CvMat用法詳解
https://blog.csdn.net/zx3517288/article/details/51760541
CvMat是OpenCV比較基礎的函式。初學者應該掌握並熟練應用。但是我認為計算機專業學習的方法是，不斷的總結並且提煉，同時還要做大量的實踐，如編碼，才能記憶深刻，體會深刻，從而引導自己想更高層次邁進。
綜述: OpenCV有針對矩陣操作的C語言函式. 許多其他方法提供了更加方便的C++介面，其效率與OpenCV一樣.
OpenCV將向量作為1維矩陣處理.
矩陣按行儲存，每行有4位元組的校整.
分配矩陣空間: CvMat* cvCreateMat(int rows, int cols, int type);
type: 矩陣元素型別. 格式為CV_(S|U|F)C.
例如: CV_8UC1 表示8位無符號單通道矩陣, CV_32SC2表示32位有符號雙通道矩陣.
例程:
CvMat* M = cvCreateMat(4,4,CV_32FC1);
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•釋放矩陣空間:
1.CvMat* M = cvCreateMat(4,4,CV_32FC1);
2.cvReleaseMat(&M);
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•複製矩陣:
1.CvMat* M1 = cvCreateMat(4,4,CV_32FC1);
2.CvMat* M2;
3.M2=cvCloneMat(M1);
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•初始化矩陣:
1.double a[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 };
2.CvMat Ma=cvMat(3, 4, CV_64FC1, a);
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另一種方法:
1.CvMat Ma;
2.cvInitMatHeader(&Ma, 3, 4, CV_64FC1, a);
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•初始化矩陣為單位陣:
1.CvMat* M = cvCreateMat(4,4,CV_32FC1);
2.cvSetIdentity(M); // 這裡似乎有問題，不成功
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存取矩陣元素
•假設需要存取一個2維浮點矩陣的第(i,j)個元素.
•間接存取矩陣元素:
1.cvmSet(M,i,j,2.0); // Set M(i,j)
2.t = cvmGet(M,i,j); // Get M(i,j)
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•直接存取，假設使用4-位元組校正:
1.CvMat* M = cvCreateMat(4,4,CV_32FC1);
2.int n = M->cols;
3.float *data = M->data.fl;
4.data[i*n+j] = 3.0;
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•直接存取，校正位元組任意:
1.CvMat* M = cvCreateMat(4,4,CV_32FC1);
2.int step = M->step/sizeof (float );
3.float *data = M->data.fl;
4.(data+i*step)[j] = 3.0;
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•直接存取一個初始化的矩陣元素:
1.double a[16];
2.CvMat Ma = cvMat(3, 4, CV_64FC1, a);
3.a[i*4+j] = 2.0; // Ma(i,j)=2.0;
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矩陣/向量操作
•矩陣-矩陣操作:
1.CvMat *Ma, *Mb, *Mc;
2.cvAdd(Ma, Mb, Mc); // Ma+Mb -> Mc
3.cvSub(Ma, Mb, Mc); // Ma-Mb -> Mc
4.cvMatMul(Ma, Mb, Mc); // Ma*Mb -> Mc
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•按元素的矩陣操作:
1.CvMat *Ma, *Mb, *Mc;
2.cvMul(Ma, Mb, Mc); // Ma.*Mb -> Mc
3.cvDiv(Ma, Mb, Mc); // Ma./Mb -> Mc
4.cvAddS(Ma, cvScalar(-10.0), Mc); // Ma.-10 -> Mc
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•向量乘積:
1.double va[] = {1, 2, 3};
2.double vb[] = {0, 0, 1};
3.double vc[3];
4.CvMat Va=cvMat(3, 1, CV_64FC1, va);
5.CvMat Vb=cvMat(3, 1, CV_64FC1, vb);
6.CvMat Vc=cvMat(3, 1, CV_64FC1, vc);
7.double res=cvDotProduct(&Va,&Vb); // 點乘: Va . Vb -> res
8.cvCrossProduct(&Va, &Vb, &Vc); // 向量積: Va x Vb -> Vc
9.end{verbatim}
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注意 Va, Vb, Vc 在向量積中向量元素個數須相同.
