加权拟合算法
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#include<cmath>#include<cstdio>#include"QSort.h"#include<ctime>#include<cstdlib>#define K (4.685 / 0.6745)#define NO_ERR 1#define cmp_pts( x, y ) ( x < y ) CV_IMPLEMENT_QSORT( floatQSort, float, cmp_pts )const int Count = 200;float X[Count], Y[Count];float Weights[Count];typedef struct {float theta;float x;float y;}LinePara;LinePara linePara;const double eps = 1e-6;int Med(float R[] , int Cnt)// cal median{ //qsort(R , Cnt , sizeof(R[0]) , Cmp); floatQSort(R , Cnt , 0); return R[Cnt/2];}int CalW(float X[] , float Y[] , int Cnt , LinePara& linePara , float W[] ){ int i = 0; float a = tan(linePara.theta); float b = linePara.y - tan(linePara.theta)*linePara.x; float Median = 0; float u; for(i = 0; i < Cnt ; i++) { W[i] = fabs(Y[i] - a * X[i] - b ); } Median = Med(W , Cnt); Median = Median > 2 ? Median : 2; //cout<< "Median : " << Median <<endl; for(i = 0 ; i < Cnt ; i++) { u = W[i]/(K * Median); //W[i] =(1 - u * u) * (1 - u * u); if(u < 1) { W[i] =(1 - u * u) * (1 - u * u); } else{ W[i] = 0; } }// for(int j = 0 ; j < Cnt/4; j++)// {// cout<< j <<" : " << W[4*j] << " " << W[4*j + 1] << " " << W[4*j + 2] << W[4*j + 3] << endl;// }return 0;}int FitLine2D( float* X, float* Y, int _count, float *weights, LinePara& linePara ){ double x = 0, y = 0, x2 = 0, y2 = 0, xy = 0, w = 0; double dx2, dy2, dxy; int i; int count = _count; float t; /* Calculating the average of x and y... */ if(weights == 0) { for( i = 0; i < count; i += 1 ) { x += X[i]; //points[i].x; y += Y[i]; //points[i].y; x2 += X[i]*X[i]; //points[i].x * points[i].x; y2 += Y[i]*Y[i]; //points[i].y * points[i].y; xy += X[i]*Y[i]; //points[i].x * points[i].y; } w = (float) count; } else { for( i = 0; i < count; i += 1 ) { x += weights[i] * X[i]; ///points[i].x; y += weights[i] * Y[i]; //points[i].y; x2 += weights[i] * X[i]*X[i]; //points[i].x * points[i].x; y2 += weights[i] * Y[i]*Y[i];//points[i].y * points[i].y; xy += weights[i] * X[i]*Y[i]; //points[i].x * points[i].y; w += weights[i]; } } x /= w; y /= w; x2 /= w; y2 /= w; xy /= w; dx2 = x2 - x * x; dy2 = y2 - y * y; dxy = xy - x * y; linePara.theta = (float) atan2( 2 * dxy, dx2 - dy2 ) / 2; linePara.x = (float) x; linePara.y = (float) y; return NO_ERR;}int main(){//测试数据 srand((unsigned int)time(NULL)); rand(); for(int i = 0 ; i < Count ; i++) { X[i] = i + rand()%20/32767.0; Y[i] = i * 2.3 + 45 + rand()%20/32767.0; } X[20] = 2; Y[100] = 4; X[30] = 3; //加权拟合 迭代20次 for(int i = 0; i < 5; i++) { CalW(X, Y, Count, linePara, Weights); for(int j = 0; j < Count; j++) { printf("%f ", Weights[j]); } FitLine2D(X, Y, Count, Weights, linePara); printf("\na: %f b: %f\n", tan(linePara.theta), linePara.y- tan(linePara.theta)*linePara.x); } //直接拟合 FitLine2D(X, Y, Count, NULL, linePara);printf("a: %f b: %f\n", tan(linePara.theta), linePara.y- tan(linePara.theta)*linePara.x); return 0;}//QSort.h
