1. 长宽比

长宽比是轮廓的宽度与高度的比值。它可以用于识别物体的形状。

$a s p e c t r a d i o = w h aspect radio = \frac{w}{h}$ aspect radio = hw

2. 矩形度

矩形度是轮廓区域面积与其最小外接矩形区域面积的比值。它是衡量轮廓与矩形相似程度的一个参数。

$r e c t a n g u l a r i t y = c o n t o u r A r e a m i n A r e a R e c t A r e a rectangularity = \frac{contourArea}{minAreaRect Area}$ rectangularity = minAreaRect AreacontourArea

3. 范围

范围是轮廓区域面积与其外接矩形区域面积的比值。它可以用于衡量轮廓的大小。

$e x t e n t = c o n t o u r A r e a b o u n d i n g R e c t A r e a extent = \frac{contourArea}{boundingRect Area}$ extent = boundingRect AreacontourArea

下面的例子是之前使用过的，分别画了一个正方形、三角形、五边形和圆。通过轮廓查找找到它们的轮廓后，计算轮廓的长宽比、矩形度、范围。

cpp 复制代码

#include <iostream>
#include <opencv2/opencv.hpp>
#include "opencv2/imgproc.hpp"
#include "opencv2/highgui.hpp"

using namespace std;
using namespace cv;

bool ascendSort(vector<Point> a,vector<Point> b)
{
    return contourArea(a) > contourArea(b);
}

int main(int argc, char **argv) {
    Mat image(1600, 1600, CV_8UC3, Scalar(0, 0, 0));

    // 画一个正方形
    rectangle(image, Point(100, 100), Point(400, 400), Scalar(255, 255, 0), -1);

    // 画一个三角形
    Point trianglePoints[3] = {Point(500, 800), Point(250, 1300), Point(800, 1100)};
    fillConvexPoly(image, trianglePoints, 3, Scalar(255, 255, 0));

    // 画一个五边形
    Point pentagonPoints[5];
    for (int i = 0; i < 5; i++) {
        pentagonPoints[i] = Point(600 + 200 * cos(2 * CV_PI * i / 5), 600 + 200 * sin(2 * CV_PI * i / 5));
    }
    fillConvexPoly(image, pentagonPoints, 5, Scalar(255, 255, 0));

    // 画一个圆形
    circle(image, Point(1200, 1200), 300, Scalar(255, 255, 0), -1);

    Mat gray,thresh;
    cvtColor(image, gray, cv::COLOR_BGR2GRAY);
    threshold(gray,thresh,0,255,THRESH_BINARY | THRESH_OTSU);
    imshow("thresh", thresh);

    vector<vector<Point>> contours;
    vector<Vec4i> hierarchy;
    findContours(thresh, contours, hierarchy, RETR_EXTERNAL, CHAIN_APPROX_SIMPLE);
    sort(contours.begin(), contours.end(), ascendSort);//ascending sort

    for (size_t i = 0; i< contours.size(); i++) {
        double area = contourArea(contours[i]);
        Rect rect = boundingRect(contours[i]);
        RotatedRect rrt = minAreaRect(contours[i]);

        float aspect_radio = (float)rect.width/rect.height;

        double rectangularity = area / (rrt.size.width*rrt.size.height);

        double extent = area / (rect.width*rect.height);

        printf("aspect_radio = %f, rectangularity = %f, extent = %f \n",aspect_radio,rectangularity,extent);
    }

    imshow("result", image);
    waitKey(0);
    return 0;
}

执行结果：

ini 复制代码

aspect_radio = 1.000000, rectangularity = 0.784830, extent = 0.780308 
aspect_radio = 1.099800, rectangularity = 0.500556, extent = 0.407986 
aspect_radio = 0.950262, rectangularity = 0.691453, extent = 0.686282 
aspect_radio = 1.000000, rectangularity = 1.000000, extent = 0.993367

之前，在该系列文章第十六篇中使用 approxPolyDP() 函数 把圆近似成16边形。现在通过计算矩形度 还是很容易区分出圆的，圆的矩形度 : $π R 2 4 R 2 = π 4 ≈ 0.785 \frac{\pi R^2}{4R^2} = \frac{\pi}{4} \approx 0.785$ 4R2πR2 = 4π ≈ 0.785

4. 极点

极点是指轮廓的最顶部，最底部，最右侧和最左侧的点。

下面的代码，读取一张树叶的图，进行二值化，再通过轮廓查找找到最大的轮廓，计算出其极点并在原图中标记出来。

cpp 复制代码

#include <iostream>
#include "opencv2/imgproc.hpp"
#include "opencv2/highgui.hpp"

using namespace std;
using namespace cv;

bool ascendSort(vector<Point> a,vector<Point> b)
{
    return contourArea(a) > contourArea(b);
}

int main(int argc, char **argv) {
    Mat src = imread(".../leaf.png");
    imshow("src", src);

