
CV_Assert( CV_IS_MASK_ARR(mask) && CV_IS_MAT_CONT(mask->type) &&
(mask->rows == 1 || mask->cols == 1) &&
mask->rows*mask->cols == count );
}
if( mask || count > 4 )
tempMask = cvCreateMat( 1, count, CV_8U );
if( !tempMask.empty() )
cvSet( tempMask, cvScalarAll(1.) );
CvHomographyEstimator estimator(4);
if( count == 4 )
method = 0;
if( method == CV_LMEDS ) //最小中值法
result = estimator.runLMeDS( M, m, &matH, tempMask, confidence, maxIters );
else if( method == CV_RANSAC ) //采用RANSAC算法
result = estimator.runRANSAC( M, m, &matH, tempMask, ransacReprojThreshold, confidence, maxIters);//(2)解析
else
result = estimator.runKernel( M, m, &matH ) > 0; //最小二乘法
if( result && count > 4 )
{
icvCompressPoints( (CvPoint2D64f*)M->data.ptr, tempMask->data.ptr, 1, count ); //保存内点集
count = icvCompressPoints( (CvPoint2D64f*)m->data.ptr, tempMask->data.ptr, 1, count );
M->cols = m->cols = count;
if( method == CV_RANSAC ) //
estimator.runKernel( M, m, &matH ); //内点集上采用最小二乘法重新估算变换矩阵
estimator.refine( M, m, &matH, 10 );//
}
if( result )
cvConvert( &matH, __H ); //保存变换矩阵
if( mask && tempMask )
{
if( CV_ARE_SIZES_EQ(mask, tempMask) )
cvCopy( tempMask, mask );
else
cvTranspose( tempMask, mask );
}
return (int)result;
}
(2) runRANSAC
maxIters:最大迭代次数
m1,m2 :数据样本
model:变换矩阵
reprojThreshold:投影误差阈值
confidence:置信度 0.995
bool CvModelEstimator2::runRANSAC( const CvMat* m1, const CvMat* m2, CvMat* model,
CvMat* mask0, double reprojThreshold,
double confidence, int maxIters )
{
bool result = false;
cv::Ptr<CvMat> mask = cvCloneMat(mask0);
cv::Ptr<CvMat> models, err, tmask;
cv::Ptr<CvMat> ms1, ms2;
int iter, niters = maxIters;
int count = m1->rows*m1->cols, maxGoodCount = 0;
CV_Assert( CV_ARE_SIZES_EQ(m1, m2) && CV_ARE_SIZES_EQ(m1, mask) );
if( count < modelPoints )
return false;
models = cvCreateMat( modelSize.height*maxBasicSolutions, modelSize.width, CV_64FC1 );
err = cvCreateMat( 1, count, CV_32FC1 );//保存每组点对应的投影误差
tmask = cvCreateMat( 1, count, CV_8UC1 );
if( count > modelPoints ) //多于4个点
{
ms1 = cvCreateMat( 1, modelPoints, m1->type );
ms2 = cvCreateMat( 1, modelPoints, m2->type );
}
else //等于4个点
{
niters = 1; //迭代一次
ms1 = cvCloneMat(m1); //保存每次随机找到的样本点
ms2 = cvCloneMat(m2);
}
for( iter = 0; iter < niters; iter++ ) //不断迭代
{
int i, goodCount, nmodels;
if( count > modelPoints )
{
//在(3)解析getSubset
bool found = getSubset( m1, m2, ms1, ms2, 300 ); //随机选择4组点，且三点之间不共线，(3)解析
if( !found )
{
if( iter == 0 )
return false;
break;
}
}
nmodels = runKernel( ms1, ms2, models ); //估算近似变换矩阵，返回1
if( nmodels <= 0 )
continue;
for( i = 0; i < nmodels; i++ )//执行一次
{
CvMat model_i;
cvGetRows( models, &model_i, i*modelSize.height, (i+1)*modelSize.height );//获取3×3矩阵元素
goodCount = findInliers( m1, m2, &model_i, err, tmask, reprojThreshold ); //找出内点，(4)解析
if( goodCount > MAX(maxGoodCount, modelPoints-1) ) //当前内点集元素个数大于最优内点集元素个数
{
std::swap(tmask, mask);
cvCopy( &model_i, model ); //更新最优模型
maxGoodCount = goodCount;
//confidence 为置信度默认0.995,modelPoints为最少所需样本数=4,niters迭代次数
niters = cvRANSACUpdateNumIters( confidence, //更新迭代次数，(5)解析
(double)(count - goodCount)/count, modelPoints, niters );
}
}
}
if( maxGoodCount > 0 )
{
if( mask != mask0 )
cvCopy( mask, mask0 );
