RANSAC算法（一）

这个算法主要是一种思想，并没有具体的代码，下面的代码是根据这种思想，进行的一维直线的拟合，也有与最小二乘法进行对比的结果

/*--------------------------------------------------------------------------------------------------*  @Copyright (c) , All rights reserved.*  @file:       myRANSAC.cpp*  @version:    ver 1.0*  @author:     闹闹*  @brief:  *  @change:*  @email:    1319144981@qq.com*  Date             Version    Changed By      Changes *  2021/5/17 15:11:30    1.0       闹闹            create写一句自己最喜欢的话吧。为天地立心，为生民立命，为往圣继绝学，为万世开太平。
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/*--------------------------------------------------------------------------------------------------
* modify_author:            闹闹
* modify_time:      2021/5/17 15:15:16
* modify_content:    此版本主要用于线拟合
* modify_reference:
https://blog.csdn.net/xrwang/article/details/6232327
https://blog.csdn.net/u010551600/article/details/79013453?utm_medium=distribute.pc_relevant.none-task-blog-baidujs_title-0&spm=1001.2101.3001.4242
https://blog.csdn.net/robinhjwy/article/details/79174914?utm_medium=distribute.pc_relevant.none-task-blog-2~default~BlogCommendFromMachineLearnPai2~default-2.control&depth_1-utm_source=distribute.pc_relevant.none-task-blog-2~default~BlogCommendFromMachineLearnPai2~default-2.control
https://blog.csdn.net/luoshixian099/article/details/50217655
https://blog.csdn.net/pamxy/article/details/9206485
* modify_other:
* modify_version:  1.0.0.2
--------------------------------------------------------------------------------------------------*/#ifndef __MYRANSAC_H__
#define __MYRANSAC_H__
#include <iostream>
#include <vector>
#include <math.h>
#include <set>
#include <stdlib.h>
#include <time.h>
class Point2D {public:Point2D(double px, double py) : x(px), y(py) {}double x;double y;
};
/*--------------------------------------------------------------------------------------------------
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inline std::ostream &operator<<(std::ostream &output, const Point2D &pnt){output << pnt.x << ' ' << pnt.y;return(output);
}/*
这个类定义了参数估计器的接口。
从它继承的类可以被RanSac类用于执行鲁棒参数估计。
*/
template<class T, class S>
class ParameterEsitmator {public:/*--------------------------------------------------------------------------------------------------* @FuncName:  * @Author:    闹闹* @Brief:    参数的精确估计。使用最小数据量估计参数（精确估计）。* @Version:   1.0.0.1* @Date:      2021/5/17 15:22* @InputParameter: data,用于估算的数据。parameters,被清除，用计算的结果填充* @OutputParameter: * @Returns:   * @Others:    --------------------------------------------------------------------------------------------------*/virtual void estimate(std::vector<T *> &data, std::vector<S> &parameters) = 0;/*--------------------------------------------------------------------------------------------------* @FuncName:  * @Author:    闹闹* @Brief:   参数的最小二乘估计。使用不止最小量的数据来估计参数，从而使估计最小化最小平方误差标准。* @Version:   1.0.0.1* @Date:      2021/5/17 15:19* @InputParameter: data,用于估算的数据。parameters,被清除，用计算的结果填充* @OutputParameter: * @Returns:   * @Others:    --------------------------------------------------------------------------------------------------*/virtual void leastSquaresEstimate(std::vector<T *> &data, std::vector<S> &parameters) = 0;/*--------------------------------------------------------------------------------------------------* @FuncName:  * @Author:    闹闹* @Brief:     该方法测试给定的数据是否与给定的模型参数一致。给定的数据是否与模型参数一致。* @Version:   1.0.0.1* @Date:    2021/5/17 15:18* @InputParameter: * @OutputParameter: * @Returns:   * @Others:    --------------------------------------------------------------------------------------------------*/virtual bool agree(std::vector<S> &parameters, T &data) = 0;
