理论与现实总是不一致的，实际情况下几乎所有角点都不是一个准确的像素点，因为图像的边缘不是之间有黑到白，而往往存在一个灰度的过度。（100，5）实际上

（100.234，5.789),而我们在跟踪、三维重建，相机校正等应用上又都需要精确的像素位置。有以下几种解决方法

1.插值法

通过周围四个点的变化情况，寻找拟合出哪一个焦点的精确位置，根据周围四个点的resp而不是真正的像素值

2.基于图像矩计算

3.曲线拟合的方式

高斯曲面（x,y,r），多项式，椭圆曲面

通过周围点的像素拟合出曲面，找到曲面的顶点，就是亚像素定位

Demo

#include"pch.h"
#include<iostream>
#include<opencv2/opencv.hpp>
#include<math.h>
using namespace std;
using namespace cv;


const char* output_title = "Sub-pixel CornerDetection Reslut";
double harris_mins_rsp;
double harris_max_rsp;
int qualityLevel = 30;
int max_corners = 30;
int max_count = 50;
Mat src, gray_src;
Mat harris_dst, harriRspImg;
//Shi-Tomasi
Mat ShiTomasiRspImg;
double ShiTomasi_max_rsp;
double ShiTomasi_min_rsp;
int SM_QualityLevel = 30;

void SubPixel_Demo(int,void*);

int main(int argc, char** argv)
{
    src = imread("1.jpg");
    imshow("input img", src);
    int blocksize = 3;
    int ksize = 3;
    double k = 0.04;
    harriRspImg = Mat::zeros(src.size(), CV_32FC1);
    harris_dst = Mat::zeros(src.size(), CV_32FC(6));
    namedWindow(output_title, CV_WINDOW_AUTOSIZE);
    cvtColor(src, gray_src, COLOR_BGR2GRAY);
    createTrackbar("Min Value:", output_title, &max_corners, max_count, SubPixel_Demo);
    SubPixel_Demo(0, 0);

    waitKey();
    return 0;
}

void SubPixel_Demo(int, void*)
{
    if (max_corners <5)
        qualityLevel = 5;

    vector<Point2f> corners;
    double qualityLevel = 0.05;
    double minDistance = 10;
    int blockSize = 3;
    double K = 0.04;
    goodFeaturesToTrack(gray_src, corners, max_corners, qualityLevel, minDistance, Mat(), blockSize, false, K);
    cout << "number of corners: " << corners.size() << endl;
    Mat resultImg = src.clone();
    for (size_t i = 0; i < corners.size(); ++i)
    {
        circle(resultImg, corners[i], 2, Scalar(0, 0, 255), 2, 8, 0);
    }
    imshow(output_title, resultImg);
    Size winSize = Size(5, 5);
    Size zerozone = Size(-1, -1);
    TermCriteria tc = TermCriteria(TermCriteria::EPS + TermCriteria::MAX_ITER, 40, 0.001);
    cornerSubPix(gray_src, corners, winSize, zerozone, tc);
    for (size_t i=0; i < corners.size(); ++i)
    {
        cout << (i + 1) << ".Point[x,y]=" << corners[i].x <<" ," << corners[i].y << endl;
    }
    return;
}