•單矩陣操作:
1.CvMat *Ma, *Mb;
2.cvTranspose(Ma, Mb); // transpose(Ma) -> Mb (不能對自身進行轉置)
3.CvScalar t = cvTrace(Ma); // trace(Ma) -> t.val[0]
4.double d = cvDet(Ma); // det(Ma) -> d
5.cvInvert(Ma, Mb); // inv(Ma) -> Mb
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•非齊次線性系統求解:
1.CvMat* A = cvCreateMat(3,3,CV_32FC1);
2.CvMat* x = cvCreateMat(3,1,CV_32FC1);
3.CvMat* b = cvCreateMat(3,1,CV_32FC1);
4.cvSolve(&A, &b, &x); // solve (Ax=b) for x
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•特徵值分析(針對對稱矩陣):
1.CvMat* A = cvCreateMat(3,3,CV_32FC1);
2.CvMat* E = cvCreateMat(3,3,CV_32FC1);
3.CvMat* l = cvCreateMat(3,1,CV_32FC1);
4.cvEigenVV(&A, &E, &l); // l = A的特徵值 (降序排列) ， E = 對應的特徵向量 (每行)
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•奇異值分解SVD:
1.CvMat* A = cvCreateMat(3,3,CV_32FC1);
2.CvMat* U = cvCreateMat(3,3,CV_32FC1);
3.CvMat* D = cvCreateMat(3,3,CV_32FC1);
4.CvMat* V = cvCreateMat(3,3,CV_32FC1);
5.cvSVD(A, D, U, V, CV_SVD_U_T|CV_SVD_V_T); // A = U D V^T
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1.初始化矩陣：
方式一、逐點賦值式：
CvMat* mat = cvCreateMat( 2, 2, CV_64FC1 );
cvZero( mat );
cvmSet( mat, 0, 0, 1 );
cvmSet( mat, 0, 1, 2 );
cvmSet( mat, 1, 0, 3 );
cvmSet( mat, 2, 2, 4 );
cvReleaseMat( &mat );
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方式二、連線現有陣列式：
double a[] = { 1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12 };
CvMat mat = cvMat( 3, 4, CV_64FC1, a ); // 64FC1 for double
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// 不需要cvReleaseMat，因為資料記憶體分配是由double定義的陣列進行的。
2.IplImage 到cvMat的轉換
方式一、cvGetMat方式：
CvMat mathdr, *mat = cvGetMat( img, &mathdr );
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方式二、cvConvert方式：
CvMat *mat = cvCreateMat( img->height, img->width, CV_64FC3 );
cvConvert( img, mat );
// #define cvConvert( src, dst ) cvConvertScale( (src), (dst), 1, 0 )
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3.cvArr(IplImage或者cvMat)轉化為cvMat
方式一、cvGetMat方式：
int coi = 0;
cvMat *mat = (CvMat*)arr;
if( !CV_IS_MAT(mat) )
{
mat = cvGetMat( mat, &matstub, &coi );
if (coi != 0) reutn; // CV_ERROR_FROM_CODE(CV_BadCOI);
}
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寫成函式為：
// This is just an example of function
// to support both IplImage and cvMat as an input
CVAPI( void ) cvIamArr( const CvArr* arr )
{
CV_FUNCNAME( "cvIamArr" );
__BEGIN__;
CV_ASSERT( mat == NULL );
CvMat matstub, *mat = (CvMat*)arr;
int coi = 0;
if( !CV_IS_MAT(mat) )
{
CV_CALL( mat = cvGetMat( mat, &matstub, &coi ) );
if (coi != 0) CV_ERROR_FROM_CODE(CV_BadCOI);
}
// Process as cvMat
__END__;
}
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4.影象直接操作
方式一：直接陣列操作 int col, row, z;
uchar b, g, r;
for( y = 0; row < img->height; y++ )
{
for ( col = 0; col < img->width; col++ )
{
b = img->imageData[img->widthStep * row + col * 3]
g = img->imageData[img->widthStep * row + col * 3 + 1];
r = img->imageData[img->widthStep * row + col * 3 + 2];
}
}
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方式二：巨集操作：
