相位相关算法实现（Phase Correlation）（FFTW版）

相位相关：

void PhaseCorrelation( UChar *ref , UChar *tpl , double *poc , int width , int height ) {
	int 	i, j, k;
	double	tmp;
	
	int step     = width;     
	int fft_size = width * height;

	/* setup pointers to images */
	UChar *ref_data = ( UChar* ) ref;
	UChar *tpl_data = ( UChar* ) tpl;
	double 	*poc_data = ( double* ) poc;
	
	/* allocate FFTW input and output arrays */
	fftw_complex *img1 = ( fftw_complex* )fftw_malloc( sizeof( fftw_complex ) * width * height );
	fftw_complex *img2 = ( fftw_complex* )fftw_malloc( sizeof( fftw_complex ) * width * height );
	fftw_complex *res  = ( fftw_complex* )fftw_malloc( sizeof( fftw_complex ) * width * height );	
	
	/* setup FFTW plans */
	fftw_plan fft_img1 = fftw_plan_dft_1d( width * height, img1, img1, FFTW_FORWARD,  FFTW_ESTIMATE );
	fftw_plan fft_img2 = fftw_plan_dft_1d( width * height, img2, img2, FFTW_FORWARD,  FFTW_ESTIMATE );
	fftw_plan ifft_res = fftw_plan_dft_1d( width * height, res,  res,  FFTW_BACKWARD, FFTW_ESTIMATE );
	
	/* load images' data to FFTW input */
	for( i = 0, k = 0 ; i < height ; i++ ) {
		for( j = 0 ; j < width ; j++, k++ ) {
			img1[k][0] = ( double )ref_data[i * step + j];
			img1[k][1] = 0.0;
			
			img2[k][0] = ( double )tpl_data[i * step + j];
			img2[k][1] = 0.0;
		}
	}
	
	/* obtain the FFT of img1 */
	fftw_execute( fft_img1 );
	
	/* obtain the FFT of img2 */
	fftw_execute( fft_img2 );
	
	/* obtain the cross power spectrum */
	for( i = 0; i < fft_size ; i++ ) {
		res[i][0] = ( img2[i][0] * img1[i][0] ) - ( img2[i][1] * ( -img1[i][1] ) );
		res[i][1] = ( img2[i][0] * ( -img1[i][1] ) ) + ( img2[i][1] * img1[i][0] );

		tmp = sqrt( pow( res[i][0] , 2.0 ) + pow( res[i][1] , 2.0 ) );

		res[i][0] /= tmp;
		res[i][1] /= tmp;
	}

	/* obtain the phase correlation array */
	fftw_execute( ifft_res );

	/* normalize and copy to result image */
	for( i = 0 ; i < fft_size ; i++ ) {
        poc_data[i] = res[i][0] / ( double )fft_size;
	}

	/* deallocate FFTW arrays and plans */
	fftw_destroy_plan( fft_img1 );
	fftw_destroy_plan( fft_img2 );
	fftw_destroy_plan( ifft_res );
	fftw_free( img1 );
	fftw_free( img2 );
	fftw_free( res );	
}

FFT使用的FFTW库，FFTW的下载地位：http://www.fftw.org/download.html

源图：

偏移图：

计算后所得结果：