#ifndef MY_QSORT_H#define MY_QSORT_H#define CV_SWAP(a,b,t) ((t) = (a), (a) = (b), (b) = (t))#ifndef MIN#define MIN(a,b) ((a) > (b) ? (b) : (a))#endif#ifndef MAX#define MAX(a,b) ((a) < (b) ? (b) : (a))#endif#define CV_IMPLEMENT_QSORT_EX( func_name, T, LT, user_data_type ) \void func_name( T *array, size_t total, user_data_type aux ) \{ \ int isort_thresh = 7; \ T t; \ int sp = 0; \ \ struct \ { \ T *lb; \ T *ub; \ } \ stack[48]; \ \ aux = aux; \ \ if( total <= 1 ) \ return; \ \ stack[0].lb = array; \ stack[0].ub = array + (total - 1); \ \ while( sp >= 0 ) \ { \ T* left = stack[sp].lb; \ T* right = stack[sp--].ub; \ \ for(;;) \ { \ int i, n = (int)(right - left) + 1, m; \ T* ptr; \ T* ptr2; \ \ if( n <= isort_thresh ) \ { \ insert_sort: \ for( ptr = left + 1; ptr <= right; ptr++ ) \ { \ for( ptr2 = ptr; ptr2 > left && LT(ptr2[0],ptr2[-1]); ptr2--) \ CV_SWAP( ptr2[0], ptr2[-1], t ); \ } \ break; \ } \ else \ { \ T* left0; \ T* left1; \ T* right0; \ T* right1; \ T* pivot; \ T* a; \ T* b; \ T* c; \ int swap_cnt = 0; \ \ left0 = left; \ right0 = right; \ pivot = left + (n/2); \ \ if( n > 40 ) \ { \ int d = n / 8; \ a = left, b = left + d, c = left + 2*d; \ left = LT(*a, *b) ? (LT(*b, *c) ? b : (LT(*a, *c) ? c : a)) \ : (LT(*c, *b) ? b : (LT(*a, *c) ? a : c)); \ \ a = pivot - d, b = pivot, c = pivot + d; \ pivot = LT(*a, *b) ? (LT(*b, *c) ? b : (LT(*a, *c) ? c : a)) \ : (LT(*c, *b) ? b : (LT(*a, *c) ? a : c)); \ \ a = right - 2*d, b = right - d, c = right; \ right = LT(*a, *b) ? (LT(*b, *c) ? b : (LT(*a, *c) ? c : a)) \ : (LT(*c, *b) ? b : (LT(*a, *c) ? a : c)); \ } \ \ a = left, b = pivot, c = right; \ pivot = LT(*a, *b) ? (LT(*b, *c) ? b : (LT(*a, *c) ? c : a)) \ : (LT(*c, *b) ? b : (LT(*a, *c) ? a : c)); \ if( pivot != left0 ) \ { \ CV_SWAP( *pivot, *left0, t ); \ pivot = left0; \ } \ left = left1 = left0 + 1; \ right = right1 = right0; \ \ for(;;) \ { \ while( left <= right && !LT(*pivot, *left) ) \ { \ if( !LT(*left, *pivot) ) \ { \ if( left > left1 ) \ CV_SWAP( *left1, *left, t ); \ swap_cnt = 1; \ left1++; \ } \ left++; \ } \ \ while( left <= right && !LT(*right, *pivot) ) \ { \ if( !LT(*pivot, *right) ) \ { \ if( right < right1 ) \ CV_SWAP( *right1, *right, t ); \ swap_cnt = 1; \ right1--; \ } \ right--; \ } \ \ if( left > right ) \ break; \ CV_SWAP( *left, *right, t ); \ swap_cnt = 1; \ left++; \ right--; \ } \ \ if( swap_cnt == 0 ) \ { \ left = left0, right = right0; \ goto insert_sort; \ } \ \ n = MIN( (int)(left1 - left0), (int)(left - left1) ); \ for( i = 0; i < n; i++ ) \ CV_SWAP( left0[i], left[i-n], t ); \ \ n = MIN( (int)(right0 - right1), (int)(right1 - right) ); \ for( i = 0; i < n; i++ ) \ CV_SWAP( left[i], right0[i-n+1], t ); \ n = (int)(left - left1); \ m = (int)(right1 - right); \ if( n > 1 ) \ { \ if( m > 1 ) \ { \ if( n > m ) \ { \ stack[++sp].lb = left0; \ stack[sp].ub = left0 + n - 1; \ left = right0 - m + 1, right = right0; \ } \ else \ { \ stack[++sp].lb = right0 - m + 1; \ stack[sp].ub = right0; \ left = left0, right = left0 + n - 1; \ } \ } \ else \ left = left0, right = left0 + n - 1; \ } \ else if( m > 1 ) \ left = right0 - m + 1, right = right0; \ else \ break; \ } \ } \ } \}#define CV_IMPLEMENT_QSORT( func_name, T, cmp ) \ CV_IMPLEMENT_QSORT_EX( func_name, T, cmp, int )#endif//编译指令
g++ -o fitline fitline.cpp
执行指令：
./fitline
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