};/*
此类估计2D线的参数。
2D线表示为：(*)dot(n，p-a)= 0 。其中n是线法线（| n | = 1），而'a'是线上的点。
满足方程式（*）的所有点'p'都在线上。
选择此行参数化的原因是它可以表示所有的直线，包括垂直和水平线。与斜率截距（y = ax + b）参数化不同。
虚函数在类内实现
*/
class LineParamEstimator : public ParameterEsitmator<Point2D, double> {public:LineParamEstimator(double delta) : m_deltaSquared(delta*delta) {};/*--------------------------------------------------------------------------------------------------* @FuncName:  * @Author:    闹闹* @Brief:    计算由给定数据点定义的线。* @Version:   1.0.0.1* @Date:   2021/5/17 15:53* @InputParameter: data,包含两个2D点的向量。parameters,清除此向量，然后填充计算出的参数。* @OutputParameter: * @Returns:   * @Others:    通过这些点[n_x，n_y，a_x，a_y]的线的参数,其中||（n_x，ny）|| = 1。如果向量包含少于两个点，则结果参数向量为空（大小= 0）。Compute the line parameters  [n_x,n_y,a_x,a_y]通过输入的两点来确定所在直线，采用法线向量的方式来表示，以兼容平行或垂直的情况其中n_x,n_y为归一化后，与原点构成的法线向量，a_x,a_y为直线上任意一点--------------------------------------------------------------------------------------------------*/virtual void estimate(std::vector<Point2D *> &data, std::vector<double> &parameters) {parameters.clear();if (data.size() < 2) return;double nx = data[1]->y - data[0]->y;double ny = data[0]->x - data[1]->x;  // 原始直线的斜率为K，则法线的斜率为-1/k , ny / nx 是法向量。double norm = sqrt(nx*nx + ny*ny);parameters.push_back(nx / norm);parameters.push_back(ny / norm);parameters.push_back(data[0]->x);parameters.push_back(data[0]->y);};/*--------------------------------------------------------------------------------------------------* @FuncName:  * @Author:    闹闹* @Brief:    计算由给定点定义的直线的最小二乘估计。该实现具有正交最小二乘误差。* @Version:   1.0.0.1* @Date:     2021/5/17 16:16* @InputParameter: data，该线应使这些点的最小二乘误差最小。parameters,清除此向量，然后填充计算出的参数。* @OutputParameter: * @Returns:   * @Others:    使用计算的线参数[n_x，n_y，a_x，a_y]填充此向量，其中||（n_x，ny）|| = 1。如果向量包含少于两点，则结果参数向量为空（大小= 0）。Compute the line parameters  [n_x,n_y,a_x,a_y]使用最小二乘法，从输入点中拟合出确定直线模型的所需参量--------------------------------------------------------------------------------------------------*/virtual void leastSquaresEstimate(std::vector<Point2D *> &data, std::vector<double> &parameters) {parameters.clear();if (data.size() < 2) return;double meanX, meanY, nx, ny, norm;double covMat11, covMat12, covMat21, covMat22;                                                          // 对称协方差矩阵的项meanX = meanY = 0.0;covMat11 = covMat12 = covMat21 = covMat22 = 0;int i, dataSize = static_cast<int>(data.size());for (i = 0; i < dataSize; i++) {meanX += data[i]->x;meanY += data[i]->y;covMat11 += data[i]->x * data[i]->x;covMat12 += data[i]->x * data[i]->y;covMat22 += data[i]->y * data[i]->y;}meanX /= dataSize;                                                                                     //均值meanY /= dataSize;covMat11 -= dataSize*meanX*meanX;covMat12 -= dataSize*meanX*meanY;covMat22 -= dataSize*meanY*meanY;covMat21 = covMat12;if (covMat11 < 1e-12) {nx = 1.0;ny = 0.0;}else {     // lamda1是协方差矩阵的最大特征值，并用于计算与最小特征值相对应的特征向量，该特征值未明确计算。double lamda1 = (covMat11 + covMat22 + sqrt((covMat11 - covMat22)*(covMat11 - covMat22) + 4 * covMat12*covMat12)) / 2.0;nx = -covMat12;ny = lamda1 - covMat22;norm = sqrt(nx*nx + ny*ny);nx /= norm;ny /= norm;}parameters.push_back(nx);parameters.push_back(ny);parameters.push_back(meanX);parameters.push_back(meanY);};/*--------------------------------------------------------------------------------------------------* @FuncName:  * @Author:    闹闹* @Brief:     如果参数定义的线与给定点之间的距离小于'delta'（请参见构造函数），则返回true。