/*M/////////////////////////////////////////////////////////////////////////////////////// // // IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. // // By downloading, copying, installing or using the software you agree to this license. // If you do not agree to this license, do not download, install, // copy or use the software. // // // Intel License Agreement // For Open Source Computer Vision Library // // Copyright (C) 2000, Intel Corporation, all rights reserved. // Third party copyrights are property of their respective owners. // // Redistribution and use in source and binary forms, with or without modification, // are permitted provided that the following conditions are met: // // * Redistribution's of source code must retain the above copyright notice, // this list of conditions and the following disclaimer. // // * Redistribution's in binary form must reproduce the above copyright notice, // this list of conditions and the following disclaimer in the documentation // and/or other materials provided with the distribution. // // * The name of Intel Corporation may not be used to endorse or promote products // derived from this software without specific prior written permission. // // This software is provided by the copyright holders and contributors "as is" and // any express or implied warranties, including, but not limited to, the implied // warranties of merchantability and fitness for a particular purpose are disclaimed. // In no event shall the Intel Corporation or contributors be liable for any direct, // indirect, incidental, special, exemplary, or consequential damages // (including, but not limited to, procurement of substitute goods or services; // loss of use, data, or profits; or business interruption) however caused // and on any theory of liability, whether in contract, strict liability, // or tort (including negligence or otherwise) arising in any way out of // the use of this software, even if advised of the possibility of such damage. // //M*/ #include "precomp.hpp" namespace cv { // On Win64 optimized versions of DFT and DCT fail the tests (fixed in VS2010) #if defined _MSC_VER && !defined CV_ICC && defined _M_X64 && _MSC_VER < 1600 # pragma optimize("", off) # pragma warning(disable: 4748) #endif /****************************************************************************************\ Discrete Fourier Transform \****************************************************************************************/ #define CV_MAX_LOCAL_DFT_SIZE (1 << 15) static unsigned char bitrevTab[] = { 0x00,0x80,0x40,0xc0,0x20,0xa0,0x60,0xe0,0x10,0x90,0x50,0xd0,0x30,0xb0,0x70,0xf0, 0x08,0x88,0x48,0xc8,0x28,0xa8,0x68,0xe8,0x18,0x98,0x58,0xd8,0x38,0xb8,0x78,0xf8, 0x04,0x84,0x44,0xc4,0x24,0xa4,0x64,0xe4,0x14,0x94,0x54,0xd4,0x34,0xb4,0x74,0xf4, 0x0c,0x8c,0x4c,0xcc,0x2c,0xac,0x6c,0xec,0x1c,0x9c,0x5c,0xdc,0x3c,0xbc,0x7c,0xfc, 0x02,0x82,0x42,0xc2,0x22,0xa2,0x62,0xe2,0x12,0x92,0x52,0xd2,0x32,0xb2,0x72,0xf2, 0x0a,0x8a,0x4a,0xca,0x2a,0xaa,0x6a,0xea,0x1a,0x9a,0x5a,0xda,0x3a,0xba,0x7a,0xfa, 0x06,0x86,0x46,0xc6,0x26,0xa6,0x66,0xe6,0x16,0x96,0x56,0xd6,0x36,0xb6,0x76,0xf6, 0x0e,0x8e,0x4e,0xce,0x2e,0xae,0x6e,0xee,0x1e,0x9e,0x5e,0xde,0x3e,0xbe,0x7e,0xfe, 0x01,0x81,0x41,0xc1,0x21,0xa1,0x61,0xe1,0x11,0x91,0x51,0xd1,0x31,0xb1,0x71,0xf1, 0x09,0x89,0x49,0xc9,0x29,0xa9,0x69,0xe9,0x19,0x99,0x59,0xd9,0x39,0xb9,0x79,0xf9, 0x05,0x85,0x45,0xc5,0x25,0xa5,0x65,0xe5,0x15,0x95,0x55,0xd5,0x35,0xb5,0x75,0xf5, 0x0d,0x8d,0x4d,0xcd,0x2d,0xad,0x6d,0xed,0x1d,0x9d,0x5d,0xdd,0x3d,0xbd,0x7d,0xfd, 0x03,0x83,0x43,0xc3,0x23,0xa3,0x63,0xe3,0x13,0x93,0x53,0xd3,0x33,0xb3,0x73,0xf3, 0x0b,0x8b,0x4b,0xcb,0x2b,0xab,0x6b,0xeb,0x1b,0x9b,0x5b,0xdb,0x3b,0xbb,0x7b,0xfb, 0x07,0x87,0x47,0xc7,0x27,0xa7,0x67,0xe7,0x17,0x97,0x57,0xd7,0x37,0xb7,0x77,0xf7, 0x0f,0x8f,0x4f,0xcf,0x2f,0xaf,0x6f,0xef,0x1f,0x9f,0x5f,0xdf,0x3f,0xbf,0x7f,0xff }; static const double DFTTab[][2] = { { 1.00000000000000000, 0.00000000000000000 }, {-1.00000000000000000, 0.00000000000000000 }, { 0.00000000000000000, 1.00000000000000000 }, { 0.70710678118654757, 0.70710678118654746 }, { 0.92387953251128674, 0.38268343236508978 }, { 0.98078528040323043, 0.19509032201612825 }, { 0.99518472667219693, 0.09801714032956060 }, { 0.99879545620517241, 0.04906767432741802 }, { 0.99969881869620425, 0.02454122852291229 }, { 0.99992470183914450, 0.01227153828571993 }, { 0.99998117528260111, 0.00613588464915448 }, { 0.99999529380957619, 0.00306795676296598 }, { 0.99999882345170188, 0.00153398018628477 }, { 0.99999970586288223, 0.00076699031874270 }, { 0.99999992646571789, 0.00038349518757140 }, { 0.99999998161642933, 0.00019174759731070 }, { 0.99999999540410733, 0.00009587379909598 }, { 0.99999999885102686, 0.00004793689960307 }, { 0.99999999971275666, 0.00002396844980842 }, { 0.99999999992818922, 0.00001198422490507 }, { 0.99999999998204725, 0.00000599211245264 }, { 0.99999999999551181, 0.00000299605622633 }, { 0.99999999999887801, 0.00000149802811317 }, { 0.99999999999971945, 0.00000074901405658 }, { 0.99999999999992983, 0.00000037450702829 }, { 0.99999999999998246, 0.00000018725351415 }, { 0.99999999999999567, 0.00000009362675707 }, { 0.99999999999999889, 0.00000004681337854 }, { 0.99999999999999978, 0.00000002340668927 }, { 0.99999999999999989, 0.00000001170334463 }, { 1.00000000000000000, 0.00000000585167232 }, { 1.00000000000000000, 0.00000000292583616 } }; #define BitRev(i,shift) \ ((int)((((unsigned)bitrevTab[(i)&255] << 24)+ \ ((unsigned)bitrevTab[((i)>> 8)&255] << 16)+ \ ((unsigned)bitrevTab[((i)>>16)&255] << 8)+ \ ((unsigned)bitrevTab[((i)>>24)])) >> (shift))) static int DFTFactorize( int n, int* factors ) { int nf = 0, f, i, j; if( n <= 5 ) { factors[0] = n; return 1; } f = (((n - 1)^n)+1) >> 1; if( f > 1 ) { factors[nf++] = f; n = f == n ? 1 : n/f; } for( f = 3; n > 1; ) { int d = n/f; if( d*f == n ) { factors[nf++] = f; n = d; } else { f += 2; if( f*f > n ) break; } } if( n > 1 ) factors[nf++] = n; f = (factors[0] & 1) == 0; for( i = f; i < (nf+f)/2; i++ ) CV_SWAP( factors[i], factors[nf-i-1+f], j ); return nf; } static void DFTInit( int n0, int nf, int* factors, int* itab, int elem_size, void* _wave, int inv_itab ) { int digits[34], radix[34]; int n = factors[0], m = 0; int* itab0 = itab; int i, j, k; Complex w, w1; double t; if( n0 <= 5 ) { itab[0] = 0; itab[n0-1] = n0-1; if( n0 != 4 ) { for( i = 1; i < n0-1; i++ ) itab[i] = i; } else { itab[1] = 2; itab[2] = 1; } if( n0 == 5 ) { if( elem_size == sizeof(Complex) ) ((Complex*)_wave)[0] = Complex(1.,0.); else ((Complex*)_wave)[0] = Complex(1.f,0.f); } if( n0 != 4 ) return; m = 2; } else { // radix[] is initialized from index 'nf' down to zero assert (nf < 34); radix[nf] = 1; digits[nf] = 0; for( i = 0; i < nf; i++ ) { digits[i] = 0; radix[nf-i-1] = radix[nf-i]*factors[nf-i-1]; } if( inv_itab && factors[0] != factors[nf-1] ) itab = (int*)_wave; if( (n & 1) == 0 ) { int a = radix[1], na2 = n*a>>1, na4 = na2 >> 1; for( m = 0; (unsigned)(1 << m) < (unsigned)n; m++ ) ; if( n <= 2 ) { itab[0] = 0; itab[1] = na2; } else if( n <= 256 ) { int shift = 10 - m; for( i = 0; i <= n - 4; i += 4 ) { j = (bitrevTab[i>>2]>>shift)*a; itab[i] = j; itab[i+1] = j + na2; itab[i+2] = j + na4; itab[i+3] = j + na2 + na4; } } else { int shift = 34 - m; for( i = 0; i < n; i += 4 ) { int i4 = i >> 2; j = BitRev(i4,shift)*a; itab[i] = j; itab[i+1] = j + na2; itab[i+2] = j + na4; itab[i+3] = j + na2 + na4; } } digits[1]++; if( nf >= 2 ) { for( i = n, j = radix[2]; i < n0; ) { for( k = 0; k < n; k++ ) itab[i+k] = itab[k] + j; if( (i += n) >= n0 ) break; j += radix[2]; for( k = 1; ++digits[k] >= factors[k]; k++ ) { digits[k] = 0; j += radix[k+2] - radix[k]; } } } } else { for( i = 0, j = 0;; ) { itab[i] = j; if( ++i >= n0 ) break; j += radix[1]; for( k = 0; ++digits[k] >= factors[k]; k++ ) { digits[k] = 0; j += radix[k+2] - radix[k]; } } } if( itab != itab0 ) { itab0[0] = 0; for( i = n0 & 1; i < n0; i += 2 ) { int k0 = itab[i]; int k1 = itab[i+1]; itab0[k0] = i; itab0[k1] = i+1; } } } if( (n0 & (n0-1)) == 0 ) { w.re = w1.re = DFTTab[m][0]; w.im = w1.im = -DFTTab[m][1]; } else { t = -CV_PI*2/n0; w.im = w1.im = sin(t); w.re = w1.re = std::sqrt(1. - w1.im*w1.im); } n = (n0+1)/2; if( elem_size == sizeof(Complex) ) { Complex* wave = (Complex*)_wave; wave[0].re = 1.; wave[0].im = 0.; if( (n0 & 1) == 0 ) { wave[n].re = -1.; wave[n].im = 0; } for( i = 1; i < n; i++ ) { wave[i] = w; wave[n0-i].re = w.re; wave[n0-i].im = -w.im; t = w.re*w1.re - w.im*w1.im; w.im = w.re*w1.im + w.im*w1.re; w.re = t; } } else { Complex* wave = (Complex*)_wave; assert( elem_size == sizeof(Complex) ); wave[0].re = 1.f; wave[0].im = 0.f; if( (n0 & 1) == 0 ) { wave[n].re = -1.f; wave[n].im = 0.f; } for( i = 1; i < n; i++ ) { wave[i].re = (float)w.re; wave[i].im = (float)w.im; wave[n0-i].re = (float)w.re; wave[n0-i].im = (float)-w.im; t = w.re*w1.re - w.im*w1.im; w.im = w.re*w1.im + w.im*w1.re; w.re = t; } } } template struct DFT_VecR4 { int operator()(Complex*, int, int, int&, const Complex*) const { return 1; } }; #if CV_SSE3 // optimized radix-4 transform template<> struct DFT_VecR4 { int operator()(Complex* dst, int N, int n0, int& _dw0, const Complex* wave) const { int n = 1, i, j, nx, dw, dw0 = _dw0; __m128 z = _mm_setzero_ps(), x02=z, x13=z, w01=z, w23=z, y01, y23, t0, t1; Cv32suf t; t.i = 0x80000000; __m128 neg0_mask = _mm_load_ss(&t.f); __m128 neg3_mask = _mm_shuffle_ps(neg0_mask, neg0_mask, _MM_SHUFFLE(0,1,2,3)); for( ; n*4 <= N; ) { nx = n; n *= 4; dw0 /= 4; for( i = 0; i < n0; i += n ) { Complexf *v0, *v1; v0 = dst + i; v1 = v0 + nx*2; x02 = _mm_loadl_pi(x02, (const __m64*)&v0[0]); x13 = _mm_loadl_pi(x13, (const __m64*)&v0[nx]); x02 = _mm_loadh_pi(x02, (const __m64*)&v1[0]); x13 = _mm_loadh_pi(x13, (const __m64*)&v1[nx]); y01 = _mm_add_ps(x02, x13); y23 = _mm_sub_ps(x02, x13); t1 = _mm_xor_ps(_mm_shuffle_ps(y01, y23, _MM_SHUFFLE(2,3,3,2)), neg3_mask); t0 = _mm_movelh_ps(y01, y23); y01 = _mm_add_ps(t0, t1); y23 = _mm_sub_ps(t0, t1); _mm_storel_pi((__m64*)&v0[0], y01); _mm_storeh_pi((__m64*)&v0[nx], y01); _mm_storel_pi((__m64*)&v1[0], y23); _mm_storeh_pi((__m64*)&v1[nx], y23); for( j = 1, dw = dw0; j < nx; j++, dw += dw0 ) { v0 = dst + i + j; v1 = v0 + nx*2; x13 = _mm_loadl_pi(x13, (const __m64*)&v0[nx]); w23 = _mm_loadl_pi(w23, (const __m64*)&wave[dw*2]); x13 = _mm_loadh_pi(x13, (const __m64*)&v1[nx]); // x1, x3 = r1 i1 r3 i3 w23 = _mm_loadh_pi(w23, (const __m64*)&wave[dw*3]); // w2, w3 = wr2 wi2 wr3 wi3 t0 = _mm_mul_ps(_mm_moveldup_ps(x13), w23); t1 = _mm_mul_ps(_mm_movehdup_ps(x13), _mm_shuffle_ps(w23, w23, _MM_SHUFFLE(2,3,0,1))); x13 = _mm_addsub_ps(t0, t1); // re(x1*w2), im(x1*w2), re(x3*w3), im(x3*w3) x02 = _mm_loadl_pi(x02, (const __m64*)&v1[0]); // x2 = r2 i2 w01 = _mm_loadl_pi(w01, (const __m64*)&wave[dw]); // w1 = wr1 wi1 x02 = _mm_shuffle_ps(x02, x02, _MM_SHUFFLE(0,0,1,1)); w01 = _mm_shuffle_ps(w01, w01, _MM_SHUFFLE(1,0,0,1)); x02 = _mm_mul_ps(x02, w01); x02 = _mm_addsub_ps(x02, _mm_movelh_ps(x02, x02)); // re(x0) im(x0) re(x2*w1), im(x2*w1) x02 = _mm_loadl_pi(x02, (const __m64*)&v0[0]); y01 = _mm_add_ps(x02, x13); y23 = _mm_sub_ps(x02, x13); t1 = _mm_xor_ps(_mm_shuffle_ps(y01, y23, _MM_SHUFFLE(2,3,3,2)), neg3_mask); t0 = _mm_movelh_ps(y01, y23); y01 = _mm_add_ps(t0, t1); y23 = _mm_sub_ps(t0, t1); _mm_storel_pi((__m64*)&v0[0], y01); _mm_storeh_pi((__m64*)&v0[nx], y01); _mm_storel_pi((__m64*)&v1[0], y23); _mm_storeh_pi((__m64*)&v1[nx], y23); } } } _dw0 = dw0; return n; } }; #endif #ifdef HAVE_IPP static void ippsDFTFwd_CToC( const Complex* src, Complex* dst, const void* spec, uchar* buf) { ippsDFTFwd_CToC_32fc( (const Ipp32fc*)src, (Ipp32fc*)dst, (const IppsDFTSpec_C_32fc*)spec, buf); } static void ippsDFTFwd_CToC( const Complex* src, Complex* dst, const void* spec, uchar* buf) { ippsDFTFwd_CToC_64fc( (const Ipp64fc*)src, (Ipp64fc*)dst, (const IppsDFTSpec_C_64fc*)spec, buf); } static void ippsDFTInv_CToC( const Complex* src, Complex* dst, const void* spec, uchar* buf) { ippsDFTInv_CToC_32fc( (const Ipp32fc*)src, (Ipp32fc*)dst, (const IppsDFTSpec_C_32fc*)spec, buf); } static void ippsDFTInv_CToC( const Complex* src, Complex* dst, const void* spec, uchar* buf) { ippsDFTInv_CToC_64fc( (const Ipp64fc*)src, (Ipp64fc*)dst, (const IppsDFTSpec_C_64fc*)spec, buf); } static void ippsDFTFwd_RToPack( const float* src, float* dst, const void* spec, uchar* buf) { ippsDFTFwd_RToPack_32f( src, dst, (const IppsDFTSpec_R_32f*)spec, buf); } static void ippsDFTFwd_RToPack( const double* src, double* dst, const void* spec, uchar* buf) { ippsDFTFwd_RToPack_64f( src, dst, (const IppsDFTSpec_R_64f*)spec, buf); } static void ippsDFTInv_PackToR( const float* src, float* dst, const void* spec, uchar* buf) { ippsDFTInv_PackToR_32f( src, dst, (const IppsDFTSpec_R_32f*)spec, buf); } static void ippsDFTInv_PackToR( const double* src, double* dst, const void* spec, uchar* buf) { ippsDFTInv_PackToR_64f( src, dst, (const IppsDFTSpec_R_64f*)spec, buf); } #endif enum { DFT_NO_PERMUTE=256, DFT_COMPLEX_INPUT_OR_OUTPUT=512 }; // mixed-radix complex discrete Fourier transform: double-precision version template static void DFT( const Complex* src, Complex* dst, int n, int nf, const int* factors, const int* itab, const Complex* wave, int tab_size, const void* #ifdef HAVE_IPP spec #endif , Complex* buf, int flags, double _scale ) { static const T sin_120 = (T)0.86602540378443864676372317075294; static const T fft5_2 = (T)0.559016994374947424102293417182819; static const T fft5_3 = (T)-0.951056516295153572116439333379382; static const T fft5_4 = (T)-1.538841768587626701285145288018455; static const T fft5_5 = (T)0.363271264002680442947733378740309; int n0 = n, f_idx, nx; int inv = flags & DFT_INVERSE; int dw0 = tab_size, dw; int i, j, k; Complex t; T scale = (T)_scale; int tab_step; #ifdef HAVE_IPP if( spec ) { if( !inv ) ippsDFTFwd_CToC( src, dst, spec, (uchar*)buf ); else ippsDFTInv_CToC( src, dst, spec, (uchar*)buf ); return; } #endif tab_step = tab_size == n ? 1 : tab_size == n*2 ? 2 : tab_size/n; // 0. shuffle data if( dst != src ) { assert( (flags & DFT_NO_PERMUTE) == 0 ); if( !inv ) { for( i = 0; i <= n - 2; i += 2, itab += 2*tab_step ) { int k0 = itab[0], k1 = itab[tab_step]; assert( (unsigned)k0 < (unsigned)n && (unsigned)k1 < (unsigned)n ); dst[i] = src[k0]; dst[i+1] = src[k1]; } if( i < n ) dst[n-1] = src[n-1]; } else { for( i = 0; i <= n - 2; i += 2, itab += 2*tab_step ) { int k0 = itab[0], k1 = itab[tab_step]; assert( (unsigned)k0 < (unsigned)n && (unsigned)k1 < (unsigned)n ); t.re = src[k0].re; t.im = -src[k0].im; dst[i] = t; t.re = src[k1].re; t.im = -src[k1].im; dst[i+1] = t; } if( i < n ) { t.re = src[n-1].re; t.im = -src[n-1].im; dst[i] = t; } } } else { if( (flags & DFT_NO_PERMUTE) == 0 ) { CV_Assert( factors[0] == factors[nf-1] ); if( nf == 1 ) { if( (n & 3) == 0 ) { int n2 = n/2; Complex* dsth = dst + n2; for( i = 0; i < n2; i += 2, itab += tab_step*2 ) { j = itab[0]; assert( (unsigned)j < (unsigned)n2 ); CV_SWAP(dst[i+1], dsth[j], t); if( j > i ) { CV_SWAP(dst[i], dst[j], t); CV_SWAP(dsth[i+1], dsth[j+1], t); } } } // else do nothing } else { for( i = 0; i < n; i++, itab += tab_step ) { j = itab[0]; assert( (unsigned)j < (unsigned)n ); if( j > i ) CV_SWAP(dst[i], dst[j], t); } } } if( inv ) { for( i = 0; i <= n - 2; i += 2 ) { T t0 = -dst[i].im; T t1 = -dst[i+1].im; dst[i].im = t0; dst[i+1].im = t1; } if( i < n ) dst[n-1].im = -dst[n-1].im; } } n = 1; // 1. power-2 transforms if( (factors[0] & 1) == 0 ) { if( factors[0] >= 4 && checkHardwareSupport(CV_CPU_SSE3)) { DFT_VecR4 vr4; n = vr4(dst, factors[0], n0, dw0, wave); } // radix-4 transform for( ; n*4 <= factors[0]; ) { nx = n; n *= 4; dw0 /= 4; for( i = 0; i < n0; i += n ) { Complex *v0, *v1; T r0, i0, r1, i1, r2, i2, r3, i3, r4, i4; v0 = dst + i; v1 = v0 + nx*2; r0 = v1[0].re; i0 = v1[0].im; r4 = v1[nx].re; i4 = v1[nx].im; r1 = r0 + r4; i1 = i0 + i4; r3 = i0 - i4; i3 = r4 - r0; r2 = v0[0].re; i2 = v0[0].im; r4 = v0[nx].re; i4 = v0[nx].im; r0 = r2 + r4; i0 = i2 + i4; r2 -= r4; i2 -= i4; v0[0].re = r0 + r1; v0[0].im = i0 + i1; v1[0].re = r0 - r1; v1[0].im = i0 - i1; v0[nx].re = r2 + r3; v0[nx].im = i2 + i3; v1[nx].re = r2 - r3; v1[nx].im = i2 - i3; for( j = 1, dw = dw0; j < nx; j++, dw += dw0 ) { v0 = dst + i + j; v1 = v0 + nx*2; r2 = v0[nx].re*wave[dw*2].re - v0[nx].im*wave[dw*2].im; i2 = v0[nx].re*wave[dw*2].im + v0[nx].im*wave[dw*2].re; r0 = v1[0].re*wave[dw].im + v1[0].im*wave[dw].re; i0 = v1[0].re*wave[dw].re - v1[0].im*wave[dw].im; r3 = v1[nx].re*wave[dw*3].im + v1[nx].im*wave[dw*3].re; i3 = v1[nx].re*wave[dw*3].re - v1[nx].im*wave[dw*3].im; r1 = i0 + i3; i1 = r0 + r3; r3 = r0 - r3; i3 = i3 - i0; r4 = v0[0].re; i4 = v0[0].im; r0 = r4 + r2; i0 = i4 + i2; r2 = r4 - r2; i2 = i4 - i2; v0[0].re = r0 + r1; v0[0].im = i0 + i1; v1[0].re = r0 - r1; v1[0].im = i0 - i1; v0[nx].re = r2 + r3; v0[nx].im = i2 + i3; v1[nx].re = r2 - r3; v1[nx].im = i2 - i3; } } } for( ; n < factors[0]; ) { // do the remaining radix-2 transform nx = n; n *= 2; dw0 /= 2; for( i = 0; i < n0; i += n ) { Complex* v = dst + i; T r0 = v[0].re + v[nx].re; T i0 = v[0].im + v[nx].im; T r1 = v[0].re - v[nx].re; T i1 = v[0].im - v[nx].im; v[0].re = r0; v[0].im = i0; v[nx].re = r1; v[nx].im = i1; for( j = 1, dw = dw0; j < nx; j++, dw += dw0 ) { v = dst + i + j; r1 = v[nx].re*wave[dw].re - v[nx].im*wave[dw].im; i1 = v[nx].im*wave[dw].re + v[nx].re*wave[dw].im; r0 = v[0].re; i0 = v[0].im; v[0].re = r0 + r1; v[0].im = i0 + i1; v[nx].re = r0 - r1; v[nx].im = i0 - i1; } } } } // 2. all the other transforms for( f_idx = (factors[0]&1) ? 