对OpenCV中3种乘法操作的理解掌握
参考了《Opencv中Mat矩阵相乘——点乘、dot、mul运算详解 》“http://blog.csdn.net/dcrmg/article/details/52404580”的相关内容。
乘法是线性代数的基本操作，在OpenCV中有三种方法实现了乘法。
一、向量乘法
这两幅图像说明的就是向量乘法。在OpenCV中采用" . "来实现，要求是第一个矩阵的列值等于第二个矩阵的行值。且每个矩阵都是float结构。
Mat A = Mat( 3, 3,CV_32FC1,Scalar( 0));
Vec3f v ( 1, 2, 3);
Mat B = Mat(v);
A.at < float >( 0, 0) = 1;
A.at < float >( 0, 1) = 2;
A.at < float >( 0, 2) = 3;
A.at < float >( 1, 0) = 4;
A.at < float >( 1, 1) = 5;
A.at < float >( 1, 2) = 6;
A.at < float >( 1, 0) = 4;
A.at < float >( 1, 1) = 5;
A.at < float >( 1, 2) = 6;
Mat AB = A *B;
二、数量乘法
对于输入的矩阵
和
数量乘法的结果为
那么可以看出来，这里要求a和b的向量结构是一样的，在OpenCV中，如果a和b是多维向量的话，那么首先是将其拉长为一维向量，然后做乘法。
Mat A
=Mat
:
:ones(
2,
3,CV_8UC1);
Mat B =Mat : :ones( 2, 3,CV_8UC1);
A.at <uchar >( 0, 0) = 1;
A.at <uchar >( 0, 1) = 2;
A.at <uchar >( 0, 2) = 3;
A.at <uchar >( 1, 0) = 4;
A.at <uchar >( 1, 1) = 5;
A.at <uchar >( 1, 2) = 6;
B.at <uchar >( 0, 0) = 1;
B.at <uchar >( 0, 1) = 2;
B.at <uchar >( 0, 2) = 3;
B.at <uchar >( 1, 0) = 4;
B.at <uchar >( 1, 1) = 5;
B.at <uchar >( 1, 2) = 6;
double AB =A.dot(B);
Mat B =Mat : :ones( 2, 3,CV_8UC1);
A.at <uchar >( 0, 0) = 1;
A.at <uchar >( 0, 1) = 2;
A.at <uchar >( 0, 2) = 3;
A.at <uchar >( 1, 0) = 4;
A.at <uchar >( 1, 1) = 5;
A.at <uchar >( 1, 2) = 6;
B.at <uchar >( 0, 0) = 1;
B.at <uchar >( 0, 1) = 2;
B.at <uchar >( 0, 2) = 3;
B.at <uchar >( 1, 0) = 4;
B.at <uchar >( 1, 1) = 5;
B.at <uchar >( 1, 2) = 6;
double AB =A.dot(B);
三、乘法
最后介绍.mul这种乘法。这种乘法就是直接理解意义上的乘法。对于
乘法的结果为
参考代码
Mat A
= Mat(
3,
3,CV_32FC1,Scalar(
0));
Mat B = Mat(v);
A.at < float >( 0, 0) = 1;
A.at < float >( 0, 1) = 2;
A.at < float >( 0, 2) = 3;
A.at < float >( 1, 0) = 4;
A.at < float >( 1, 1) = 5;
A.at < float >( 1, 2) = 6;
A.at < float >( 1, 0) = 4;
A.at < float >( 1, 1) = 5;
A.at < float >( 1, 2) = 6;
Mat AB = A *B;
//
Mat C = Mat( 3, 3,CV_32FC1,Scalar( 0));
C = A.clone();
Mat AC = A.mul(C);
Mat B = Mat(v);
A.at < float >( 0, 0) = 1;
A.at < float >( 0, 1) = 2;
A.at < float >( 0, 2) = 3;
A.at < float >( 1, 0) = 4;
A.at < float >( 1, 1) = 5;
A.at < float >( 1, 2) = 6;
A.at < float >( 1, 0) = 4;
A.at < float >( 1, 1) = 5;
A.at < float >( 1, 2) = 6;
Mat AB = A *B;
//
Mat C = Mat( 3, 3,CV_32FC1,Scalar( 0));
C = A.clone();
Mat AC = A.mul(C);
四、小结
1、以上三种函数，都是以Mat作为输入参数和输出结果的；
2、. 这种乘法要求两个矩阵都是float结果，后两者只要求两个矩阵的结果是一样的；
3、可以看到，.这种乘法要求第一个矩阵的行值等于第二个矩阵的列值，而后两种乘法则要求参加运算的两个矩阵结构完全一样。