* @Version:   1.0.0.1* @Date:     2021/5/17 16:19* @InputParameter: parameters, 线参数[n_x,n_y,a_x,a_y]。 data，检查该点与直线之间的距离是否小于“ delta”。* @OutputParameter: * @Returns:   * @Others:   Given the line parameters  [n_x,n_y,a_x,a_y] check if [n_x, n_y] dot [data.x-a_x, data.y-a_y] < m_delta通过与已知法线的点乘结果，确定待测点与已知直线的匹配程度；结果越小则越符合，为零则表明点在直线上--------------------------------------------------------------------------------------------------*/virtual bool agree(std::vector<double> &parameters, Point2D &data) {double signedDistance = parameters[0] * (data.x - parameters[2]) + parameters[1] * (data.y - parameters[3]);return ((signedDistance*signedDistance) < m_deltaSquared);};/*--------------------------------------------------------------------------------------------------* @FuncName:  * @Author:    闹闹* @Brief:     测试类方法。* @Version:   1.0.0.1* @Date:      2021/5/17 16:24* @InputParameter: * @OutputParameter: * @Returns:   * @Others:    --------------------------------------------------------------------------------------------------*/static void debugTest(std::ostream &out) {std::vector<double> lineParameters;LineParamEstimator lpEstimator(0.5);std::vector<Point2D *> pointData;pointData.push_back(new Point2D(7, 7));pointData.push_back(new Point2D(-1, -1));lpEstimator.estimate(pointData, lineParameters);out << "[n_x,n_y,a_x,a_y] [ " << lineParameters[0] << ", " << lineParameters[1] << ", ";out << lineParameters[2] << ", " << lineParameters[3] << " ]" << std::endl;lpEstimator.leastSquaresEstimate(pointData, lineParameters);out << "[n_x,n_y,a_x,a_y] [ " << lineParameters[0] << ", " << lineParameters[1] << ", ";out << lineParameters[2] << ", " << lineParameters[3] << " ]" << std::endl;delete pointData[0];delete pointData[1];pointData.clear();pointData.push_back(new Point2D(6, 12));pointData.push_back(new Point2D(6, 6));lpEstimator.estimate(pointData, lineParameters);out << "[n_x,n_y,a_x,a_y] [ " << lineParameters[0] << ", " << lineParameters[1] << ", ";out << lineParameters[2] << ", " << lineParameters[3] << " ]" << std::endl;lpEstimator.leastSquaresEstimate(pointData, lineParameters);out << "[n_x,n_y,a_x,a_y] [ " << lineParameters[0] << ", " << lineParameters[1] << ", ";out << lineParameters[2] << ", " << lineParameters[3] << " ]" << std::endl;delete pointData[0];delete pointData[1];pointData.clear();pointData.push_back(new Point2D(7, 9));pointData.push_back(new Point2D(10, 9));lpEstimator.estimate(pointData, lineParameters);out << "[n_x,n_y,a_x,a_y] [ " << lineParameters[0] << ", " << lineParameters[1] << ", ";out << lineParameters[2] << ", " << lineParameters[3] << " ]" << std::endl;lpEstimator.leastSquaresEstimate(pointData, lineParameters);out << "[n_x,n_y,a_x,a_y] [ " << lineParameters[0] << ", " << lineParameters[1] << ", ";out << lineParameters[2] << ", " << lineParameters[3] << " ]" << std::endl;delete pointData[0];delete pointData[1];pointData.clear();};private:double m_deltaSquared; //给定线L和点P，如果dist（L，P）^ 2 <m_delta ^ 2，则该点在线上
};/*
此类实现了随机样本一致性（Ransac）框架，该框架用于可靠的参数估计。给定包含异常值的数据，我们使用原始数据的子集来估计模型参数。
1.从数据中选择最小子集，以计算精确的模型参数。
2.查看多少输入数据与计算出的参数一致。
3.转到步骤1。最多可以执行（m选择N）次，其中m是精确估计所需的数据对象数，而N是数据对象总数。
4.取得同意参数的最大对象子集，并使用它们计算最小二乘拟合。
类模板参数T 是用于参数估计的T对象（例如Point2D）。 S-参数类型（例如double）。