0 : 1; f_idx < nf; f_idx++ ) { int factor = factors[f_idx]; nx = n; n *= factor; dw0 /= factor; if( factor == 3 ) { // radix-3 for( i = 0; i < n0; i += n ) { Complex* v = dst + i; T r1 = v[nx].re + v[nx*2].re; T i1 = v[nx].im + v[nx*2].im; T r0 = v[0].re; T i0 = v[0].im; T r2 = sin_120*(v[nx].im - v[nx*2].im); T i2 = sin_120*(v[nx*2].re - v[nx].re); v[0].re = r0 + r1; v[0].im = i0 + i1; r0 -= (T)0.5*r1; i0 -= (T)0.5*i1; v[nx].re = r0 + r2; v[nx].im = i0 + i2; v[nx*2].re = r0 - r2; v[nx*2].im = i0 - i2; for( j = 1, dw = dw0; j < nx; j++, dw += dw0 ) { v = dst + i + j; r0 = v[nx].re*wave[dw].re - v[nx].im*wave[dw].im; i0 = v[nx].re*wave[dw].im + v[nx].im*wave[dw].re; i2 = v[nx*2].re*wave[dw*2].re - v[nx*2].im*wave[dw*2].im; r2 = v[nx*2].re*wave[dw*2].im + v[nx*2].im*wave[dw*2].re; r1 = r0 + i2; i1 = i0 + r2; r2 = sin_120*(i0 - r2); i2 = sin_120*(i2 - r0); r0 = v[0].re; i0 = v[0].im; v[0].re = r0 + r1; v[0].im = i0 + i1; r0 -= (T)0.5*r1; i0 -= (T)0.5*i1; v[nx].re = r0 + r2; v[nx].im = i0 + i2; v[nx*2].re = r0 - r2; v[nx*2].im = i0 - i2; } } } else if( factor == 5 ) { // radix-5 for( i = 0; i < n0; i += n ) { for( j = 0, dw = 0; j < nx; j++, dw += dw0 ) { Complex* v0 = dst + i + j; Complex* v1 = v0 + nx*2; Complex* v2 = v1 + nx*2; T r0, i0, r1, i1, r2, i2, r3, i3, r4, i4, r5, i5; r3 = v0[nx].re*wave[dw].re - v0[nx].im*wave[dw].im; i3 = v0[nx].re*wave[dw].im + v0[nx].im*wave[dw].re; r2 = v2[0].re*wave[dw*4].re - v2[0].im*wave[dw*4].im; i2 = v2[0].re*wave[dw*4].im + v2[0].im*wave[dw*4].re; r1 = r3 + r2; i1 = i3 + i2; r3 -= r2; i3 -= i2; r4 = v1[nx].re*wave[dw*3].re - v1[nx].im*wave[dw*3].im; i4 = v1[nx].re*wave[dw*3].im + v1[nx].im*wave[dw*3].re; r0 = v1[0].re*wave[dw*2].re - v1[0].im*wave[dw*2].im; i0 = v1[0].re*wave[dw*2].im + v1[0].im*wave[dw*2].re; r2 = r4 + r0; i2 = i4 + i0; r4 -= r0; i4 -= i0; r0 = v0[0].re; i0 = v0[0].im; r5 = r1 + r2; i5 = i1 + i2; v0[0].re = r0 + r5; v0[0].im = i0 + i5; r0 -= (T)0.25*r5; i0 -= (T)0.25*i5; r1 = fft5_2*(r1 - r2); i1 = fft5_2*(i1 - i2); r2 = -fft5_3*(i3 + i4); i2 = fft5_3*(r3 + r4); i3 *= -fft5_5; r3 *= fft5_5; i4 *= -fft5_4; r4 *= fft5_4; r5 = r2 + i3; i5 = i2 + r3; r2 -= i4; i2 -= r4; r3 = r0 + r1; i3 = i0 + i1; r0 -= r1; i0 -= i1; v0[nx].re = r3 + r2; v0[nx].im = i3 + i2; v2[0].re = r3 - r2; v2[0].im = i3 - i2; v1[0].re = r0 + r5; v1[0].im = i0 + i5; v1[nx].re = r0 - r5; v1[nx].im = i0 - i5; } } } else { // radix-"factor" - an odd number int p, q, factor2 = (factor - 1)/2; int d, dd, dw_f = tab_size/factor; Complex* a = buf; Complex* b = buf + factor2; for( i = 0; i < n0; i += n ) { for( j = 0, dw = 0; j < nx; j++, dw += dw0 ) { Complex* v = dst + i + j; Complex v_0 = v[0]; Complex vn_0 = v_0; if( j == 0 ) { for( p = 1, k = nx; p <= factor2; p++, k += nx ) { T r0 = v[k].re + v[n-k].re; T i0 = v[k].im - v[n-k].im; T r1 = v[k].re - v[n-k].re; T i1 = v[k].im + v[n-k].im; vn_0.re += r0; vn_0.im += i1; a[p-1].re = r0; a[p-1].im = i0; b[p-1].re = r1; b[p-1].im = i1; } } else { const Complex* wave_ = wave + dw*factor; d = dw; for( p = 1, k = nx; p <= factor2; p++, k += nx, d += dw ) { T r2 = v[k].re*wave[d].re - v[k].im*wave[d].im; T i2 = v[k].re*wave[d].im + v[k].im*wave[d].re; T r1 = v[n-k].re*wave_[-d].re - v[n-k].im*wave_[-d].im; T i1 = v[n-k].re*wave_[-d].im + v[n-k].im*wave_[-d].re; T r0 = r2 + r1; T i0 = i2 - i1; r1 = r2 - r1; i1 = i2 + i1; vn_0.re += r0; vn_0.im += i1; a[p-1].re = r0; a[p-1].im = i0; b[p-1].re = r1; b[p-1].im = i1; } } v[0] = vn_0; for( p = 1, k = nx; p <= factor2; p++, k += nx ) { Complex s0 = v_0, s1 = v_0; d = dd = dw_f*p; for( q = 0; q < factor2; q++ ) { T r0 = wave[d].re * a[q].re; T i0 = wave[d].im * a[q].im; T r1 = wave[d].re * b[q].im; T i1 = wave[d].im * b[q].re; s1.re += r0 + i0; s0.re += r0 - i0; s1.im += r1 - i1; s0.im += r1 + i1; d += dd; d -= -(d >= tab_size) & tab_size; } v[k] = s0; v[n-k] = s1; } } } } } if( scale != 1 ) { T re_scale = scale, im_scale = scale; if( inv ) im_scale = -im_scale; for( i = 0; i < n0; i++ ) { T t0 = dst[i].re*re_scale; T t1 = dst[i].im*im_scale; dst[i].re = t0; dst[i].im = t1; } } else if( inv ) { for( i = 0; i <= n0 - 2; i += 2 ) { T t0 = -dst[i].im; T t1 = -dst[i+1].im; dst[i].im = t0; dst[i+1].im = t1; } if( i < n0 ) dst[n0-1].im = -dst[n0-1].im; } } /* FFT of real vector output vector format: re(0), re(1), im(1), ... , re(n/2-1), im((n+1)/2-1) [, re((n+1)/2)] OR ... re(0), 0, re(1), im(1), ..., re(n/2-1), im((n+1)/2-1) [, re((n+1)/2), 0] */ template static void RealDFT( const T* src, T* dst, int n, int nf, int* factors, const int* itab, const Complex* wave, int tab_size, const void* #ifdef HAVE_IPP spec #endif , Complex* buf, int flags, double _scale ) { int complex_output = (flags & DFT_COMPLEX_INPUT_OR_OUTPUT) != 0; T scale = (T)_scale; int j, n2 = n >> 1; dst += complex_output; #ifdef HAVE_IPP if( spec ) { ippsDFTFwd_RToPack( src, dst, spec, (uchar*)buf ); goto finalize; } #endif assert( tab_size == n ); if( n == 1 ) { dst[0] = src[0]*scale; } else if( n == 2 ) { T t = (src[0] + src[1])*scale; dst[1] = (src[0] - src[1])*scale; dst[0] = t; } else if( n & 1 ) { dst -= complex_output; Complex* _dst = (Complex*)dst; _dst[0].re = src[0]*scale; _dst[0].im = 0; for( j = 1; j < n; j += 2 ) { T t0 = src[itab[j]]*scale; T t1 = src[itab[j+1]]*scale; _dst[j].re = t0; _dst[j].im = 0; _dst[j+1].re = t1; _dst[j+1].im = 0; } DFT( _dst, _dst, n, nf, factors, itab, wave, tab_size, 0, buf, DFT_NO_PERMUTE, 1 ); if( !complex_output ) dst[1] = dst[0]; } else { T t0, t; T h1_re, h1_im, h2_re, h2_im; T scale2 = scale*(T)0.5; factors[0] >>= 1; DFT( (Complex*)src, (Complex*)dst, n2, nf - (factors[0] == 1), factors + (factors[0] == 1), itab, wave, tab_size, 0, buf, 0, 1 ); factors[0] <<= 1; t = dst[0] - dst[1]; dst[0] = (dst[0] + dst[1])*scale; dst[1] = t*scale; t0 = dst[n2]; t = dst[n-1]; dst[n-1] = dst[1]; for( j = 2, wave++; j < n2; j += 2, wave++ ) { /* calc odd */ h2_re = scale2*(dst[j+1] + t); h2_im = scale2*(dst[n-j] - dst[j]); /* calc even */ h1_re = scale2*(dst[j] + dst[n-j]); h1_im = scale2*(dst[j+1] - t); /* rotate */ t = h2_re*wave->re - h2_im*wave->im; h2_im = h2_re*wave->im + h2_im*wave->re; h2_re = t; t = dst[n-j-1]; dst[j-1] = h1_re + h2_re; dst[n-j-1] = h1_re - h2_re; dst[j] = h1_im + h2_im; dst[n-j] = h2_im - h1_im; } if( j <= n2 ) { dst[n2-1] = t0*scale; dst[n2] = -t*scale; } } #ifdef HAVE_IPP finalize: #endif if( complex_output && (n & 1) == 0 ) { dst[-1] = dst[0]; dst[0] = 0; if( (n & 1) == 0 ) dst[n] = 0; } } /* Inverse FFT of complex conjugate-symmetric vector input vector format: re[0], re[1], im[1], ... , re[n/2-1], im[n/2-1], re[n/2] OR re(0), 0, re(1), im(1), ..., re(n/2-1), im((n+1)/2-1) [, re((n+1)/2), 0] */ template static void CCSIDFT( const T* src, T* dst, int n, int nf, int* factors, const int* itab, const Complex* wave, int tab_size, const void* #ifdef HAVE_IPP spec #endif , Complex* buf, int flags, double _scale ) { int complex_input = (flags & DFT_COMPLEX_INPUT_OR_OUTPUT) != 0; int j, k, n2 = (n+1) >> 1; T scale = (T)_scale; T save_s1 = 0.; T t0, t1, t2, t3, t; assert( tab_size == n ); if( complex_input ) { assert( src != dst ); save_s1 = src[1]; ((T*)src)[1] = src[0]; src++; } #ifdef HAVE_IPP if( spec ) { ippsDFTInv_PackToR( src, dst, spec, (uchar*)buf ); goto finalize; } #endif if( n == 1 ) { dst[0] = (T)(src[0]*scale); } else if( n == 2 ) { t = (src[0] + src[1])*scale; dst[1] = (src[0] - src[1])*scale; dst[0] = t; } else if( n & 1 ) { Complex* _src = (Complex*)(src-1); Complex* _dst = (Complex*)dst; _dst[0].re = src[0]; _dst[0].im = 0; for( j = 1; j < n2; j++ ) { int k0 = itab[j], k1 = itab[n-j]; t0 = _src[j].re; t1 = _src[j].im; _dst[k0].re = t0; _dst[k0].im = -t1; _dst[k1].re = t0; _dst[k1].im = t1; } DFT( _dst, _dst, n, nf, factors, itab, wave, tab_size, 0, buf, DFT_NO_PERMUTE, 1. ); dst[0] *= scale; for( j = 1; j < n; j += 2 ) { t0 = dst[j*2]*scale; t1 = dst[j*2+2]*scale; dst[j] = t0; dst[j+1] = t1; } } else { int inplace = src == dst; const Complex* w = wave; t = src[1]; t0 = (src[0] + src[n-1]); t1 = (src[n-1] - src[0]); dst[0] = t0; dst[1] = t1; for( j = 2, w++; j < n2; j += 2, w++ ) { T h1_re, h1_im, h2_re, h2_im; h1_re = (t + src[n-j-1]); h1_im = (src[j] - src[n-j]); h2_re = (t - src[n-j-1]); h2_im = (src[j] + src[n-j]); t = h2_re*w->re + h2_im*w->im; h2_im = h2_im*w->re - h2_re*w->im; h2_re = t; t = src[j+1]; t0 = h1_re - h2_im; t1 = -h1_im - h2_re; t2 = h1_re + h2_im; t3 = h1_im - h2_re; if( inplace ) { dst[j] = t0; dst[j+1] = t1; dst[n-j] = t2; dst[n-j+1]= t3; } else { int j2 = j >> 1; k = itab[j2]; dst[k] = t0; dst[k+1] = t1; k = itab[n2-j2]; dst[k] = t2; dst[k+1]= t3; } } if( j <= n2 ) { t0 = t*2; t1 = src[n2]*2; if( inplace ) { dst[n2] = t0; dst[n2+1] = t1; } else { k = itab[n2]; dst[k*2] = t0; dst[k*2+1] = t1; } } factors[0] >>= 1; DFT( (Complex*)dst, (Complex*)dst, n2, nf - (factors[0] == 1), factors + (factors[0] == 1), itab, wave, tab_size, 0, buf, inplace ? 0 : DFT_NO_PERMUTE, 1. ); factors[0] <<= 1; for( j = 0; j < n; j += 2 ) { t0 = dst[j]*scale; t1 = dst[j+1]*(-scale); dst[j] = t0; dst[j+1] = t1; } } #ifdef HAVE_IPP finalize: #endif if( complex_input ) ((T*)src)[0] = (T)save_s1; } static void CopyColumn( const uchar* _src, size_t src_step, uchar* _dst, size_t dst_step, int len, size_t elem_size ) { int i, t0, t1; const int* src = (const int*)_src; int* dst = (int*)_dst; src_step /= sizeof(src[0]); dst_step /= sizeof(dst[0]); if( elem_size == sizeof(int) ) { for( i = 0; i < len; i++, src += src_step, dst += dst_step ) dst[0] = src[0]; } else if( elem_size == sizeof(int)*2 ) { for( i = 0; i < len; i++, src += src_step, dst += dst_step ) { t0 = src[0]; t1 = src[1]; dst[0] = t0; dst[1] = t1; } } else if( elem_size == sizeof(int)*4 ) { for( i = 0; i < len; i++, src += src_step, dst += dst_step ) { t0 = src[0]; t1 = src[1]; dst[0] = t0; dst[1] = t1; t0 = src[2]; t1 = src[3]; dst[2] = t0; dst[3] = t1; } } } static void CopyFrom2Columns( const uchar* _src, size_t src_step, uchar* _dst0, uchar* _dst1, int len, size_t elem_size ) { int i, t0, t1; const int* src = (const int*)_src; int* dst0 = (int*)_dst0; int* dst1 = (int*)_dst1; src_step /= sizeof(src[0]); if( elem_size == sizeof(int) ) { for( i = 0; i < len; i++, src += src_step ) { t0 = src[0]; t1 = src[1]; dst0[i] = t0; dst1[i] = t1; } } else if( elem_size == sizeof(int)*2 ) { for( i = 0; i < len*2; i += 2, src += src_step ) { t0 = src[0]; t1 = src[1]; dst0[i] = t0; dst0[i+1] = t1; t0 = src[2]; t1 = src[3]; dst1[i] = t0; dst1[i+1] = t1; } } else if( elem_size == sizeof(int)*4 ) { for( i = 0; i < len*4; i += 4, src += src_step ) { t0 = src[0]; t1 = src[1]; dst0[i] = t0; dst0[i+1] = t1; t0 = src[2]; t1 = src[3]; dst0[i+2] = t0; dst0[i+3] = t1; t0 = src[4]; t1 = src[5]; dst1[i] = t0; dst1[i+1] = t1; t0 = src[6]; t1 = src[7]; dst1[i+2] = t0; dst1[i+3] = t1; } } } static void CopyTo2Columns( const uchar* _src0, const uchar* _src1, uchar* _dst, size_t dst_step, int len, size_t elem_size ) { int i, t0, t1; const int* src0 = (const int*)_src0; const int* src1 = (const int*)_src1; int* dst = (int*)_dst; dst_step /= sizeof(dst[0]); if( elem_size == sizeof(int) ) { for( i = 0; i < len; i++, dst += dst_step ) { t0 = src0[i]; t1 = src1[i]; dst[0] = t0; dst[1] = t1; } } else if( elem_size == sizeof(int)*2 ) { for( i = 0; i < len*2; i += 2, dst += dst_step ) { t0 = src0[i]; t1 = src0[i+1]; dst[0] = t0; dst[1] = t1; t0 = src1[i]; t1 = src1[i+1]; dst[2] = t0; dst[3] = t1; } } else if( elem_size == sizeof(int)*4 ) { for( i = 0; i < len*4; i += 4, dst += dst_step ) { t0 = src0[i]; t1 = src0[i+1]; dst[0] = t0; dst[1] = t1; t0 = src0[i+2]; t1 = src0[i+3]; dst[2] = t0; dst[3] = t1; t0 = src1[i]; t1 = src1[i+1]; dst[4] = t0; dst[5] = t1; t0 = src1[i+2]; t1 = src1[i+3]; dst[6] = t0; dst[7] = t1; } } } static void ExpandCCS( uchar* _ptr, int len, int elem_size ) { int i; _ptr -= elem_size; memcpy( _ptr, _ptr + elem_size, elem_size ); memset( _ptr + elem_size, 0, elem_size ); if( (len & 1) == 0 ) memset( _ptr + (len+1)*elem_size, 0, elem_size ); if( elem_size == sizeof(float) ) { Complex* ptr = (Complex*)_ptr; for( i = 1; i < (len+1)/2; i++ ) { Complex t; t.re = ptr[i].re; t.im = -ptr[i].im; ptr[len-i] = t; } } else { Complex* ptr = (Complex*)_ptr; for( i = 1; i < (len+1)/2; i++ ) { Complex t; t.re = ptr[i].re; t.im = -ptr[i].im; ptr[len-i] = t; } } } typedef void (*DFTFunc)( const void* src, void* dst, int n, int nf, int* factors, const int* itab, const void* wave, int tab_size, const void* spec, void* buf, int inv, double scale ); static void DFT_32f( const Complexf* src, Complexf* dst, int n, int nf, const int* factors, const int* itab, const Complexf* wave, int tab_size, const void* spec, Complexf* buf, int flags, double scale ) { DFT(src, dst, n, nf, factors, itab, wave, tab_size, spec, buf, flags, scale); } static void DFT_64f( const Complexd* src, Complexd* dst, int n, int nf, const int* factors, const int* itab, const Complexd* wave, int tab_size, const void* spec, Complexd* buf, int flags, double scale ) { DFT(src, dst, n, nf, factors, itab, wave, tab_size, spec, buf, flags, scale); } static void RealDFT_32f( const float* src, float* dst, int n, int nf, int* factors, const int* itab, const Complexf* wave, int tab_size, const void* spec, Complexf* buf, int flags, double scale ) { RealDFT( src, dst, n, nf, factors, itab, wave, tab_size, spec, buf, flags, scale); } static void RealDFT_64f( const double* src, double* dst, int n, int nf, int* factors, const int* itab, const Complexd* wave, int tab_size, const void* spec, Complexd* buf, int flags, double scale ) { RealDFT( src, dst, n, nf, factors, itab, wave, tab_size, spec, buf, flags, scale); } static void CCSIDFT_32f( const float* src, float* dst, int n, int nf, int* factors, const int* itab, const Complexf* wave, int tab_size, const void* spec, Complexf* buf, int flags, double scale ) { CCSIDFT( src, dst, n, nf, factors, itab, wave, tab_size, spec, buf, flags, scale); } static void CCSIDFT_64f( const double* src, double* dst, int n, int nf, int* factors, const int* itab, const Complexd* wave, int tab_size, const void* spec, Complexd* buf, int flags, double scale ) { CCSIDFT( src, dst, n, nf, factors, itab, wave, tab_size, spec, buf, flags, scale); } } void cv::dft( InputArray _src0, OutputArray _dst, int flags, int nonzero_rows ) { static DFTFunc dft_tbl[6] = { (DFTFunc)DFT_32f, (DFTFunc)RealDFT_32f, (DFTFunc)CCSIDFT_32f, (DFTFunc)DFT_64f, (DFTFunc)RealDFT_64f, (DFTFunc)CCSIDFT_64f }; AutoBuffer buf; void *spec = 0; Mat src0 = _src0.getMat(), src = src0; int prev_len = 0, stage = 0; bool inv = (flags & DFT_INVERSE) != 0; int nf = 0, real_transform = src.channels() == 1 || (inv && (flags & DFT_REAL_OUTPUT)!=0); int type = src.type(), depth = src.depth(); int elem_size = (int)src.elemSize1(), complex_elem_size = elem_size*2; int factors[34]; bool inplace_transform = false; #ifdef HAVE_IPP void *spec_r = 0, *spec_c = 0; int ipp_norm_flag = !(flags & DFT_SCALE) ? 8 : inv ? 2 : 1; #endif CV_Assert( type == CV_32FC1 || type == CV_32FC2 || type == CV_64FC1 || type == CV_64FC2 ); if( !inv && src.channels() == 1 && (flags & DFT_COMPLEX_OUTPUT) ) _dst.create( src.size(), CV_MAKETYPE(depth, 2) ); else if( inv && src.channels() == 2 && (flags & DFT_REAL_OUTPUT) ) _dst.create( src.size(), depth ); else _dst.create( src.size(), type ); Mat dst = _dst.getMat(); if( !real_transform ) elem_size = complex_elem_size; if( src.cols == 1 && nonzero_rows > 0 ) CV_Error( CV_StsNotImplemented, "This mode (using nonzero_rows with a single-column matrix) breaks the function's logic, so it is prohibited.