int row, col;
uchar b, g, r;
for( row = 0; row < img->height; row++ )
{
for ( col = 0; col < img->width; col++ )
{
b = CV_IMAGE_ELEM( img, uchar, row, col * 3 );
g = CV_IMAGE_ELEM( img, uchar, row, col * 3 + 1 );
r = CV_IMAGE_ELEM( img, uchar, row, col * 3 + 2 );
}
}
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注：CV_IMAGE_ELEM( img, uchar, row, col * img->nChannels + ch )
5.cvMat的直接操作
陣列的直接操作比較鬱悶，這是由於其決定於陣列的資料型別。
對於CV_32FC1 (1 channel float)：
CvMat* M = cvCreateMat( 4, 4, CV_32FC1 );
M->data.fl[ row * M->cols + col ] = (float)3.0;
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對於CV_64FC1 (1 channel double)：
CvMat* M = cvCreateMat( 4, 4, CV_64FC1 );
M->data.db[ row * M->cols + col ] = 3.0;
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一般的，對於1通道的陣列：
CvMat* M = cvCreateMat( 4, 4, CV_64FC1 );
CV_MAT_ELEM( *M, double, row, col ) = 3.0;
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注意double要根據陣列的資料型別來傳入，這個巨集對多通道無能為力。
對於多通道：
看看這個巨集的定義：
#define CV_MAT_ELEM_CN( mat, elemtype, row, col ) \
(*(elemtype*)((mat).data.ptr + (size_t)(mat).step*(row) + sizeof(elemtype)*(col)))
if( CV_MAT_DEPTH(M->type) == CV_32F )
CV_MAT_ELEM_CN( *M, float, row, col * CV_MAT_CN(M->type) + ch ) = 3.0;
if( CV_MAT_DEPTH(M->type) == CV_64F )
CV_MAT_ELEM_CN( *M, double, row, col * CV_MAT_CN(M->type) + ch ) = 3.0;
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更優化的方法是：
#define CV_8U 0
#define CV_8S 1
#define CV_16U 2
#define CV_16S 3
#define CV_32S 4
#define CV_32F 5
#define CV_64F 6
#define CV_USRTYPE1 7
int elem_size = CV_ELEM_SIZE( mat->type );
for( col = start_col; col < end_col; col++ ) {
for( row = 0; row < mat->rows; row++ ) {
for( elem = 0; elem < elem_size; elem++ ) {
(mat->data.ptr + ((size_t)mat->step * row) + (elem_size * col))[elem] =
(submat->data.ptr + ((size_t)submat->step * row) + (elem_size * (col - start_col)))[elem];
}
}
}
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對於多通道的陣列，以下操作是推薦的：
for(row=0; row< mat->rows; row++)
{
p = mat->data.fl + row * (mat->step/4);
for(col = 0; col < mat->cols; col++)
{
*p = (float) row+col;
*(p+1) = (float) row+col+1;
*(p+2) =(float) row+col+2;
p+=3;
}
}
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對於兩通道和四通道而言：
CvMat* vector = cvCreateMat( 1, 3, CV_32SC2 );
CV_MAT_ELEM( *vector, CvPoint, 0, 0 ) = cvPoint(100,100);
CvMat* vector = cvCreateMat( 1, 3, CV_64FC4 );
CV_MAT_ELEM( *vector, CvScalar, 0, 0 ) = cvScalar(0,0,0,0);
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6.間接訪問cvMat
cvmGet/Set是訪問CV_32FC1 和 CV_64FC1型陣列的最簡便的方式，其訪問速度和直接訪問幾乎相同
cvmSet( mat, row, col, value );
cvmGet( mat, row, col );
舉例：列印一個數組
inline void cvDoubleMatPrint( const CvMat* mat )
{
int i, j;
for( i = 0; i < mat->rows; i++ )
{
for( j = 0; j < mat->cols; j++ )
{
printf( "%f ",cvmGet( mat, i, j ) );
}
printf( "\n" );
}
}
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而對於其他的，比如是多通道的後者是其他資料型別的，cvGet/Set2D是個不錯的選擇
CvScalar scalar = cvGet2D( mat, row, col );
cvSet2D( mat, row, col, cvScalar( r, g, b ) );
