CV_EXPORTS_W void approxPolyDP( InputArray curve,
OutputArray approxCurve,
double epsilon, bool closed );

@param curve Input vector of a 2D point stored in std::vector or Mat
@param approxCurve Result of the approximation. The type should match the type of the input curve.
@param epsilon Parameter specifying the approximation accuracy. This is the maximum distance
between the original curve and its approximation.
@param closed If true, the approximated curve is closed (its first and last vertices are
connected). Otherwise, it is not closed.

The function cv::approxPolyDP approximates a curve or a polygon with another curve/polygon with less
vertices so that the distance between them is less or equal to the specified precision. It uses the
Douglas-Peucker algorithm <http://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm>

主要功能是把一个连续光滑曲线折线化：

参数有4个：

InputArray curve：输入曲线，数据类型可以为vector<Point>。

OutputArray approxCurve：输出折线，数据类型可以为vector<Point>。

double epsilon：判断点到相对应的line segment 的距离的阈值。（距离大于此阈值则舍弃，小于此阈值则保留，epsilon越小，折线的形状越“接近”曲线。）

bool closed：曲线是否闭合的标志位。

程序示例：

#include<opencv2/opencv.hpp>
#include<iostream>

using namespace std;
using namespace cv;

void main()
{
	Mat srcImg = imread("01.jpg");
	imshow("src", srcImg);
	Mat dstImg(srcImg.size(), CV_8UC3, Scalar::all(0));//纯黑图像

	cvtColor(srcImg, srcImg, CV_BGR2GRAY);
	threshold(srcImg, srcImg, 200, 255, CV_THRESH_BINARY_INV);
	vector<vector<Point>> contours;
	vector<Vec4i> hierarcy;
	findContours(srcImg, contours, hierarcy, 0, CV_CHAIN_APPROX_NONE);

	vector<vector<Point>> contours_poly(contours.size());//用于存放折线点集

	for (int i = 0; i<contours.size(); i++)
	{
		approxPolyDP(Mat(contours[i]), contours_poly[i], 15, true);
		drawContours(dstImg, contours_poly, i, Scalar(0, 255, 255), 2, 8);  //绘制
	}
	imshow("approx", dstImg);

	waitKey(0);
}

　　图像“01.jpg”：

epsilon为15：

 epsilon为5：

OpenCV中approxPolyDP()函数