*/
template<class T, class S>
class Ransac {public:/*--------------------------------------------------------------------------------------------------* @FuncName:  * @Author:    闹闹* @Brief:    使用Ransac框架估算模型参数。* @Version:   1.0.0.1* @Date:     2021/5/17 17:24* @InputParameter:parameters, 一个将包含估计参数的向量。 如果输入中有错误，则此向量将为空。 错误如下：1.数据对象比完全适合的数据对象少。paramEstimator,可以使用精确拟合或最小二乘拟合来估计所需参数的对象。data, 估计参数所依据的输入。numForEstimate,完全适合所需的数据对象数。desiredProbabilityForNoOutliers,至少一个选定子集不包含异常值的概率。maximalOutlierPercentage,离群值的最大预期百分比。* @OutputParameter: * @Returns:   返回最小二乘估计中使用的数据百分比。* @Others:    --------------------------------------------------------------------------------------------------*/static double compute(std::vector<S> &parameters,ParameterEsitmator<T, S> *paramEstimator,std::vector<T> &data,int numForEstimate,double desiredProbabilityForNoOutliers,double maximalOutlierPercentage);/*--------------------------------------------------------------------------------------------------* @FuncName:  * @Author:    闹闹* @Brief:    通过遍历所有可能的子集（暴力法），使用最大共识集估计模型参数。* @Version:   1.0.0.1* @Date:      2021/5/17 17:30* @InputParameter: parameters,一个包含估计参数的向量，如果输入中有错误，则该向量将为空。 错误如下：1.数据对象比完全适合的要少。paramEstimator,可以使用精确拟合或最小二乘法拟合估计所需参数的对象。data,估计参数所依据的输入。numForEstimate,完全适合所需的数据对象数。* @OutputParameter: * @Returns:   返回最小二乘估计中使用的数据百分比。* @Others:   Given: n -  data.size()k - numForEstimateWe go over all n choose k subsets       n!*                                     ------------*                                      (n-k)! * k!仅当n选择k较小（即k或（n-k）大约等于n）时才应使用此方法--------------------------------------------------------------------------------------------------*/static double compute(std::vector<S> &parameters,ParameterEsitmator<T, S> *paramEstimator,std::vector<T> &data,int numForEstimate);private:static void computeAllChoices(ParameterEsitmator<T, S> *paramEstimator, std::vector<T> &data, int numForEstimate,short *bestVotes, short *curVotes, int &numVotesForBest, int startIndex, int n, int k, int arrIndex, int *arr);static void estimate(ParameterEsitmator<T, S> *paramEstimator, std::vector<T> &data, int numForEstimate,short *bestVotes, short *curVotes, int &numVotesForBest, int *arr);class SubSetIndexComparator { //子集序列比较器private:int m_length;public:SubSetIndexComparator(int arrayLength) : m_length(arrayLength) {}bool operator()(const int *arr1, const int *arr2) const {for (int i = 0; i < m_length; i++) {if (arr1[i] < arr2[i]) {return true;}}return false;}};};/*--------------------------------------------------------------------------------------------------
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template<class T, class S>
double Ransac<T, S>::compute(std::vector<S> &parameters,ParameterEsitmator<T, S> *paramEstimator,std::vector<T> &data,int numForEstimate,double desiredProbabilityForNoOutliers,double maximalOutlierPercentage){int numDataObjects = data.size();if (numDataObjects < numForEstimate || maximalOutlierPercentage >= 1.0) return 0;   //数据对象的数量少于完全拟合所需的最小值，还是所有数据都是离群值？