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注意：資料不能為int，因為cvGet2D得到的實質是double型別。
舉例：列印一個多通道矩陣：
inline void cv3DoubleMatPrint( const CvMat* mat )
{
int i, j;
for( i = 0; i < mat->rows; i++ )
{
for( j = 0; j < mat->cols; j++ )
{
CvScalar scal = cvGet2D( mat, i, j );
printf( "(%f,%f,%f) ", scal.val[0], scal.val[1], scal.val[2] );
}
printf( "\n" );
}
}
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7.修改矩陣的形狀——cvReshape的操作
經實驗表明矩陣操作的進行的順序是：首先滿足通道，然後滿足列，最後是滿足行。
注意：這和Matlab是不同的，Matlab是行、列、通道的順序。
我們在此舉例如下：
對於一通道：
// 1 channel
CvMat *mat, mathdr;
double data[] = { 11, 12, 13, 14,
21, 22, 23, 24,
31, 32, 33, 34 };
CvMat* orig = &cvMat( 3, 4, CV_64FC1, data );
//11 12 13 14
//21 22 23 24
//31 32 33 34
mat = cvReshape( orig, &mathdr, 1, 1 ); // new_ch, new_rows
cvDoubleMatPrint( mat ); // above
// 11 12 13 14 21 22 23 24 31 32 33 34
mat = cvReshape( mat, &mathdr, 1, 3 ); // new_ch, new_rows
cvDoubleMatPrint( mat ); // above
//11 12 13 14
//21 22 23 24
//31 32 33 34
mat = cvReshape( orig, &mathdr, 1, 12 ); // new_ch, new_rows
cvDoubleMatPrint( mat ); // above
// 11
// 12
// 13
// 14
// 21
// 22
// 23
// 24
// 31
// 32
// 33
// 34
mat = cvReshape( mat, &mathdr, 1, 3 ); // new_ch, new_rows
cvDoubleMatPrint( mat ); // above
//11 12 13 14
//21 22 23 24
//31 32 33 34
mat = cvReshape( orig, &mathdr, 1, 2 ); // new_ch, new_rows
cvDoubleMatPrint( mat ); // above
//11 12 13 14 21 22
//23 24 31 32 33 34
mat = cvReshape( mat, &mathdr, 1, 3 ); // new_ch, new_rows
cvDoubleMatPrint( mat ); // above
//11 12 13 14
//21 22 23 24
//31 32 33 34
mat = cvReshape( orig, &mathdr, 1, 6 ); // new_ch, new_rows
cvDoubleMatPrint( mat ); // above
// 11 12
// 13 14
// 21 22
// 23 24
// 31 32
// 33 34
mat = cvReshape( mat, &mathdr, 1, 3 ); // new_ch, new_rows
cvDoubleMatPrint( mat ); // above
//11 12 13 14
//21 22 23 24
//31 32 33 34
// Use cvTranspose and cvReshape( mat, &mathdr, 1, 2 ) to get
// 11 23
// 12 24
// 13 31
// 14 32
// 21 33
// 22 34
// Use cvTranspose again when to recover
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對於三通道
// 3 channels
CvMat mathdr, *mat;
double data[] = { 111, 112, 113, 121, 122, 123,
211, 212, 213, 221, 222, 223 };
CvMat* orig = &cvMat( 2, 2, CV_64FC3, data );
//(111,112,113) (121,122,123)
//(211,212,213) (221,222,223)
mat = cvReshape( orig, &mathdr, 3, 1 ); // new_ch, new_rows
cv3DoubleMatPrint( mat ); // above
// (111,112,113) (121,122,123) (211,212,213) (221,222,223)
// concatinate in column first order
mat = cvReshape( orig, &mathdr, 1, 1 );// new_ch, new_rows
cvDoubleMatPrint( mat ); // above
// 111 112 113 121 122 123 211 212 213 221 222 223
// concatinate in channel first, column second, row third
mat = cvReshape( orig, &mathdr, 1, 3); // new_ch, new_rows
cvDoubleMatPrint( mat ); // above
//111 112 113 121
//122 123 211 212
//213 221 222 223
// channel first, column second, row third
mat = cvReshape( orig, &mathdr, 1, 4 ); // new_ch, new_rows
cvDoubleMatPrint( mat ); // above
//111 112 113
//121 122 123
