void interp_step( IplImage*** dog_pyr, int octv, int intvl, int r, int c,
double* xi, double* xr, double* xc )
{
CvMat* dD, * H, * H_inv, X;
double x[3] = { 0 };
dD = deriv_3D( dog_pyr, octv, intvl, r, c );
H = hessian_3D( dog_pyr, octv, intvl, r, c );
H_inv = cvCreateMat( 3, 3, CV_64FC1 );
cvInvert( H, H_inv, CV_SVD );
cvInitMatHeader( &X, 3, 1, CV_64FC1, x, CV_AUTOSTEP );
cvGEMM( H_inv, dD, -1, NULL, 0, &X, 0 );
cvReleaseMat( &dD );
cvReleaseMat( &H );
cvReleaseMat( &H_inv );
*xi = x[2];
*xr = x[1];
*xc = x[0];
}
/*
Performs one step of extremum interpolation. Based on Eqn. (3) in Lowe's paper.
@param dog_pyr difference of Gaussians scale space pyramid
@param octv octave of scale space
@param intvl interval being interpolated
@param r row being interpolated
@param c column being interpolated
@param xi output as interpolated subpixel increment to interval
@param xr output as interpolated subpixel increment to row
@param xc output as interpolated subpixel increment to col
*/
static void interp_step( IplImage*** dog_pyr, int octv, int intvl, int r, int c,
double* xi, double* xr, double* xc )
{
CvMat* dD, * H, * H_inv, X;
double x[3] = { 0 };
//在DoG金字塔中计算某点的x方向、y方向以及尺度方向上的偏导数，结果存放在列向量dD中
dD = deriv_3D( dog_pyr, octv, intvl, r, c );
//在DoG金字塔中计算某点的3*3海森矩阵
H = hessian_3D( dog_pyr, octv, intvl, r, c );
H_inv = cvCreateMat( 3, 3, CV_64FC1 );//海森矩阵的逆阵
cvInvert( H, H_inv, CV_SVD );
cvInitMatHeader( &X, 3, 1, CV_64FC1, x, CV_AUTOSTEP );
//X = - H^(-1) * dD，H的三个元素分别是x,y,σ方向上的偏移量(具体见SIFT算法说明)
cvGEMM( H_inv, dD, -1, NULL, 0, &X, 0 );
cvReleaseMat( &dD );
cvReleaseMat( &H );
cvReleaseMat( &H_inv );
*xi = x[2];//σ方向(层方向)偏移量
*xr = x[1];//y方向上偏移量
*xc = x[0];//x方向上偏移量
}
