RANSAC算法详解

parameters.clear(); if(data.size()<2) return; meanX = meanY = 0.0; covMat11 = covMat12 = covMat21 = covMat22 = 0; for(i=0; ix; 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; 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 is the largest eigen-value of the covariance matrix //and is used to compute the eigne-vector corresponding to the smallest //eigenvalue, which isn't computed explicitly. 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); } /*****************************************************************************/ /* * 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 */ bool LineParamEstimator::agree(std::vector ¶meters, Point2D &data) { double signedDistance = parameters[0]*(data.x-parameters[2]) + parameters[1]*(data.y-parameters[3]); return ((signedDistance*signedDistance) < m_deltaSquared); }

RANSAC寻找匹配的代码如下： C代码 /*****************************************************************************/ template double Ransac::compute(std::vector ¶meters, ParameterEsitmator *paramEstimator, std::vector &data, int numForEstimate) { std::vector 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]; //one if data[i] agrees with the current model, otherwise zero short *bestVotes = new short[numDataObjects]; //one if data[i] agrees with the best model, otherwise zero //there are less data objects than the minimum required for an exact fit if(numDataObjects < numForEstimate) return 0; // 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); //compute the least squares estimate using the largest sub set for(int j=0; jleastSquaresEstimate(leastSquaresEstimateData,parameters); delete [] arr; delete [] bestVotes; delete [] curVotes; return (double)leastSquaresEstimateData.size()/(double)numDataObjects; }

在模型确定以及最大迭代次数允许的情况下，RANSAC总是能找到最优解。经过我的实验，对于包含80%误差的数据集，RANSAC的效果远优于直接的最小二乘法。

RANSAC可以用于哪些场景呢？最著名的莫过于图片的拼接技术。优于镜头的限制，往往需要多张照片才能拍下那种巨幅的风景。在多幅图像合成时，事先会在待合成的图片中提取一些关键的特征点。计算机视觉的研究表明，不同视角下物体往往可以通过一个透视矩（3X3或2X2）阵的变换而得到。 RANSAC被用于拟合这个模型的参数（矩阵各行列的值），由此便可识别出不同照片中的同一物体。可参考下图：