c++拉格朗日图像程序

以下是一个基于 OpenCV 的 C++ 拉格朗日插值图像程序的示例：

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

using namespace std;
using namespace cv;

int main(int argc, char** argv)
{
    if (argc != 2)
    {
        cout << "Usage: ./lagrange_interp <image_path>" << endl;
        return -1;
    }

    // 读取原始图像
    Mat img = imread(argv[1], IMREAD_GRAYSCALE);
    if (img.empty())
    {
        cout << "Error: failed to read image file" << endl;
        return -1;
    }

    // 定义插值后图像的大小
    int new_width = img.cols * 4;
    int new_height = img.rows * 4;

    // 创建插值后图像
    Mat interp_img(new_height, new_width, CV_8UC1);

    // 拉格朗日插值
    for (int i = 0; i < new_height; i++)
    {
        float y = (float)i / (float)new_height * (float)img.rows;
        for (int j = 0; j < new_width; j++)
        {
            float x = (float)j / (float)new_width * (float)img.cols;
            uchar val = 0;
            for (int m = -2; m < 3; m++)
            {
                float w = 1.0;
                for (int n = -2; n < 3; n++)
                {
                    if (m == 0 && n == 0)
                        continue;
                    float xk = x + n;
                    float yk = y + m;
                    w *= (x - xk) / ((float)n * (float)n - (float)m * (float)m);
                }
                int x_idx = (int)(x + 0.5) + m;
                int y_idx = (int)(y + 0.5) + m;
                if (x_idx >= 0 && x_idx < img.cols && y_idx >= 0 && y_idx < img.rows)
                {
                    val += w * img.at<uchar>(y_idx, x_idx);
                }
            }
            interp_img.at<uchar>(i, j) = val;
        }
    }

    // 显示原始图像和插值后图像
    namedWindow("Original", WINDOW_NORMAL);
    namedWindow("Interpolated", WINDOW_NORMAL);
    imshow("Original", img);
    imshow("Interpolated", interp_img);
    waitKey(0);

    return 0;
}

该程序读取一张灰度图像作为输入，并输出一张拉格朗日插值后的图像，插值方法是基于 5x5 的窗口进行的。你可以根据需要调整窗口大小和插值方法。