result = true;
}
return result;
}
(3)getSubset
ms1,ms2:保存随机找到的4个样本
maxAttempts:最大迭代次数，300
bool CvModelEstimator2::getSubset( const CvMat* m1, const CvMat* m2,
CvMat* ms1, CvMat* ms2, int maxAttempts )
{
cv::AutoBuffer<int> _idx(modelPoints); //modelPoints 所需要最少的样本点个数
int* idx = _idx;
int i = 0, j, k, idx_i, iters = 0;
int type = CV_MAT_TYPE(m1->type), elemSize = CV_ELEM_SIZE(type);
const int *m1ptr = m1->data.i, *m2ptr = m2->data.i;
int *ms1ptr = ms1->data.i, *ms2ptr = ms2->data.i;
int count = m1->cols*m1->rows;
assert( CV_IS_MAT_CONT(m1->type & m2->type) && (elemSize % sizeof(int) == 0) );
elemSize /= sizeof(int); //每个数据占用字节数
for(; iters < maxAttempts; iters++)
{
for( i = 0; i < modelPoints && iters < maxAttempts; )
{
idx[i] = idx_i = cvRandInt(&rng) % count; // 随机选取1组点
for( j = 0; j < i; j++ ) // 检测是否重复选择
if( idx_i == idx[j] )
break;
if( j < i )
continue; //重新选择
for( k = 0; k < elemSize; k++ ) //拷贝点数据
{
ms1ptr[i*elemSize + k] = m1ptr[idx_i*elemSize + k];
ms2ptr[i*elemSize + k] = m2ptr[idx_i*elemSize + k];
}
if( checkPartialSubsets && (!checkSubset( ms1, i+1 ) || !checkSubset( ms2, i+1 )))//检测点之间是否共线
{
iters++; //若共线，重新选择一组
continue;
}
i++;
}
if( !checkPartialSubsets && i == modelPoints &&
(!checkSubset( ms1, i ) || !checkSubset( ms2, i )))
continue;
break;
}
return i == modelPoints && iters < maxAttempts; //返回找到的样本点个数
}
(4) findInliers & computerReprojError
int CvModelEstimator2::findInliers( const CvMat* m1, const CvMat* m2,
const CvMat* model, CvMat* _err,
CvMat* _mask, double threshold )
{
int i, count = _err->rows*_err->cols, goodCount = 0;
const float* err = _err->data.fl;
uchar* mask = _mask->data.ptr;
computeReprojError( m1, m2, model, _err ); //计算每组点的投影误差
threshold *= threshold;
for( i = 0; i < count; i++ )
goodCount += mask[i] = err[i] <= threshold;//误差在限定范围内，加入‘内点集’
return goodCount;
}
//--------------------------------------
void CvHomographyEstimator::computeReprojError( const CvMat* m1, const CvMat* m2,const CvMat* model, CvMat* _err )
{
int i, count = m1->rows*m1->cols;
const CvPoint2D64f* M = (const CvPoint2D64f*)m1->data.ptr;
const CvPoint2D64f* m = (const CvPoint2D64f*)m2->data.ptr;
const double* H = model->data.db;
float* err = _err->data.fl;
for( i = 0; i < count; i++ ) //保存每组点的投影误差，对应上述变换公式
{
double ww = 1./(H[6]*M[i].x + H[7]*M[i].y + 1.);
double dx = (H[0]*M[i].x + H[1]*M[i].y + H[2])*ww - m[i].x;
double dy = (H[3]*M[i].x + H[4]*M[i].y + H[5])*ww - m[i].y;
err[i] = (float)(dx*dx + dy*dy);
}
}(5)cvRANSACUpdateNumIters
对应上述k的计算公式
p：置信度
ep:外点比例
cvRANSACUpdateNumIters( double p, double ep,
int model_points, int max_iters )
{
if( model_points <= 0 )
CV_Error( CV_StsOutOfRange, "the number of model points should be positive" );
p = MAX(p, 0.);
p = MIN(p, 1.);
ep = MAX(ep, 0.);
ep = MIN(ep, 1.);
// avoid inf's & nan's
double num = MAX(1. - p, DBL_MIN); //num=1-p,做分子
double denom = 1. - pow(1. - ep,model_points);//做分母
if( denom < DBL_MIN )
return 0;
num = log(num);
denom = log(denom);
return denom >= 0 || -num >= max_iters*(-denom) ?
max_iters : cvRound(num/denom);
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原文地址：http://blog.csdn.net/luoshixian099/article/details/50217655