std::vector<T *> exactEstimateData;std::vector<T *> leastSquaresEstimateData;std::vector<S> exactEstimateParameters;int i, j, k, l, numVotesForBest, numVotesForCur, maxIndex, numTries;short *bestVotes = new short[numDataObjects];                                      //如果data [i]符合最佳模型，则为1，否则为0short *curVotes  = new short[numDataObjects];                                     //如果data [i]与当前模型一致，则为1，否则为0short *notChosen = new short[numDataObjects];                                        //如果未选择data [i]来计算精确拟合，则不为零；否则为零SubSetIndexComparator subSetIndexComparator(numForEstimate);std::set<int *, SubSetIndexComparator > chosenSubSets(subSetIndexComparator);int *curSubSetIndexes;double outlierPercentage = maximalOutlierPercentage;double numerator = log(1.0 - desiredProbabilityForNoOutliers);double denominator = log(1 - pow(1 - maximalOutlierPercentage, numForEstimate));parameters.clear();numVotesForBest = -1;                                                               //用-1初始化，以便将第一个计算设置为最佳srand((unsigned)time(NULL));                                                       //种子随机数生成器numTries = (int)(numerator / denominator + 0.5);for (i = 0; i < numTries; i++) {memset(notChosen, '1', numDataObjects * sizeof(short));                         //随机选择用于精确模型拟合的数据（“ numForEstimate”对象）。curSubSetIndexes = new int[numForEstimate];exactEstimateData.clear();maxIndex = numDataObjects - 1;for (l = 0; l < numForEstimate; l++) {int selectedIndex = (int)(((float)rand() / (float)RAND_MAX)*maxIndex + 0.5); //selectedIndex在[0，maxIndex]中for (j = -1, k = 0; k < numDataObjects && j < selectedIndex; k++) {if (notChosen[k])j++;}k--;exactEstimateData.push_back(&(data[k]));notChosen[k] = 0;maxIndex--;}for (l = 0, j = 0; j < numDataObjects; j++) {                                    //获取所选对象的索引，以便我们可以检查是否尚未选择此子集if (!notChosen[j]) {curSubSetIndexes[l] = j + 1;l++;}}std::pair< std::set<int *, SubSetIndexComparator >::iterator, bool > res = chosenSubSets.insert(curSubSetIndexes);//检查刚刚选择的子集是否唯一if (res.second == true) {                                                     //第一次我们选择了这个子集               paramEstimator->estimate(exactEstimateData, exactEstimateParameters);       //使用选定的数据进行精确的模型参数拟合numVotesForCur = 0;                                                            //看看有多少人同意这个估计memset(curVotes, '\0', numDataObjects * sizeof(short));for (j = 0; j < numDataObjects; j++) {if (paramEstimator->agree(exactEstimateParameters, data[j])) {curVotes[j] = 1;numVotesForCur++;}}if (numVotesForCur > numVotesForBest) {numVotesForBest = numVotesForCur;memcpy(bestVotes, curVotes, numDataObjects * sizeof(short));}outlierPercentage = 1 - (double)numVotesForCur / (double)numDataObjects;   //更新离群值的估计和我们需要的迭代次数if (outlierPercentage < maximalOutlierPercentage) {maximalOutlierPercentage = outlierPercentage;denominator = log(1 - pow(1 - maximalOutlierPercentage, numForEstimate));numTries = (int)(numerator / denominator + 0.5);}}else {                                                                         //该子集已经出现，不计此迭代delete[] curSubSetIndexes;i--;}}std::set<int *, SubSetIndexComparator >::iterator it = chosenSubSets.begin();      //释放内存std::set<int *, SubSetIndexComparator >::iterator chosenSubSetsEnd = chosenSubSets.end();while (it != chosenSubSetsEnd) {delete[](*it);it++;}chosenSubSets.clear();for (j = 0; j < numDataObjects; j++) {                                             //使用最大子集计算最小二乘估计if (bestVotes[j])leastSquaresEstimateData.push_back(&(data[j]));}paramEstimator->leastSquaresEstimate(leastSquaresEstimateData, parameters);delete[] bestVotes;delete[] curVotes;delete[] notChosen;return (double)numVotesForBest / (double)numDataObjects;
}/*--------------------------------------------------------------------------------------------------