\n" "For fast convolution/correlation use 2-column matrix or single-row matrix instead" ); // determine, which transform to do first - row-wise // (stage 0) or column-wise (stage 1) transform if( !(flags & DFT_ROWS) && src.rows > 1 && ((src.cols == 1 && (!src.isContinuous() || !dst.isContinuous())) || (src.cols > 1 && inv && real_transform)) ) stage = 1; for(;;) { double scale = 1; uchar* wave = 0; int* itab = 0; uchar* ptr; int i, len, count, sz = 0; int use_buf = 0, odd_real = 0; DFTFunc dft_func; if( stage == 0 ) // row-wise transform { len = !inv ? src.cols : dst.cols; count = src.rows; if( len == 1 && !(flags & DFT_ROWS) ) { len = !inv ? src.rows : dst.rows; count = 1; } odd_real = real_transform && (len & 1); } else { len = dst.rows; count = !inv ? src0.cols : dst.cols; sz = 2*len*complex_elem_size; } spec = 0; #ifdef HAVE_IPP if( len*count >= 64 ) // use IPP DFT if available { int ipp_sz = 0; if( real_transform && stage == 0 ) { if( depth == CV_32F ) { if( spec_r ) IPPI_CALL( ippsDFTFree_R_32f( (IppsDFTSpec_R_32f*)spec_r )); IPPI_CALL( ippsDFTInitAlloc_R_32f( (IppsDFTSpec_R_32f**)&spec_r, len, ipp_norm_flag, ippAlgHintNone )); IPPI_CALL( ippsDFTGetBufSize_R_32f( (IppsDFTSpec_R_32f*)spec_r, &ipp_sz )); } else { if( spec_r ) IPPI_CALL( ippsDFTFree_R_64f( (IppsDFTSpec_R_64f*)spec_r )); IPPI_CALL( ippsDFTInitAlloc_R_64f( (IppsDFTSpec_R_64f**)&spec_r, len, ipp_norm_flag, ippAlgHintNone )); IPPI_CALL( ippsDFTGetBufSize_R_64f( (IppsDFTSpec_R_64f*)spec_r, &ipp_sz )); } spec = spec_r; } else { if( depth == CV_32F ) { if( spec_c ) IPPI_CALL( ippsDFTFree_C_32fc( (IppsDFTSpec_C_32fc*)spec_c )); IPPI_CALL( ippsDFTInitAlloc_C_32fc( (IppsDFTSpec_C_32fc**)&spec_c, len, ipp_norm_flag, ippAlgHintNone )); IPPI_CALL( ippsDFTGetBufSize_C_32fc( (IppsDFTSpec_C_32fc*)spec_c, &ipp_sz )); } else { if( spec_c ) IPPI_CALL( ippsDFTFree_C_64fc( (IppsDFTSpec_C_64fc*)spec_c )); IPPI_CALL( ippsDFTInitAlloc_C_64fc( (IppsDFTSpec_C_64fc**)&spec_c, len, ipp_norm_flag, ippAlgHintNone )); IPPI_CALL( ippsDFTGetBufSize_C_64fc( (IppsDFTSpec_C_64fc*)spec_c, &ipp_sz )); } spec = spec_c; } sz += ipp_sz; } else #endif { if( len != prev_len ) nf = DFTFactorize( len, factors ); inplace_transform = factors[0] == factors[nf-1]; sz += len*(complex_elem_size + sizeof(int)); i = nf > 1 && (factors[0] & 1) == 0; if( (factors[i] & 1) != 0 && factors[i] > 5 ) sz += (factors[i]+1)*complex_elem_size; if( (stage == 0 && ((src.data == dst.data && !inplace_transform) || odd_real)) || (stage == 1 && !inplace_transform) ) { use_buf = 1; sz += len*complex_elem_size; } } ptr = (uchar*)buf; buf.allocate( sz + 32 ); if( ptr != (uchar*)buf ) prev_len = 0; // because we release the buffer, // force recalculation of // twiddle factors and permutation table ptr = (uchar*)buf; if( !spec ) { wave = ptr; ptr += len*complex_elem_size; itab = (int*)ptr; ptr = (uchar*)cvAlignPtr( ptr + len*sizeof(int), 16 ); if( len != prev_len || (!inplace_transform && inv && real_transform)) DFTInit( len, nf, factors, itab, complex_elem_size, wave, stage == 0 && inv && real_transform ); // otherwise reuse the tables calculated on the previous stage } if( stage == 0 ) { uchar* tmp_buf = 0; int dptr_offset = 0; int dst_full_len = len*elem_size; int _flags = (int)inv + (src.channels() != dst.channels() ? DFT_COMPLEX_INPUT_OR_OUTPUT : 0); if( use_buf ) { tmp_buf = ptr; ptr += len*complex_elem_size; if( odd_real && !inv && len > 1 && !(_flags & DFT_COMPLEX_INPUT_OR_OUTPUT)) dptr_offset = elem_size; } if( !inv && (_flags & DFT_COMPLEX_INPUT_OR_OUTPUT) ) dst_full_len += (len & 1) ? elem_size : complex_elem_size; dft_func = dft_tbl[(!real_transform ? 0 : !inv ? 1 : 2) + (depth == CV_64F)*3]; if( count > 1 && !(flags & DFT_ROWS) && (!inv || !real_transform) ) stage = 1; else if( flags & CV_DXT_SCALE ) scale = 1./(len * (flags & DFT_ROWS ? 1 : count)); if( nonzero_rows <= 0 || nonzero_rows > count ) nonzero_rows = count; for( i = 0; i < nonzero_rows; i++ ) { uchar* sptr = src.data + i*src.step; uchar* dptr0 = dst.data + i*dst.step; uchar* dptr = dptr0; if( tmp_buf ) dptr = tmp_buf; dft_func( sptr, dptr, len, nf, factors, itab, wave, len, spec, ptr, _flags, scale ); if( dptr != dptr0 ) memcpy( dptr0, dptr + dptr_offset, dst_full_len ); } for( ; i < count; i++ ) { uchar* dptr0 = dst.data + i*dst.step; memset( dptr0, 0, dst_full_len ); } if( stage != 1 ) break; src = dst; } else { int a = 0, b = count; uchar *buf0, *buf1, *dbuf0, *dbuf1; uchar* sptr0 = src.data; uchar* dptr0 = dst.data; buf0 = ptr; ptr += len*complex_elem_size; buf1 = ptr; ptr += len*complex_elem_size; dbuf0 = buf0, dbuf1 = buf1; if( use_buf ) { dbuf1 = ptr; dbuf0 = buf1; ptr += len*complex_elem_size; } dft_func = dft_tbl[(depth == CV_64F)*3]; if( real_transform && inv && src.cols > 1 ) stage = 0; else if( flags & CV_DXT_SCALE ) scale = 1./(len * count); if( real_transform ) { int even; a = 1; even = (count & 1) == 0; b = (count+1)/2; if( !inv ) { memset( buf0, 0, len*complex_elem_size ); CopyColumn( sptr0, src.step, buf0, complex_elem_size, len, elem_size ); sptr0 += dst.channels()*elem_size; if( even ) { memset( buf1, 0, len*complex_elem_size ); CopyColumn( sptr0 + (count-2)*elem_size, src.step, buf1, complex_elem_size, len, elem_size ); } } else if( src.channels() == 1 ) { CopyColumn( sptr0, src.step, buf0 + elem_size, elem_size, len, elem_size ); ExpandCCS( buf0 + elem_size, len, elem_size ); if( even ) { CopyColumn( sptr0 + (count-1)*elem_size, src.step, buf1 + elem_size, elem_size, len, elem_size ); ExpandCCS( buf1 + elem_size, len, elem_size ); } sptr0 += elem_size; } else { CopyColumn( sptr0, src.step, buf0, complex_elem_size, len, complex_elem_size ); if( even ) { CopyColumn( sptr0 + b*complex_elem_size, src.step, buf1, complex_elem_size, len, complex_elem_size ); } sptr0 += complex_elem_size; } if( even ) dft_func( buf1, dbuf1, len, nf, factors, itab, wave, len, spec, ptr, inv, scale ); dft_func( buf0, dbuf0, len, nf, factors, itab, wave, len, spec, ptr, inv, scale ); if( dst.channels() == 1 ) { if( !inv ) { // copy the half of output vector to the first/last column. // before doing that, defgragment the vector memcpy( dbuf0 + elem_size, dbuf0, elem_size ); CopyColumn( dbuf0 + elem_size, elem_size, dptr0, dst.step, len, elem_size ); if( even ) { memcpy( dbuf1 + elem_size, dbuf1, elem_size ); CopyColumn( dbuf1 + elem_size, elem_size, dptr0 + (count-1)*elem_size, dst.step, len, elem_size ); } dptr0 += elem_size; } else { // copy the real part of the complex vector to the first/last column CopyColumn( dbuf0, complex_elem_size, dptr0, dst.step, len, elem_size ); if( even ) CopyColumn( dbuf1, complex_elem_size, dptr0 + (count-1)*elem_size, dst.step, len, elem_size ); dptr0 += elem_size; } } else { assert( !inv ); CopyColumn( dbuf0, complex_elem_size, dptr0, dst.step, len, complex_elem_size ); if( even ) CopyColumn( dbuf1, complex_elem_size, dptr0 + b*complex_elem_size, dst.step, len, complex_elem_size ); dptr0 += complex_elem_size; } } for( i = a; i < b; i += 2 ) { if( i+1 < b ) { CopyFrom2Columns( sptr0, src.step, buf0, buf1, len, complex_elem_size ); dft_func( buf1, dbuf1, len, nf, factors, itab, wave, len, spec, ptr, inv, scale ); } else CopyColumn( sptr0, src.step, buf0, complex_elem_size, len, complex_elem_size ); dft_func( buf0, dbuf0, len, nf, factors, itab, wave, len, spec, ptr, inv, scale ); if( i+1 < b ) CopyTo2Columns( dbuf0, dbuf1, dptr0, dst.step, len, complex_elem_size ); else CopyColumn( dbuf0, complex_elem_size, dptr0, dst.step, len, complex_elem_size ); sptr0 += 2*complex_elem_size; dptr0 += 2*complex_elem_size; } if( stage != 0 ) break; src = dst; } } #ifdef HAVE_IPP if( spec_c ) { if( depth == CV_32F ) ippsDFTFree_C_32fc( (IppsDFTSpec_C_32fc*)spec_c ); else ippsDFTFree_C_64fc( (IppsDFTSpec_C_64fc*)spec_c ); } if( spec_r ) { if( depth == CV_32F ) ippsDFTFree_R_32f( (IppsDFTSpec_R_32f*)spec_r ); else ippsDFTFree_R_64f( (IppsDFTSpec_R_64f*)spec_r ); } #endif } void cv::idft( InputArray src, OutputArray dst, int flags, int nonzero_rows ) { dft( src, dst, flags | DFT_INVERSE, nonzero_rows ); } void cv::mulSpectrums( InputArray _srcA, InputArray _srcB, OutputArray _dst, int flags, bool conjB ) { Mat srcA = _srcA.getMat(), srcB = _srcB.getMat(); int depth = srcA.depth(), cn = srcA.channels(), type = srcA.type(); int rows = srcA.rows, cols = srcA.cols; int j, k; CV_Assert( type == srcB.type() && srcA.size() == srcB.size() ); CV_Assert( type == CV_32FC1 || type == CV_32FC2 || type == CV_64FC1 || type == CV_64FC2 ); _dst.create( srcA.rows, srcA.cols, type ); Mat dst = _dst.getMat(); bool is_1d = (flags & DFT_ROWS) || (rows == 1 || (cols == 1 && srcA.isContinuous() && srcB.isContinuous() && dst.isContinuous())); if( is_1d && !