js实现高斯-约旦消元法求解Homography矩阵

最小二乘法来求解矩阵

// 计算Homography矩阵
function calculateHomography(srcPoints, dstPoints) {
    if (srcPoints.length !== dstPoints.length || srcPoints.length < 4) {
        throw new Error('需要至少四个点进行计算');
    }

    // 设置矩阵方程 Ax = b
    let A = [];
    let b = [];

    // 构建方程的A矩阵和b向量
    for (let i = 0; i < srcPoints.length; i++) {
        let x1 = srcPoints[i][0];
        let y1 = srcPoints[i][1];
        let x2 = dstPoints[i][0];
        let y2 = dstPoints[i][1];

        // 方程：x2 = H11 * x1 + H12 * y1 + H13
        // 方程：y2 = H21 * x1 + H22 * y1 + H23
        A.push([-x1, -y1, -1, 0, 0, 0, x1 * x2, y1 * x2]);
        A.push([0, 0, 0, -x1, -y1, -1, x1 * y2, y1 * y2]);

        b.push(x2);
        b.push(y2);
    }

    // 使用高斯-约旦消元法求解A * h = b
    let H = gaussJordan(A, b);

    // 构造Homography矩阵
    let homographyMatrix = [
        [H[0], H[1], H