帮我写出用c++对一张图片进行主成分分析得到方向和均值点，并在图中画出方向的代码

以下是用 C 语言对一张图片进行主成分分析得到方向和均值点，并在图中画出方向的代码：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define WIDTH 256
#define HEIGHT 256

typedef struct {
    double x;
    double y;
} Point;

int main() {
    FILE *fp;
    unsigned char img[WIDTH][HEIGHT];
    Point points[WIDTH * HEIGHT];
    int num_points = ;
    double sum_x = ., sum_y = .;
    double cov_xx = ., cov_xy = ., cov_yy = .;
    double eigenvalue1, eigenvalue2;
    Point eigenvector1, eigenvector2;
    Point mean_point;
    int i, j;

    // 读取图片
    fp = fopen("image.bmp", "rb");
    fseek(fp, 54, SEEK_SET);
    fread(img, sizeof(unsigned char), WIDTH * HEIGHT, fp);
    fclose(fp);

    // 提取点集
    for (i = ; i < WIDTH; i++) {
        for (j = ; j < HEIGHT; j++) {
            if (img[i][j] > 128) {
                points[num_points].x = i;
                points[num_points].y = j;
                num_points++;
                sum_x += i;
                sum_y += j;
            }
        }
    }

    // 计算均值点
    mean_point.x = sum_x / num_points;
    mean_point.y = sum_y / num_points;

    // 计算协方差矩阵
    for (i = ; i < num_points; i++) {
        cov_xx += (points[i].x - mean_point.x) * (points[i].x - mean_point.x);
        cov_xy += (points[i].x - mean_point.x) * (points[i].y - mean_point.y);
        cov_yy += (points[i].y - mean_point.y) * (points[i].y - mean_point.y);
    }

    // 计算特征值和特征向量
    eigenvalue1 = (cov_xx + cov_yy + sqrt((cov_xx - cov_yy) * (cov_xx - cov_yy) + 4 * cov_xy * cov_xy)) / 2;
    eigenvalue2 = (cov_xx + cov_yy - sqrt((cov_xx - cov_yy) * (cov_xx - cov_yy) + 4 * cov_xy * cov_xy)) / 2;
    eigenvector1.x = eigenvalue1 - cov_yy;
    eigenvector1.y = cov_xy;
    eigenvector2.x = eigenvalue2 - cov_yy;
    eigenvector2.y = cov_xy;

    // 画出方向
    fp = fopen("image_direction.bmp", "wb");
    fseek(fp, , SEEK_SET);
    fwrite(img, sizeof(unsigned char), 54, fp);
    for (i = ; i < WIDTH; i++) {
        for (j = ; j < HEIGHT; j++) {
            if (img[i][j] > 128) {
                double dx1 = i - mean_point.x + eigenvector1.x;
                double dy1 = j - mean_point.y + eigenvector1.y;
                double dx2 = i - mean_point.x + eigenvector2.x;
                double dy2 = j - mean_point.y + eigenvector2.y;
                if (dx1 * dx1 + dy1 * dy1 > dx2 * dx2 + dy2 * dy2) {
                    img[i][j] = ;
                } else {
                    img[i][j] = 255;
                }
            }
        }
    }
    fwrite(img, sizeof(unsigned char), WIDTH * HEIGHT, fp);
    fclose(fp);

    return ;
}