OpenCV + CPP 系列（卌九） 聚类与图像分割（GMM- 混合高斯模型）

文章目录

GMM 简介

关于高斯混合模型理论：​​https://zhuanlan.zhihu.com/p/30483076​​​ 关于高斯混合模型理论：高斯混合模型 (GMM) 为关于数据的高斯分布与观测数据在总体分布中密度概率 的数据分析模型。

• 当样本数据$X$ 是一维数据（Univariate）时，高斯分布遵从下方概率密度函数（Probability Density Function）：
  $P(x|\theta) = \frac{1}{\sqrt{2\pi \sigma^2}}\exp(-\frac{(x-\mu)^2}{2\sigma^2})$
  其中 $\mu$ 为数据均值（期望）， $\sigma$
• 当样本数据 X 是多维数据（Multivariate）时，高斯分布遵从下方概率密度函数：
  $P(x|\theta) = \frac{1}{(2\pi)^{\frac{D}{2}}|\Sigma|^{\frac{1}{2}}}\exp \left(-\frac{(x-\mu)^T \Sigma^{-1}(x-\mu)}{2} \right)$
  其中，$\mu$ 为数据均值（期望），$\Sigma$ 为协方差（Covariance），$D$

GMM特点

1. 跟K-Means相比较，属于软分类
2. 实现方法-期望最大化(E-M)
3. 停止条件-收敛

头文件 ​​machine_learning_all.h​​：

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

using namespace cv;
using namespace std;


class Machine_learning{
public:
  void GMM_data_demo();
  void GMM_image_demo(Mat& image);
};

主函数​​main.cpp​​

#include "machine_learning_all.h"


int main(int argc, char** argv) {
  const char* input_path = "D:\\Desktop\\meinv3.png";
  Mat src = imread(input_path);
  if (src.empty()) {
    cout << "Read image failed!" << endl;
    return -1;
  }

  Machine_learning ml;
  ml.GMM_data_demo();
  ml.GMM_image_demo(src);

  imshow("src", src);
  waitKey(0);
  destroyAllWindows();
  return 0;
}

GMM 聚类数据演示

void Machine_learning::GMM_data_demo() {
  Mat img = Mat::zeros(450, 450, CV_8UC3);
  RNG rng(1233);

  Scalar colorTab[] = {
    Scalar(0,0,255),
    Scalar(0,255,0),
    Scalar(255,0,0),
    Scalar(0,255,255),
    Scalar(255,0,255),
    Scalar(255,255,0)
  };

  int numCluster = rng.uniform(2, 5);
  cout << "Number of cluster: " << numCluster << endl;

  int sampleCount = rng.uniform(500, 1000);
  Mat points(sampleCount, 2, CV_32FC1); //生成数据 (height,width)=(sampleCount,2)
  Mat labels;
  Mat centers;
  cout << "points.size():" << points.size() << endl;

  //生成随机数
  for (int k = 0; k < numCluster; k++) {
    Point center;
    center.x = rng.uniform(0, img.cols);
    center.y = rng.uniform(0, img.rows);
    Mat PointChunk = points.rowRange(
      k * sampleCount / numCluster,
      k == numCluster - 1 ? sampleCount : (k + 1) * sampleCount / numCluster
    );
    rng.fill(PointChunk, RNG::NORMAL, Scalar(center.x, center.y), Scalar(img.cols * 0.05, img.rows * 0.05));
  }
  randShuffle(points, 1, &rng);

  // 初始化模型参数
  Ptr<ml::EM> em_model = ml::EM::create();
  em_model->setClustersNumber(numCluster);
  em_model->setCovarianceMatrixType(ml::EM::COV_MAT_SPHERICAL);
  em_model->setTermCriteria(TermCriteria(TermCriteria::EPS + TermCriteria::COUNT, 100, 0.1));
  em_model->trainEM(points, noArray(), labels, noArray());

  // 分类图像像素
  Mat sample = Mat::zeros(1, 2, CV_32FC1);
  for (int row = 0; row < img.rows; row++) {
    for (int col = 0; col < img.cols; col++) {
      sample.at<float>(0) = (float)col;
      sample.at<float>(1) = (float)row;
      int response = cvRound(em_model->predict2(sample, noArray())[1]);
      Scalar c = colorTab[response];
      circle(img, Point(col, row), 1, c * 0.75, -1);
    }
  }

  // draw the clusters(point)
  for (int i = 0; i < sampleCount; i++) {
    Point p(cvRound(points.at<float>(i, 0)), points.at<float>(i, 1));
    circle(img, p, 1, colorTab[labels.at<int>(i)], -1);
  }
  imshow("GMM-EM Demo", img);
}

GMM 图像分割示例

void Machine_learning::GMM_image_demo(Mat& src) {
  RNG rng(1212);
  //int numCluster = rng.uniform(2, 5);
  int numCluster = 5;
  Scalar colorTab[] = {
    Scalar(0,0,255),
    Scalar(0,255,0),
    Scalar(255,0,0),
    Scalar(0,255,255),
    Scalar(255,0,255),
    Scalar(255,255,0)
  };

  int width = src.cols;
  int height = src.rows;
  int dims = src.channels();
  int nsamples = width * height;
  Mat points(nsamples, dims, CV_64FC1);
  Mat labels;
  Mat result = Mat::zeros(src.size(), CV_8UC3);

  // 图像RGB像素数据转换为样本数据 
  int index = 0;
  for (int row = 0; row < height; row++) {
    Vec3b* bgr_ptr = src.ptr<Vec3b>(row);
    for (int col = 0; col < width; col++) {
      index = row * width + col;
      points.at<double>(index, 0) = static_cast<int>(bgr_ptr[col][0]);
      points.at<double>(index, 1) = static_cast<int>(bgr_ptr[col][1]);
      points.at<double>(index, 2) = static_cast<int>(bgr_ptr[col][2]);
    }
  }

  // EM Cluster Train
  Ptr<ml::EM> em_model = ml::EM::create();
  em_model->setClustersNumber(numCluster);
  em_model->setCovarianceMatrixType(ml::EM::COV_MAT_SPHERICAL);
  em_model->setTermCriteria(TermCriteria(TermCriteria::EPS + TermCriteria::COUNT, 100, 0.1));
  em_model->trainEM(points, noArray(), labels, noArray());

  // 对每个像素标记颜色与显示
  Mat sample = Mat::zeros(dims, 1, CV_64FC1);
  double time = getTickCount();
  int r = 0, g = 0, b = 0;
  for (int row = 0; row < height; row++) {
    Vec3b* src_ptr = src.ptr<Vec3b>(row);
    uchar* result_ptr = result.ptr<uchar>(row);
    for (int col = 0; col < width; col++) {
      index = row * width + col;
      sample.at<double>(0) = src_ptr[col][0];
      sample.at<double>(1) = src_ptr[col][1];
      sample.at<double>(2) = src_ptr[col][2];
      int response = cvRound(em_model->predict2(sample, noArray())[1]);
      Scalar c = colorTab[response];
      *result_ptr++ = c[0];
      *result_ptr++ = c[1];
      *result_ptr++ = c[2];
    }
  }
  printf("execution time(ms) : %.2f\n", (getTickCount() - time) / getTickFrequency() * 1000);
  imshow("EM-Segmentation", result);
  imwrite("D:\\Desktop\\EM-Segmentation.png", result);
}

聚类分割的细腻度（左侧图kmeans,中间图GMM,右侧原图）

GMM更能够反应颜色数据的真实分布状态