(flags & DFT_ROWS) ) cols = cols + rows - 1, rows = 1; int ncols = cols*cn; int j0 = cn == 1; int j1 = ncols - (cols % 2 == 0 && cn == 1); if( depth == CV_32F ) { const float* dataA = (const float*)srcA.data; const float* dataB = (const float*)srcB.data; float* dataC = (float*)dst.data; size_t stepA = srcA.step/sizeof(dataA[0]); size_t stepB = srcB.step/sizeof(dataB[0]); size_t stepC = dst.step/sizeof(dataC[0]); if( !is_1d && cn == 1 ) { for( k = 0; k < (cols % 2 ? 1 : 2); k++ ) { if( k == 1 ) dataA += cols - 1, dataB += cols - 1, dataC += cols - 1; dataC[0] = dataA[0]*dataB[0]; if( rows % 2 == 0 ) dataC[(rows-1)*stepC] = dataA[(rows-1)*stepA]*dataB[(rows-1)*stepB]; if( !conjB ) for( j = 1; j <= rows - 2; j += 2 ) { double re = (double)dataA[j*stepA]*dataB[j*stepB] - (double)dataA[(j+1)*stepA]*dataB[(j+1)*stepB]; double im = (double)dataA[j*stepA]*dataB[(j+1)*stepB] + (double)dataA[(j+1)*stepA]*dataB[j*stepB]; dataC[j*stepC] = (float)re; dataC[(j+1)*stepC] = (float)im; } else for( j = 1; j <= rows - 2; j += 2 ) { double re = (double)dataA[j*stepA]*dataB[j*stepB] + (double)dataA[(j+1)*stepA]*dataB[(j+1)*stepB]; double im = (double)dataA[(j+1)*stepA]*dataB[j*stepB] - (double)dataA[j*stepA]*dataB[(j+1)*stepB]; dataC[j*stepC] = (float)re; dataC[(j+1)*stepC] = (float)im; } if( k == 1 ) dataA -= cols - 1, dataB -= cols - 1, dataC -= cols - 1; } } for( ; rows--; dataA += stepA, dataB += stepB, dataC += stepC ) { if( is_1d && cn == 1 ) { dataC[0] = dataA[0]*dataB[0]; if( cols % 2 == 0 ) dataC[j1] = dataA[j1]*dataB[j1]; } if( !conjB ) for( j = j0; j < j1; j += 2 ) { double re = (double)dataA[j]*dataB[j] - (double)dataA[j+1]*dataB[j+1]; double im = (double)dataA[j+1]*dataB[j] + (double)dataA[j]*dataB[j+1]; dataC[j] = (float)re; dataC[j+1] = (float)im; } else for( j = j0; j < j1; j += 2 ) { double re = (double)dataA[j]*dataB[j] + (double)dataA[j+1]*dataB[j+1]; double im = (double)dataA[j+1]*dataB[j] - (double)dataA[j]*dataB[j+1]; dataC[j] = (float)re; dataC[j+1] = (float)im; } } } else { const double* dataA = (const double*)srcA.data; const double* dataB = (const double*)srcB.data; double* dataC = (double*)dst.data; size_t stepA = srcA.step/sizeof(dataA[0]); size_t stepB = srcB.step/sizeof(dataB[0]); size_t stepC = dst.step/sizeof(dataC[0]); if( !is_1d && cn == 1 ) { for( k = 0; k < (cols % 2 ? 1 : 2); k++ ) { if( k == 1 ) dataA += cols - 1, dataB += cols - 1, dataC += cols - 1; dataC[0] = dataA[0]*dataB[0]; if( rows % 2 == 0 ) dataC[(rows-1)*stepC] = dataA[(rows-1)*stepA]*dataB[(rows-1)*stepB]; if( !conjB ) for( j = 1; j <= rows - 2; j += 2 ) { double re = dataA[j*stepA]*dataB[j*stepB] - dataA[(j+1)*stepA]*dataB[(j+1)*stepB]; double im = dataA[j*stepA]*dataB[(j+1)*stepB] + dataA[(j+1)*stepA]*dataB[j*stepB]; dataC[j*stepC] = re; dataC[(j+1)*stepC] = im; } else for( j = 1; j <= rows - 2; j += 2 ) { double re = dataA[j*stepA]*dataB[j*stepB] + dataA[(j+1)*stepA]*dataB[(j+1)*stepB]; double im = dataA[(j+1)*stepA]*dataB[j*stepB] - dataA[j*stepA]*dataB[(j+1)*stepB]; dataC[j*stepC] = re; dataC[(j+1)*stepC] = im; } if( k == 1 ) dataA -= cols - 1, dataB -= cols - 1, dataC -= cols - 1; } } for( ; rows--; dataA += stepA, dataB += stepB, dataC += stepC ) { if( is_1d && cn == 1 ) { dataC[0] = dataA[0]*dataB[0]; if( cols % 2 == 0 ) dataC[j1] = dataA[j1]*dataB[j1]; } if( !conjB ) for( j = j0; j < j1; j += 2 ) { double re = dataA[j]*dataB[j] - dataA[j+1]*dataB[j+1]; double im = dataA[j+1]*dataB[j] + dataA[j]*dataB[j+1]; dataC[j] = re; dataC[j+1] = im; } else for( j = j0; j < j1; j += 2 ) { double re = dataA[j]*dataB[j] + dataA[j+1]*dataB[j+1]; double im = dataA[j+1]*dataB[j] - dataA[j]*dataB[j+1]; dataC[j] = re; dataC[j+1] = im; } } } } /****************************************************************************************\ Discrete Cosine Transform \****************************************************************************************/ namespace cv { /* DCT is calculated using DFT, as described here: http://www.ece.utexas.edu/~bevans/courses/ee381k/lectures/09_DCT/lecture9/: */ template static void DCT( const T* src, int src_step, T* dft_src, T* dft_dst, T* dst, int dst_step, int n, int nf, int* factors, const int* itab, const Complex* dft_wave, const Complex* dct_wave, const void* spec, Complex* buf ) { static const T sin_45 = (T)0.70710678118654752440084436210485; int j, n2 = n >> 1; src_step /= sizeof(src[0]); dst_step /= sizeof(dst[0]); T* dst1 = dst + (n-1)*dst_step; if( n == 1 ) { dst[0] = src[0]; return; } for( j = 0; j < n2; j++, src += src_step*2 ) { dft_src[j] = src[0]; dft_src[n-j-1] = src[src_step]; } RealDFT( dft_src, dft_dst, n, nf, factors, itab, dft_wave, n, spec, buf, 0, 1.0 ); src = dft_dst; dst[0] = (T)(src[0]*dct_wave->re*sin_45); dst += dst_step; for( j = 1, dct_wave++; j < n2; j++, dct_wave++, dst += dst_step, dst1 -= dst_step ) { T t0 = dct_wave->re*src[j*2-1] - dct_wave->im*src[j*2]; T t1 = -dct_wave->im*src[j*2-1] - dct_wave->re*src[j*2]; dst[0] = t0; dst1[0] = t1; } dst[0] = src[n-1]*dct_wave->re; } template static void IDCT( const T* src, int src_step, T* dft_src, T* dft_dst, T* dst, int dst_step, int n, int nf, int* factors, const int* itab, const Complex* dft_wave, const Complex* dct_wave, const void* spec, Complex* buf ) { static const T sin_45 = (T)0.70710678118654752440084436210485; int j, n2 = n >> 1; src_step /= sizeof(src[0]); dst_step /= sizeof(dst[0]); const T* src1 = src + (n-1)*src_step; if( n == 1 ) { dst[0] = src[0]; return; } dft_src[0] = (T)(src[0]*2*dct_wave->re*sin_45); src += src_step; for( j = 1, dct_wave++; j < n2; j++, dct_wave++, src += src_step, src1 -= src_step ) { T t0 = dct_wave->re*src[0] - dct_wave->im*src1[0]; T t1 = -dct_wave->im*src[0] - dct_wave->re*src1[0]; dft_src[j*2-1] = t0; dft_src[j*2] = t1; } dft_src[n-1] = (T)(src[0]*2*dct_wave->re); CCSIDFT( dft_src, dft_dst, n, nf, factors, itab, dft_wave, n, spec, buf, 0, 1.0 ); for( j = 0; j < n2; j++, dst += dst_step*2 ) { dst[0] = dft_dst[j]; dst[dst_step] = dft_dst[n-j-1]; } } static void DCTInit( int n, int elem_size, void* _wave, int inv ) { static const double DctScale[] = { 0.707106781186547570, 0.500000000000000000, 0.353553390593273790, 0.250000000000000000, 0.176776695296636890, 0.125000000000000000, 0.088388347648318447, 0.062500000000000000, 0.044194173824159223, 0.031250000000000000, 0.022097086912079612, 0.015625000000000000, 0.011048543456039806, 0.007812500000000000, 0.005524271728019903, 0.003906250000000000, 0.002762135864009952, 0.001953125000000000, 0.001381067932004976, 0.000976562500000000, 0.000690533966002488, 0.000488281250000000, 0.000345266983001244, 0.000244140625000000, 0.000172633491500622, 0.000122070312500000, 0.000086316745750311, 0.000061035156250000, 0.000043158372875155, 0.000030517578125000 }; int i; Complex w, w1; double t, scale; if( n == 1 ) return; assert( (n&1) == 0 ); if( (n & (n - 1)) == 0 ) { int m; for( m = 0; (unsigned)(1 << m) < (unsigned)n; m++ ) ; scale = (!inv ? 2 : 1)*DctScale[m]; w1.re = DFTTab[m+2][0]; w1.im = -DFTTab[m+2][1]; } else { t = 1./(2*n); scale = (!inv ? 