    Mat gray,thresh;
    cvtColor(src, gray, cv::COLOR_BGR2GRAY);

    threshold(gray,thresh,0,255,THRESH_BINARY_INV | THRESH_OTSU);
    imshow("thresh", thresh);

    vector<vector<Point>> contours;
    vector<Vec4i> hierarchy;
    findContours(thresh, contours, hierarchy, RETR_EXTERNAL, CHAIN_APPROX_SIMPLE);
    sort(contours.begin(), contours.end(), ascendSort);//ascending sort
    cout << "contours.size() = " << contours.size() << endl;

    //计算轮廓极值点
    Point left = *min_element(contours[0].begin(), contours[0].end(),
                              [](const Point& lhs, const Point& rhs) {
                                  return lhs.x < rhs.x;
                              });
    Point right = *max_element(contours[0].begin(), contours[0].end(),
                               [](const Point& lhs, const Point& rhs) {
                                   return lhs.x < rhs.x;
                               });
    Point top = *min_element(contours[0].begin(), contours[0].end(),
                             [](const Point& lhs, const Point& rhs) {
                                 return lhs.y < rhs.y;
                             });
    Point bottom = *max_element(contours[0].begin(), contours[0].end(),
                                [](const Point& lhs, const Point& rhs) {
                                    return lhs.y < rhs.y;
                                });

    circle(src,left,2,Scalar(255,0,0),8);
    circle(src,right,2,Scalar(255,0,0),8);
    circle(src,top,2,Scalar(255,0,0),8);
    circle(src,bottom,2,Scalar(255,0,0),8);

    int fontFace = FONT_HERSHEY_PLAIN;
    double fontScale = 2;
    int thickness = 6;

    putText(src,"left",left,fontFace,fontScale,Scalar(255, 0, 0),thickness);
    putText(src,"right",right,fontFace,fontScale,Scalar(255, 0, 0),thickness);
    putText(src,"top",top,fontFace,fontScale,Scalar(255, 0, 0),thickness);
    putText(src,"bottom",bottom,fontFace,fontScale,Scalar(255, 0, 0),thickness);

    imshow("result", src);

    waitKey(0);
    return 0;
}

5. 方向

方向是是轮廓的倾斜角度。方向可以用于识别物体的方向。

下面的代码，通过将轮廓进行椭圆拟合来获取轮廓的方向。

ini 复制代码

#include "opencv2/imgproc.hpp"
#include "opencv2/highgui.hpp"

using namespace std;
using namespace cv;

bool ascendSort(vector<Point> a,vector<Point> b)
{
    return contourArea(a) > contourArea(b);
}

int main(int argc, char **argv) {
    Mat src = imread(".../spoon.jpg");
    imshow("src", src);

    Mat gray,thresh;
    cvtColor(src, gray, cv::COLOR_BGR2GRAY);

    threshold(gray,thresh,0,255,THRESH_BINARY_INV | THRESH_OTSU);
    imshow("thresh", thresh);

    vector<vector<Point>> contours;
    vector<Vec4i> hierarchy;
    findContours(thresh, contours, hierarchy, RETR_EXTERNAL, CHAIN_APPROX_SIMPLE);
    sort(contours.begin(), contours.end(), ascendSort);//ascending sort

    for (size_t i = 0; i< contours.size(); i++) {
        double area = contourArea(contours[i]);

        if (area < 1000) {
            continue;
        }

        RotatedRect rrt = fitEllipse(contours[i]);
        Point2f center = rrt.center;
        float angle = rrt.angle;
        ellipse(src,rrt, Scalar(0, 0, 255), 8, 8);

        std::string text = "angle:" + to_string(angle);
        int fontFace = FONT_HERSHEY_PLAIN;
        double fontScale = 5;
        int thickness = 8;
        putText(src,text,center,fontFace,fontScale,Scalar(255, 0, 0),thickness);
    }
    imshow("result", src);

    waitKey(0);
    return 0;
}

6. 等效直径

等效直径是面积与轮廓面积相同的圆的直径。它可以用于衡量轮廓的大小和形状。

$e q u i v a l e n t d i a m e t e r = 4 ∗ c o n t o u r A r e a π equivalent diameter = \sqrt{\frac{4*contourArea}{\pi}}$ equivalent diameter = π4∗contourArea

7. 坚实度

坚实度是轮廓区域面积与其凸包区域面积的比值。它可以用于衡量轮廓的密实程度。

$s o l i d i t y = c o n t o u r A r e a c o n v e x H u l l A r e a solidity = \frac{contourArea}{convexHull Area}$ solidity = convexHull AreacontourArea

8. 总结

本文介绍了很多轮廓的属性，这些属性可以根据特定的应用需求进行选择。例如，在物体识别中，可以使用轮廓的长宽比、矩形度、范围和坚实度来识别物体的形状和大小。在形状分析中，可以使用轮廓的等效直径和方向来分析形状的几何特性。

OpenCV 笔记(18)：轮廓的更多属性