OpenCV 支持向量（SupportVectors）介绍

简述

opencv中的SVM中，支持向量是非常重要的一部分，最近在用CVSVM时，运行官方实例，LINEAR核（线性），得到的支持向量总觉得很奇怪，代码如下：

#include <opencv2/core.hpp>
#include <opencv2/imgproc.hpp>
#include "opencv2/imgcodecs.hpp"
#include <opencv2/highgui.hpp>
#include <opencv2/ml.hpp>

using namespace cv;
using namespace cv::ml;

int main(int, char**)
{
    // Data for visual representation
    int width = 512, height = 512;
    Mat image = Mat::zeros(height, width, CV_8UC3);

    // Set up training data
    //! [setup1]
    int labels[4] = {1, -1, -1, -1};
    float trainingData[4][2] = { {501, 10}, {255, 10}, {501, 255}, {10, 501} };
    //! [setup1]
    //! [setup2]
    Mat trainingDataMat(4, 2, CV_32FC1, trainingData);
    Mat labelsMat(4, 1, CV_32SC1, labels);
    //! [setup2]


    // Train the SVM
    //! [init]
    Ptr<SVM> svm = SVM::create();
    svm->setType(SVM::C_SVC);
    svm->setKernel(SVM::LINEAR);
    svm->setDegree(1.0);
    svm->setTermCriteria(TermCriteria(TermCriteria::MAX_ITER, 100, 1e-6));
    //! [init]
    //! [train]
    svm->train(trainingDataMat, ROW_SAMPLE, labelsMat);
    //! [train]

    // Show the decision regions given by the SVM
    //! [show]
    Vec3b green(0,255,0), blue (255,0,0);
    for (int i = 0; i < image.rows; ++i)
        for (int j = 0; j < image.cols; ++j)
        {
            Mat sampleMat = (Mat_<float>(1,2) << j,i);
            float response = svm->predict(sampleMat);

            if (response == 1)
                image.at<Vec3b>(i,j)  = green;
            else if (response == -1)
                image.at<Vec3b>(i,j)  = blue;
        }
    //! [show]

    // Show the training data
    //! [show_data]
    int thickness = -1;
    int lineType = 8;
    circle( image, Point(501,  10), 5, Scalar(  0,   0,   0), thickness, lineType );
    circle( image, Point(255,  10), 5, Scalar(255, 255, 255), thickness, lineType );
    circle( image, Point(501, 255), 5, Scalar(255, 255, 255), thickness, lineType );
    circle( image, Point( 10, 501), 5, Scalar(255, 255, 255), thickness, lineType );
    //! [show_data]

    // Show support vectors
    //! [show_vectors]
    thickness = 2;
    lineType  = 8;
    Mat sv = svm->getSupportVectors();

    for (int i = 0; i < sv.rows; ++i)
    {
        const float* v = sv.ptr<float>(i);
        circle( image,  Point( (int) v[0], (int) v[1]),   6,  CV_RGB(255, 0, 0), thickness, lineType);
    }
    //! [show_vectors]

    imwrite("result.png", image);        // save the image

    imshow("SVM Simple Example", image); // show it to the user
    waitKey(0);
}

运行结果如下，红色矩形圈出部分为绘制的支持向量位置：

OpenCV 支持向量（SupportVectors）介绍

输出的支持向量为
[-0.008130081, 0.008163265]

刚开始表示不理解，后面查了官方文档：

Hi, guys! This is not a bug, in case of linear kernel we can compress all support vectors into one. Here is the details: https://github.com/Itseez/opencv/blob/2.4/modules/ml/src/svm.cpp#L1531

其实就是将所有支持向量压缩成一个，据说这样做可以极大地优化线性核时的运行效率。

如果不习惯，而且一定要用线性核的话，可以使用多项式核POLY，然后degree设置为1.0即可：

svm->setKernel(SVM::POLY);
svm->setDegree(1.0);

运行结果：

OpenCV 支持向量（SupportVectors）介绍