2 : 1)*std::sqrt(t); w1.im = sin(-CV_PI*t); w1.re = std::sqrt(1. - w1.im*w1.im); } n >>= 1; if( elem_size == sizeof(Complex) ) { Complex* wave = (Complex*)_wave; w.re = scale; w.im = 0.; for( i = 0; i <= n; i++ ) { wave[i] = w; t = w.re*w1.re - w.im*w1.im; w.im = w.re*w1.im + w.im*w1.re; w.re = t; } } else { Complex* wave = (Complex*)_wave; assert( elem_size == sizeof(Complex) ); w.re = (float)scale; w.im = 0.f; for( i = 0; i <= n; i++ ) { wave[i].re = (float)w.re; wave[i].im = (float)w.im; t = w.re*w1.re - w.im*w1.im; w.im = w.re*w1.im + w.im*w1.re; w.re = t; } } } typedef void (*DCTFunc)(const void* src, int src_step, void* dft_src, void* dft_dst, void* dst, int dst_step, int n, int nf, int* factors, const int* itab, const void* dft_wave, const void* dct_wave, const void* spec, void* buf ); static void DCT_32f(const float* src, int src_step, float* dft_src, float* dft_dst, float* dst, int dst_step, int n, int nf, int* factors, const int* itab, const Complexf* dft_wave, const Complexf* dct_wave, const void* spec, Complexf* buf ) { DCT(src, src_step, dft_src, dft_dst, dst, dst_step, n, nf, factors, itab, dft_wave, dct_wave, spec, buf); } static void IDCT_32f(const float* src, int src_step, float* dft_src, float* dft_dst, float* dst, int dst_step, int n, int nf, int* factors, const int* itab, const Complexf* dft_wave, const Complexf* dct_wave, const void* spec, Complexf* buf ) { IDCT(src, src_step, dft_src, dft_dst, dst, dst_step, n, nf, factors, itab, dft_wave, dct_wave, spec, buf); } static void DCT_64f(const double* src, int src_step, double* dft_src, double* dft_dst, double* dst, int dst_step, int n, int nf, int* factors, const int* itab, const Complexd* dft_wave, const Complexd* dct_wave, const void* spec, Complexd* buf ) { DCT(src, src_step, dft_src, dft_dst, dst, dst_step, n, nf, factors, itab, dft_wave, dct_wave, spec, buf); } static void IDCT_64f(const double* src, int src_step, double* dft_src, double* dft_dst, double* dst, int dst_step, int n, int nf, int* factors, const int* itab, const Complexd* dft_wave, const Complexd* dct_wave, const void* spec, Complexd* buf ) { IDCT(src, src_step, dft_src, dft_dst, dst, dst_step, n, nf, factors, itab, dft_wave, dct_wave, spec, buf); } } void cv::dct( InputArray _src0, OutputArray _dst, int flags ) { static DCTFunc dct_tbl[4] = { (DCTFunc)DCT_32f, (DCTFunc)IDCT_32f, (DCTFunc)DCT_64f, (DCTFunc)IDCT_64f }; bool inv = (flags & DCT_INVERSE) != 0; Mat src0 = _src0.getMat(), src = src0; int type = src.type(), depth = src.depth(); void /* *spec_dft = 0, */ *spec = 0; double scale = 1.; int prev_len = 0, nf = 0, stage, end_stage; uchar *src_dft_buf = 0, *dst_dft_buf = 0; uchar *dft_wave = 0, *dct_wave = 0; int* itab = 0; uchar* ptr = 0; int elem_size = (int)src.elemSize(), complex_elem_size = elem_size*2; int factors[34], inplace_transform; int i, len, count; AutoBuffer buf; CV_Assert( type == CV_32FC1 || type == CV_64FC1 ); _dst.create( src.rows, src.cols, type ); Mat dst = _dst.getMat(); DCTFunc dct_func = dct_tbl[(int)inv + (depth == CV_64F)*2]; if( (flags & DFT_ROWS) || src.rows == 1 || (src.cols == 1 && (src.isContinuous() && dst.isContinuous()))) { stage = end_stage = 0; } else { stage = src.cols == 1; end_stage = 1; } for( ; stage <= end_stage; stage++ ) { uchar *sptr = src.data, *dptr = dst.data; size_t sstep0, sstep1, dstep0, dstep1; if( stage == 0 ) { len = src.cols; count = src.rows; if( len == 1 && !(flags & DFT_ROWS) ) { len = src.rows; count = 1; } sstep0 = src.step; dstep0 = dst.step; sstep1 = dstep1 = elem_size; } else { len = dst.rows; count = dst.cols; sstep1 = src.step; dstep1 = dst.step; sstep0 = dstep0 = elem_size; } if( len != prev_len ) { int sz; if( len > 1 && (len & 1) ) CV_Error( CV_StsNotImplemented, "Odd-size DCT\'s are not implemented" ); sz = len*elem_size; sz += (len/2 + 1)*complex_elem_size; spec = 0; inplace_transform = 1; /*if( len*count >= 64 && DFTInitAlloc_R_32f_p ) { int ipp_sz = 0; if( depth == CV_32F ) { if( spec_dft ) IPPI_CALL( DFTFree_R_32f_p( spec_dft )); IPPI_CALL( DFTInitAlloc_R_32f_p( &spec_dft, len, 8, cvAlgHintNone )); IPPI_CALL( DFTGetBufSize_R_32f_p( spec_dft, &ipp_sz )); } else { if( spec_dft ) IPPI_CALL( DFTFree_R_64f_p( spec_dft )); IPPI_CALL( DFTInitAlloc_R_64f_p( &spec_dft, len, 8, cvAlgHintNone )); IPPI_CALL( DFTGetBufSize_R_64f_p( spec_dft, &ipp_sz )); } spec = spec_dft; sz += ipp_sz; } else*/ { sz += len*(complex_elem_size + sizeof(int)) + complex_elem_size; nf = DFTFactorize( len, factors ); inplace_transform = factors[0] == factors[nf-1]; i = nf > 1 && (factors[0] & 1) == 0; if( (factors[i] & 1) != 0 && factors[i] > 5 ) sz += (factors[i]+1)*complex_elem_size; if( !inplace_transform ) sz += len*elem_size; } buf.allocate( sz + 32 ); ptr = (uchar*)buf; if( !spec ) { dft_wave = ptr; ptr += len*complex_elem_size; itab = (int*)ptr; ptr = (uchar*)cvAlignPtr( ptr + len*sizeof(int), 16 ); DFTInit( len, nf, factors, itab, complex_elem_size, dft_wave, inv ); } dct_wave = ptr; ptr += (len/2 + 1)*complex_elem_size; src_dft_buf = dst_dft_buf = ptr; ptr += len*elem_size; if( !inplace_transform ) { dst_dft_buf = ptr; ptr += len*elem_size; } DCTInit( len, complex_elem_size, dct_wave, inv ); if( !inv ) scale += scale; prev_len = len; } // otherwise reuse the tables calculated on the previous stage for( i = 0; i < count; i++ ) { dct_func( sptr + i*sstep0, (int)sstep1, src_dft_buf, dst_dft_buf, dptr + i*dstep0, (int)dstep1, len, nf, factors, itab, dft_wave, dct_wave, spec, ptr ); } src = dst; } } void cv::idct( InputArray src, OutputArray dst, int flags ) { dct( src, dst, flags | DCT_INVERSE ); } namespace cv { static const int optimalDFTSizeTab[] = { 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 90, 96, 100, 108, 120, 125, 128, 135, 144, 150, 160, 162, 180, 192, 200, 216, 225, 240, 243, 250, 256, 270, 288, 300, 320, 324, 360, 375, 384, 400, 405, 432, 450, 480, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675, 720, 729, 750, 768, 800, 810, 864, 900, 960, 972, 1000, 1024, 1080, 1125, 1152, 1200, 1215, 1250, 1280, 1296, 1350, 1440, 1458, 1500, 1536, 1600, 1620, 1728, 1800, 1875, 1920, 1944, 2000, 2025, 2048, 2160, 2187, 2250, 2304, 2400, 2430, 2500, 2560, 2592, 2700, 2880, 2916, 3000, 3072, 3125, 3200, 3240, 3375, 3456, 3600, 3645, 3750, 3840, 3888, 4000, 4050, 4096, 4320, 4374, 4500, 4608, 4800, 4860, 5000, 5120, 5184, 5400, 5625, 5760, 5832, 6000, 6075, 6144, 6250, 6400, 6480, 6561, 6750, 6912, 7200, 7290, 7500, 7680, 7776, 8000, 8100, 8192, 8640, 8748, 9000, 9216, 9375, 9600, 9720, 10000, 10125, 10240, 10368, 10800, 10935, 11250, 11520, 11664, 12000, 12150, 12288, 12500, 12800, 12960, 13122, 13500, 13824, 14400, 14580, 15000, 15360, 15552, 15625, 16000, 16200, 16384, 16875, 17280, 17496, 18000, 18225, 18432, 18750, 19200, 19440, 19683, 20000, 20250, 20480, 20736, 21600, 21870, 22500, 23040, 23328, 24000, 24300, 24576, 25000, 25600, 25920, 26244, 27000, 27648, 28125, 28800, 29160, 30000, 30375, 30720, 31104, 31250, 32000, 32400, 32768, 32805, 33750, 34560, 34992, 36000, 36450, 36864, 37500, 38400, 38880, 39366, 40000, 40500, 40960, 41472, 43200, 43740, 45000, 46080, 46656, 46875, 48000, 48600, 49152, 50000, 50625, 51200, 51840, 52488, 54000, 54675, 55296, 56250, 57600, 58320, 59049, 60000, 60750, 61440, 62208, 62500, 64000, 64800, 65536, 65610, 67500, 69120, 69984, 72000, 72900, 73728, 75000, 76800, 77760, 78125, 78732, 80000, 81000, 81920, 82944, 84375, 86400, 87480, 90000, 91125, 92160, 93312, 93750, 96000, 97200, 98304, 98415, 100000, 101250, 102400, 103680, 104976, 108000, 109350, 110592, 112500, 115200, 116640, 118098, 120000, 121500, 122880, 124416, 125000, 128000, 129600, 131072, 131220, 135000, 138240, 139968, 140625, 144000, 145800, 147456, 150000, 151875, 153600, 155520, 156250, 157464, 160000, 162000, 163840, 164025, 165888, 168750, 172800, 174960, 177147, 180000, 182250, 184320, 186624, 187500, 192000, 194400, 196608, 196830, 200000, 202500, 204800, 207360, 209952, 216000, 218700, 221184, 225000, 230400, 233280, 234375, 236196, 240000, 243000, 245760, 248832, 250000, 253125, 256000, 259200, 262144, 262440, 270000, 273375, 276480, 279936, 281250, 288000, 291600, 294912, 295245, 300000, 303750, 307200, 311040, 312500, 314928, 320000, 324000, 327680, 328050, 331776, 337500, 345600, 349920, 354294, 360000, 364500, 368640, 373248, 375000, 384000, 388800, 390625, 393216, 393660, 400000, 405000, 409600, 414720, 419904, 421875, 432000, 437400, 442368, 450000, 455625, 460800, 466560, 468750, 472392, 480000, 486000, 491520, 492075, 497664, 500000, 506250, 512000, 518400, 524288, 524880, 531441, 540000, 546750, 552960, 559872, 562500, 576000, 583200, 589824, 590490, 600000, 607500, 614400, 622080, 625000, 629856, 640000, 648000, 655360, 656100, 663552, 675000, 691200, 699840, 703125, 708588, 720000, 729000, 737280, 746496, 750000, 759375, 768000, 777600, 781250, 786432, 787320, 800000, 810000, 819200, 820125, 829440, 839808, 843750, 864000, 874800, 884736, 885735, 900000, 911250, 921600, 933120, 937500, 944784, 960000, 