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template<class T, class S>
double Ransac<T, S>::compute(std::vector<S> &parameters,ParameterEsitmator<T, S> *paramEstimator,std::vector<T> &data,int numForEstimate){std::vector<T *> leastSquaresEstimateData;int numDataObjects = data.size();int numVotesForBest = -1;int *arr = new int[numForEstimate];                                                  // numForEstimate表示拟合模型所需要的最少点数，对本例的直线来说，该值为2  short *curVotes = new short[numDataObjects];                                      //如果data [i]与当前模型一致，则为1，否则为0short *bestVotes = new short[numDataObjects];                                        //如果data [i]符合最佳模型，则为1，否则为0                         if (numDataObjects < numForEstimate) return 0;                                     //数据对象的数量少于完全拟合所需的最小值// 计算所有可能的直线，寻找其中误差最小的解。对于100点的直线拟合来说，大约需要100*99*0.5=4950次运算，复杂度无疑是庞大的。一般采用随机选取子集的方式。computeAllChoices(paramEstimator, data, numForEstimate,bestVotes, curVotes, numVotesForBest, 0, data.size(), numForEstimate, 0, arr);for (int j = 0; j < numDataObjects; j++) {                                           //使用最大子集计算最小二乘估计if (bestVotes[j])leastSquaresEstimateData.push_back(&(data[j]));}paramEstimator->leastSquaresEstimate(leastSquaresEstimateData, parameters);          // 对局内点再次用最小二乘法拟合出模型 delete[] arr;delete[] bestVotes;delete[] curVotes;return (double)leastSquaresEstimateData.size() / (double)numDataObjects;
}/*--------------------------------------------------------------------------------------------------
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template<class T, class S>
void Ransac<T, S>::computeAllChoices(ParameterEsitmator<T, S> *paramEstimator, std::vector<T> &data, int numForEstimate,short *bestVotes, short *curVotes, int &numVotesForBest, int startIndex, int n, int k, int arrIndex, int *arr){if (k == 0) {                                                                        //我们有新的索引选择estimate(paramEstimator, data, numForEstimate, bestVotes, curVotes, numVotesForBest, arr);return;}int endIndex = n - k;                                                             //继续递归地生成索引的选择for (int i = startIndex; i <= endIndex; i++) {arr[arrIndex] = i;computeAllChoices(paramEstimator, data, numForEstimate, bestVotes, curVotes, numVotesForBest,i + 1, n, k - 1, arrIndex + 1, arr);}
}/*--------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------*/
template<class T, class S>
void Ransac<T, S>::estimate(ParameterEsitmator<T, S> *paramEstimator, std::vector<T> &data, int numForEstimate,short *bestVotes, short *curVotes, int &numVotesForBest, int *arr){std::vector<T *> exactEstimateData;std::vector<S> exactEstimateParameters;int numDataObjects;int numVotesForCur;                                                                     //以-1初始化，以便将第一个计算设置为最佳int j;numDataObjects = data.size();memset(curVotes, '\0', numDataObjects * sizeof(short));numVotesForCur = 0;for (j = 0; j < numForEstimate; j++)exactEstimateData.push_back(&(data[arr[j]]));paramEstimator->estimate(exactEstimateData, exactEstimateParameters);for (j = 0; j < numDataObjects; j++) {if (paramEstimator->agree(exactEstimateParameters, data[j])) {curVotes[j] = 1;numVotesForCur++;}}if (numVotesForCur > numVotesForBest) {numVotesForBest = numVotesForCur;memcpy(bestVotes, curVotes, numDataObjects * sizeof(short));}
}
#endif  //__MYRANSAC_H__