//211 212 213
//221 222 223
// channel first, column second, row third
// memorize this transform because this is useful to
// add (or do something) color channels
CvMat* mat2 = cvCreateMat( mat->cols, mat->rows, mat->type );
cvTranspose( mat, mat2 );
cvDoubleMatPrint( mat2 ); // above
//111 121 211 221
//112 122 212 222
//113 123 213 223
cvReleaseMat( &mat2 );
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8.計算色彩距離
我們要計算img1,img2的每個畫素的距離，用dist表示，定義如下
IplImage *img1 = cvCreateImage( cvSize(w,h), IPL_DEPTH_8U, 3 );
IplImage *img2 = cvCreateImage( cvSize(w,h), IPL_DEPTH_8U, 3 );
CvMat *dist = cvCreateMat( h, w, CV_64FC1 );
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比較笨的思路是：cvSplit->cvSub->cvMul->cvAdd
程式碼如下：
IplImage *img1B = cvCreateImage( cvGetSize(img1), img1->depth, 1 );
IplImage *img1G = cvCreateImage( cvGetSize(img1), img1->depth, 1 );
IplImage *img1R = cvCreateImage( cvGetSize(img1), img1->depth, 1 );
IplImage *img2B = cvCreateImage( cvGetSize(img1), img1->depth, 1 );
IplImage *img2G = cvCreateImage( cvGetSize(img1), img1->depth, 1 );
IplImage *img2R = cvCreateImage( cvGetSize(img1), img1->depth, 1 );
IplImage *diff = cvCreateImage( cvGetSize(img1), IPL_DEPTH_64F, 1 );
cvSplit( img1, img1B, img1G, img1R );
cvSplit( img2, img2B, img2G, img2R );
cvSub( img1B, img2B, diff );
cvMul( diff, diff, dist );
cvSub( img1G, img2G, diff );
cvMul( diff, diff, diff);
cvAdd( diff, dist, dist );
cvSub( img1R, img2R, diff );
cvMul( diff, diff, diff );
cvAdd( diff, dist, dist );
cvReleaseImage( &img1B );
cvReleaseImage( &img1G );
cvReleaseImage( &img1R );
cvReleaseImage( &img2B );
cvReleaseImage( &img2G );
cvReleaseImage( &img2R );
cvReleaseImage( &diff );
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比較聰明的思路是
int D = img1->nChannels; // D: Number of colors (dimension)
int N = img1->width * img1->height; // N: number of pixels
CvMat mat1hdr, *mat1 = cvReshape( img1, &mat1hdr, 1, N ); // N x D(colors)
CvMat mat2hdr, *mat2 = cvReshape( img2, &mat2hdr, 1, N ); // N x D(colors)
CvMat diffhdr, *diff = cvCreateMat( N, D, CV_64FC1 ); // N x D, temporal buff
cvSub( mat1, mat2, diff );
cvMul( diff, diff, diff );
dist = cvReshape( dist, &disthdr, 1, N ); // nRow x nCol to N x 1
cvReduce( diff, dist, 1, CV_REDUCE_SUM ); // N x D to N x 1
dist = cvReshape( dist, &disthdr, 1, img1->height ); // Restore N x 1 to nRow x nCol
cvReleaseMat( &diff );
#pragma comment( lib, "cxcore.lib" )
#include "cv.h"
#include <stdio.h>
int main()
{
CvMat* mat = cvCreateMat(3,3,CV_32FC1);
cvZero(mat);//將矩陣置0
//為矩陣元素賦值
CV_MAT_ELEM( *mat, float, 0, 0 ) = 1.f;
CV_MAT_ELEM( *mat, float, 0, 1 ) = 2.f;
CV_MAT_ELEM( *mat, float, 0, 2 ) = 3.f;
CV_MAT_ELEM( *mat, float, 1, 0 ) = 4.f;
CV_MAT_ELEM( *mat, float, 1, 1 ) = 5.f;
CV_MAT_ELEM( *mat, float, 1, 2 ) = 6.f;
CV_MAT_ELEM( *mat, float, 2, 0 ) = 7.f;
CV_MAT_ELEM( *mat, float, 2, 1 ) = 8.f;
CV_MAT_ELEM( *mat, float, 2, 2 ) = 9.f;
//獲得矩陣元素(0,2)的值
float *p = (float*)cvPtr2D(mat, 0, 2);
printf("%f\n",*p);
return 0;
}