矩阵逆的最快方法

Question

我想处理具有反函数和许多函数的图像。为了使代码快速运行，可以在 3 种反转方法中建议快速方法吗？

double cvInvert(const CvArr* src, CvArr* dst, int method=CV_LU)

• CV_LU 选择最优枢轴元件的高斯消除
• CV_SVD 奇异值分解（SVD）方法
• 对称正定义矩阵的CV_SVD_SYM SVD 方法。

Answer 1

在OpenCV2.x中，有一个名为Mat::inv(int method)的新接口来计算矩阵的逆。请参阅参考资料。

C++： MatExpr Mat：：inv（int method=DECOMP_LU） const

参数： 方法–

   Matrix inversion method. Possible values are the following:
        DECOMP_LU is the LU decomposition. The matrix must be non-singular.
        DECOMP_CHOLESKY is the Cholesky LL^T decomposition for symmetrical positively defined matrices only. This type is about twice faster than LU on big matrices.
        DECOMP_SVD is the SVD decomposition. If the matrix is singular or even non-square, the pseudo inversion is computed.

我用每种方法进行了测试，它表明DECOMP_CHOLESKY是测试用例中最快的，LU 给出了类似的结果。

#include <opencv2/core/core.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <iostream>
int main(void)
{
    cv::Mat img1 = cv::imread("2.png");
    cv::Mat img2, img3, img;
    cv::cvtColor(img1, img2, CV_BGR2GRAY);
    img2.convertTo(img3, CV_32FC1);
    cv::resize(img3, img, cv::Size(200,200));
    double freq = cv::getTickFrequency();
    double t1 = 0.0, t2 = 0.0;
    t1 = (double)cv::getTickCount();
    cv::Mat m4 = img.inv(cv::DECOMP_LU);
    t2 = (cv::getTickCount()-t1)/freq;
    std::cout << "LU:" << t2 << std::endl;
    t1 = (double)cv::getTickCount();
    cv::Mat m5 = img.inv(cv::DECOMP_SVD);
    t2 = (cv::getTickCount()-t1)/freq;
    std::cout << "DECOMP_SVD:" << t2 << std::endl;
    t1 = (double)cv::getTickCount();
    cv::Mat m6 = img.inv(cv::DECOMP_CHOLESKY);
    t2 = (cv::getTickCount()-t1)/freq;
    std::cout << "DECOMP_CHOLESKY:" << t2 << std::endl;
    cv::waitKey(0);
}

以下是正在运行的回复：

卢：0.000423759

DECOMP_SVD：0.0583525

DECOMP_CHOLESKY：9.3453e-05