/*----------------------------------------------------------------------------- (C) COPYRIGHT LEI *****END OF FILE------------------------------------------------------------------------------*/

example.cpp

#include "myRANSAC.hpp"int  main(int argc, char* argv[])
{std::vector<double> lineParameters;LineParamEstimator lpEstimator(0.5); //要使点在直线上，它必须与直线之间的距离小于0.5个单位std::vector<Point2D> pointData;std::vector<Point2D *> pointDataPtr;int numForEstimate = 2;int numSamples = 40;                                    //样本点int numOutliers = 60;                                   //噪点double desiredProbabilityForNoOutliers = 0.999;double maximalOutlierPercentage = 0.1 + (double)numOutliers / (double)(numSamples + numOutliers);double noiseSpreadRadius = 0.4;                              //噪声传播半径double outlierSpreadRadius = 10;                             //离群点传播半径int i;double newX, newY, dx, dy, norm;//1.与异常值一起创建数据//随机选择一个方向[dx，dy]并为在该线上采样的每个点创建一条穿过原点的线，这会添加随机噪声，最后在线法线方向上添加偏外点。srand((unsigned)time(NULL)); //种子随机数生成器//得到随机方向dx = rand();dy = rand();norm = sqrt(dx*dx + dy*dy);dx /= norm;dy /= norm;dx *= (rand() > RAND_MAX / 2 ? 1 : -1);dy *= (rand() > RAND_MAX / 2 ? 1 : -1);//添加'numSamples'点for (i = 0; i < numSamples; i++) {newX = i*dx + noiseSpreadRadius*(double)rand() / (double)RAND_MAX * (rand() > RAND_MAX / 2 ? 1 : -1);newY = i*dy + noiseSpreadRadius*(double)rand() / (double)RAND_MAX * (rand() > RAND_MAX / 2 ? 1 : -1);pointDataPtr.push_back(new Point2D(newX, newY));pointData.push_back(*(pointDataPtr[i]));}//'numOutliers'点double centerX = -dy * 100;double centerY = dx * 100;for (i = 0; i < numOutliers; i++) {newX = centerX + outlierSpreadRadius * (double)rand() / (double)RAND_MAX * (rand() > RAND_MAX / 2 ? 1 : -1);newY = centerY + outlierSpreadRadius * (double)rand() / (double)RAND_MAX * (rand() > RAND_MAX / 2 ? 1 : -1);pointDataPtr.push_back(new Point2D(newX, newY));pointData.push_back(*(pointDataPtr[pointDataPtr.size() - 1]));}double dotProd;//2. Compare least squares approach to Ransacstd::cout << "总的点数(包含噪点): " << pointData.size() << std::endl;std::cout << "噪点数: " << numOutliers << std::endl;//std::cout << "真实的线的参数 [nx,ny,ax,ay]\n\t [ " << -dy << ", " << dx << ", 0, 0 ]" << std::endl;//最小二乘法估计的线参数lpEstimator.leastSquaresEstimate(pointDataPtr, lineParameters);std::cout << "最小二乘法估计的线参数: [n_x,n_y,a_x,a_y]\n\t [ " << lineParameters[0] << ", " << lineParameters[1] << ", ";std::cout << lineParameters[2] << ", " << lineParameters[3] << " ]" << std::endl;dotProd = lineParameters[0] * (-dy) + lineParameters[1] * dx;std::cout << "\t 实线和计算线法线的点积 [+-1=correct]: " << dotProd << std::endl;dotProd = (-dy)*(lineParameters[2]) + dx*lineParameters[3];std::cout << "\t 检查计算点是否在实线上 [0=correct]: " << dotProd << std::endl;//A RANSAC estimate of the line parametersdouble usedData = Ransac<Point2D, double>::compute(lineParameters,&lpEstimator,pointData,numForEstimate);std::cout << "RANSAC 线参数 [n_x,n_y,a_x,a_y]\n\t [ " << lineParameters[0] << ", " << lineParameters[1] << ", ";std::cout << lineParameters[2] << ", " << lineParameters[3] << " ]" << std::endl;dotProd = lineParameters[0] * (-dy) + lineParameters[1] * dx;std::cout << "\t  实线和计算线法线的点积[+-1=correct]: " << dotProd << std::endl;dotProd = (-dy)*(lineParameters[2]) + dx*lineParameters[3];std::cout << "\t检查计算点是否在实线上  [0=correct]: " << dotProd << std::endl;std::cout << "\t 用于最终估算的点数百分比: " << usedData << std::endl;system("pause");return 0;
}

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