一、fitLine函数
1、函数原型
从 2D 或 3D 点集拟合到直线。函数 fitLine 通过最小化 将线拟合到 2D 或 3D 点集，其中 是第个点之间的距离，线和 是距离函数，以下之一：
该算法基于 M-estimator技术，该技术使用加权最小二乘算法迭代拟合线。 在每次迭代之后，权重 被调整为与 成反比。
2、参数详解
二、OpenCV源码
1、源码路径
opencv\modules\imgproc\src\linefit.cpp
2、源码代码
static void fitLine2D( const Point2f * points, int count, int dist,float _param, float reps, float aeps, float *line ){double EPS = count*FLT_EPSILON;void (*calc_weights) (float *, int, float *) = 0;void (*calc_weights_param) (float *, int, float *, float) = 0;int i, j, k;float _line[4], _lineprev[4];float rdelta = reps != 0 ? reps : 1.0f;float adelta = aeps != 0 ? aeps : 0.01f;double min_err = DBL_MAX, err = 0;RNG rng((uint64)-1);memset( line, 0, 4*sizeof(line[0]) );switch (dist){case CV_DIST_L2:return fitLine2D_wods( points, count, 0, line );case CV_DIST_L1:calc_weights = weightL1;break;case CV_DIST_L12:calc_weights = weightL12;break;case CV_DIST_FAIR:calc_weights_param = weightFair;break;case CV_DIST_WELSCH:calc_weights_param = weightWelsch;break;case CV_DIST_HUBER:calc_weights_param = weightHuber;break;/*case DIST_USER:calc_weights = (void ( * )(float *, int, float *)) _PFP.fp;break;*/default:CV_Error(CV_StsBadArg, "Unknown distance type");}AutoBuffer<float> wr(count*2);float *w = wr.data(), *r = w + count;for( k = 0; k < 20; k++ ){int first = 1;for( i = 0; i < count; i++ )w[i] = 0.f;for( i = 0; i < MIN(count,10); ){j = rng.uniform(0, count);if( w[j] < FLT_EPSILON ){w[j] = 1.f;i++;}}fitLine2D_wods( points, count, w, _line );for( i = 0; i < 30; i++ ){double sum_w = 0;if( first ){first = 0;}else{double t = _line[0] * _lineprev[0] + _line[1] * _lineprev[1];t = MAX(t,-1.);t = MIN(t,1.);if( fabs(acos(t)) < adelta ){float x, y, d;x = (float) fabs( _line[2] - _lineprev[2] );y = (float) fabs( _line[3] - _lineprev[3] );d = x > y ? x : y;if( d < rdelta )break;}}/* calculate distances */err = calcDist2D( points, count, _line, r );if (err < min_err){min_err = err;memcpy(line, _line, 4 * sizeof(line[0]));if (err < EPS)break;}/* calculate weights */if( calc_weights )calc_weights( r, count, w );elsecalc_weights_param( r, count, w, _param );for( j = 0; j < count; j++ )sum_w += w[j];if( fabs(sum_w) > FLT_EPSILON ){sum_w = 1./sum_w;for( j = 0; j < count; j++ )w[j] = (float)(w[j]*sum_w);}else{for( j = 0; j < count; j++ )w[j] = 1.f;}/* save the line parameters */memcpy( _lineprev, _line, 4 * sizeof( float ));/* Run again... */fitLine2D_wods( points, count, w, _line );}if( err < min_err ){min_err = err;memcpy( line, _line, 4 * sizeof(line[0]));if( err < EPS )break;}}}/* Takes an array of 3D points, type of distance (including user-defineddistance specified by callbacks, fills the array of four floats with lineparameters A, B, C, D, E, F, where (A, B, C) is the normalized direction vector,(D, E, F) is the point that belongs to the line. */static void fitLine3D( Point3f * points, int count, int dist,float _param, float reps, float aeps, float *line ){double EPS = count*FLT_EPSILON;void (*calc_weights) (float *, int, float *) = 0;void (*calc_weights_param) (float *, int, float *, float) = 0;int i, j, k;float _line[6]={0,0,0,0,0,0}, _lineprev[6]={0,0,0,0,0,0};float rdelta = reps != 0 ? reps : 1.0f;float adelta = aeps != 0 ? aeps : 0.01f;double min_err = DBL_MAX, err = 0;RNG rng((uint64)-1);switch (dist){case CV_DIST_L2:return fitLine3D_wods( points, count, 0, line );case CV_DIST_L1:calc_weights = weightL1;break;case CV_DIST_L12:calc_weights = weightL12;break;case CV_DIST_FAIR:calc_weights_param = weightFair;break;case CV_DIST_WELSCH:calc_weights_param = weightWelsch;break;case CV_DIST_HUBER:calc_weights_param = weightHuber;break;default:CV_Error(CV_StsBadArg, "Unknown distance");}AutoBuffer<float> buf(count*2);float *w = buf.data(), *r = w + count;for( k = 0; k < 20; k++ ){int first = 1;for( i = 0; i < count; i++ )w[i] = 0.f;for( i = 0; i < MIN(count,10); ){j = rng.uniform(0, count);if( w[j] < FLT_EPSILON ){w[j] = 1.f;i++;}}fitLine3D_wods( points, count, w, _line );for( i = 0; i < 30; i++ ){double sum_w = 0;if( first ){first = 0;}else{double t = _line[0] * _lineprev[0] + _line[1] * _lineprev[1] + _line[2] * _lineprev[2];t = MAX(t,-1.);t = MIN(t,1.);if( fabs(acos(t)) < adelta ){float x, y, z, ax, ay, az, dx, dy, dz, d;x = _line[3] - _lineprev[3];y = _line[4] - _lineprev[4];z = _line[5] - _lineprev[5];ax = _line[0] - _lineprev[0];ay = _line[1] - _lineprev[1];az = _line[2] - _lineprev[2];dx = (float) fabs( y * az - z * ay );dy = (float) fabs( z * ax - x * az );dz = (float) fabs( x * ay - y * ax );d = dx > dy ? (dx > dz ? dx : dz) : (dy > dz ? dy : dz);if( d < rdelta )break;}}/* calculate distances */err = calcDist3D( points, count, _line, r );if (err < min_err){min_err = err;memcpy(line, _line, 6 * sizeof(line[0]));if (err < EPS)break;}/* calculate weights */if( calc_weights )calc_weights( r, count, w );elsecalc_weights_param( r, count, w, _param );for( j = 0; j < count; j++ )sum_w += w[j];if( fabs(sum_w) > FLT_EPSILON ){sum_w = 1./sum_w;for( j = 0; j < count; j++ )w[j] = (float)(w[j]*sum_w);}else{for( j = 0; j < count; j++ )w[j] = 1.f;}/* save the line parameters */memcpy( _lineprev, _line, 6 * sizeof( float ));/* Run again... */fitLine3D_wods( points, count, w, _line );}if( err < min_err ){min_err = err;memcpy( line, _line, 6 * sizeof(line[0]));if( err < EPS )break;}}}}void cv::fitLine( InputArray _points, OutputArray _line, int distType,double param, double reps, double aeps ){CV_INSTRUMENT_REGION();Mat points = _points.getMat();float linebuf[6]={0.f};int npoints2 = points.checkVector(2, -1, false);int npoints3 = points.checkVector(3, -1, false);CV_Assert( npoints2 >= 0 || npoints3 >= 0 );if( points.depth() != CV_32F || !points.isContinuous() ){Mat temp;points.convertTo(temp, CV_32F);points = temp;}if( npoints2 >= 0 )fitLine2D( points.ptr<Point2f>(), npoints2, distType,(float)param, (float)reps, (float)aeps, linebuf);elsefitLine3D( points.ptr<Point3f>(), npoints3, distType,(float)param, (float)reps, (float)aeps, linebuf);Mat(npoints2 >= 0 ? 4 : 6, 1, CV_32F, linebuf).copyTo(_line);}
三、示例参考
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