972000, 983040, 984150, 995328, 1000000, 1012500, 1024000, 1036800, 1048576, 1049760, 1062882, 1080000, 1093500, 1105920, 1119744, 1125000, 1152000, 1166400, 1171875, 1179648, 1180980, 1200000, 1215000, 1228800, 1244160, 1250000, 1259712, 1265625, 1280000, 1296000, 1310720, 1312200, 1327104, 1350000, 1366875, 1382400, 1399680, 1406250, 1417176, 1440000, 1458000, 1474560, 1476225, 1492992, 1500000, 1518750, 1536000, 1555200, 1562500, 1572864, 1574640, 1594323, 1600000, 1620000, 1638400, 1640250, 1658880, 1679616, 1687500, 1728000, 1749600, 1769472, 1771470, 1800000, 1822500, 1843200, 1866240, 1875000, 1889568, 1920000, 1944000, 1953125, 1966080, 1968300, 1990656, 2000000, 2025000, 2048000, 2073600, 2097152, 2099520, 2109375, 2125764, 2160000, 2187000, 2211840, 2239488, 2250000, 2278125, 2304000, 2332800, 2343750, 2359296, 2361960, 2400000, 2430000, 2457600, 2460375, 2488320, 2500000, 2519424, 2531250, 2560000, 2592000, 2621440, 2624400, 2654208, 2657205, 2700000, 2733750, 2764800, 2799360, 2812500, 2834352, 2880000, 2916000, 2949120, 2952450, 2985984, 3000000, 3037500, 3072000, 3110400, 3125000, 3145728, 3149280, 3188646, 3200000, 3240000, 3276800, 3280500, 3317760, 3359232, 3375000, 3456000, 3499200, 3515625, 3538944, 3542940, 3600000, 3645000, 3686400, 3732480, 3750000, 3779136, 3796875, 3840000, 3888000, 3906250, 3932160, 3936600, 3981312, 4000000, 4050000, 4096000, 4100625, 4147200, 4194304, 4199040, 4218750, 4251528, 4320000, 4374000, 4423680, 4428675, 4478976, 4500000, 4556250, 4608000, 4665600, 4687500, 4718592, 4723920, 4782969, 4800000, 4860000, 4915200, 4920750, 4976640, 5000000, 5038848, 5062500, 5120000, 5184000, 5242880, 5248800, 5308416, 5314410, 5400000, 5467500, 5529600, 5598720, 5625000, 5668704, 5760000, 5832000, 5859375, 5898240, 5904900, 5971968, 6000000, 6075000, 6144000, 6220800, 6250000, 6291456, 6298560, 6328125, 6377292, 6400000, 6480000, 6553600, 6561000, 6635520, 6718464, 6750000, 6834375, 6912000, 6998400, 7031250, 7077888, 7085880, 7200000, 7290000, 7372800, 7381125, 7464960, 7500000, 7558272, 7593750, 7680000, 7776000, 7812500, 7864320, 7873200, 7962624, 7971615, 8000000, 8100000, 8192000, 8201250, 8294400, 8388608, 8398080, 8437500, 8503056, 8640000, 8748000, 8847360, 8857350, 8957952, 9000000, 9112500, 9216000, 9331200, 9375000, 9437184, 9447840, 9565938, 9600000, 9720000, 9765625, 9830400, 9841500, 9953280, 10000000, 10077696, 10125000, 10240000, 10368000, 10485760, 10497600, 10546875, 10616832, 10628820, 10800000, 10935000, 11059200, 11197440, 11250000, 11337408, 11390625, 11520000, 11664000, 11718750, 11796480, 11809800, 11943936, 12000000, 12150000, 12288000, 12301875, 12441600, 12500000, 12582912, 12597120, 12656250, 12754584, 12800000, 12960000, 13107200, 13122000, 13271040, 13286025, 13436928, 13500000, 13668750, 13824000, 13996800, 14062500, 14155776, 14171760, 14400000, 14580000, 14745600, 14762250, 14929920, 15000000, 15116544, 15187500, 15360000, 15552000, 15625000, 15728640, 15746400, 15925248, 15943230, 16000000, 16200000, 16384000, 16402500, 16588800, 16777216, 16796160, 16875000, 17006112, 17280000, 17496000, 17578125, 17694720, 17714700, 17915904, 18000000, 18225000, 18432000, 18662400, 18750000, 18874368, 18895680, 18984375, 19131876, 19200000, 19440000, 19531250, 19660800, 19683000, 19906560, 20000000, 20155392, 20250000, 20480000, 20503125, 20736000, 20971520, 20995200, 21093750, 21233664, 21257640, 21600000, 21870000, 22118400, 22143375, 22394880, 22500000, 22674816, 22781250, 23040000, 23328000, 23437500, 23592960, 23619600, 23887872, 23914845, 24000000, 24300000, 24576000, 24603750, 24883200, 25000000, 25165824, 25194240, 25312500, 25509168, 25600000, 25920000, 26214400, 26244000, 26542080, 26572050, 26873856, 27000000, 27337500, 27648000, 27993600, 28125000, 28311552, 28343520, 28800000, 29160000, 29296875, 29491200, 29524500, 29859840, 30000000, 30233088, 30375000, 30720000, 31104000, 31250000, 31457280, 31492800, 31640625, 31850496, 31886460, 32000000, 32400000, 32768000, 32805000, 33177600, 33554432, 33592320, 33750000, 34012224, 34171875, 34560000, 34992000, 35156250, 35389440, 35429400, 35831808, 36000000, 36450000, 36864000, 36905625, 37324800, 37500000, 37748736, 37791360, 37968750, 38263752, 38400000, 38880000, 39062500, 39321600, 39366000, 39813120, 39858075, 40000000, 40310784, 40500000, 40960000, 41006250, 41472000, 41943040, 41990400, 42187500, 42467328, 42515280, 43200000, 43740000, 44236800, 44286750, 44789760, 45000000, 45349632, 45562500, 46080000, 46656000, 46875000, 47185920, 47239200, 47775744, 47829690, 48000000, 48600000, 48828125, 49152000, 49207500, 49766400, 50000000, 50331648, 50388480, 50625000, 51018336, 51200000, 51840000, 52428800, 52488000, 52734375, 53084160, 53144100, 53747712, 54000000, 54675000, 55296000, 55987200, 56250000, 56623104, 56687040, 56953125, 57600000, 58320000, 58593750, 58982400, 59049000, 59719680, 60000000, 60466176, 60750000, 61440000, 61509375, 62208000, 62500000, 62914560, 62985600, 63281250, 63700992, 63772920, 64000000, 64800000, 65536000, 65610000, 66355200, 66430125, 67108864, 67184640, 67500000, 68024448, 68343750, 69120000, 69984000, 70312500, 70778880, 70858800, 71663616, 72000000, 72900000, 73728000, 73811250, 74649600, 75000000, 75497472, 75582720, 75937500, 76527504, 76800000, 77760000, 78125000, 78643200, 78732000, 79626240, 79716150, 80000000, 80621568, 81000000, 81920000, 82012500, 82944000, 83886080, 83980800, 84375000, 84934656, 85030560, 86400000, 87480000, 87890625, 88473600, 88573500, 89579520, 90000000, 90699264, 91125000, 92160000, 93312000, 93750000, 94371840, 94478400, 94921875, 95551488, 95659380, 96000000, 97200000, 97656250, 98304000, 98415000, 99532800, 100000000, 100663296, 100776960, 101250000, 102036672, 102400000, 102515625, 103680000, 104857600, 104976000, 105468750, 106168320, 106288200, 107495424, 108000000, 109350000, 110592000, 110716875, 111974400, 112500000, 113246208, 113374080, 113906250, 115200000, 116640000, 117187500, 117964800, 118098000, 119439360, 119574225, 120000000, 120932352, 121500000, 122880000, 123018750, 124416000, 125000000, 125829120, 125971200, 126562500, 127401984, 127545840, 128000000, 129600000, 131072000, 131220000, 132710400, 132860250, 134217728, 134369280, 135000000, 136048896, 136687500, 138240000, 139968000, 140625000, 141557760, 141717600, 143327232, 144000000, 145800000, 146484375, 147456000, 147622500, 149299200, 150000000, 150994944, 151165440, 151875000, 153055008, 153600000, 155520000, 156250000, 157286400, 157464000, 158203125, 159252480, 159432300, 160000000, 161243136, 162000000, 163840000, 164025000, 165888000, 167772160, 167961600, 168750000, 169869312, 170061120, 170859375, 172800000, 174960000, 175781250, 176947200, 177147000, 179159040, 180000000, 181398528, 182250000, 184320000, 184528125, 186624000, 187500000, 188743680, 188956800, 189843750, 191102976, 191318760, 192000000, 194400000, 195312500, 196608000, 196830000, 199065600, 199290375, 200000000, 201326592, 201553920, 202500000, 204073344, 204800000, 205031250, 207360000, 209715200, 209952000, 210937500, 212336640, 212576400, 214990848, 216000000, 218700000, 221184000, 221433750, 223948800, 225000000, 226492416, 226748160, 227812500, 230400000, 233280000, 234375000, 235929600, 236196000, 238878720, 239148450, 240000000, 241864704, 243000000, 244140625, 245760000, 246037500, 248832000, 250000000, 251658240, 251942400, 253125000, 254803968, 255091680, 256000000, 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1139062500, 1146617856, 1152000000, 1166400000, 1171875000, 1179648000, 1180980000, 1194393600, 1195742250, 1200000000, 1207959552, 1209323520, 1215000000, 1220703125, 1224440064, 1228800000, 1230187500, 1244160000, 1250000000, 1258291200, 1259712000, 1265625000, 1274019840, 1275458400, 1280000000, 1289945088, 1296000000, 1310720000, 1312200000, 1318359375, 1327104000, 1328602500, 1342177280, 1343692800, 1350000000, 1358954496, 1360488960, 1366875000, 1382400000, 1399680000, 1406250000, 1415577600, 1417176000, 1423828125, 1433272320, 1440000000, 1451188224, 1458000000, 1464843750, 1474560000, 1476225000, 1492992000, 1500000000, 1509949440, 1511654400, 1518750000, 1528823808, 1530550080, 1536000000, 1537734375, 1555200000, 1562500000, 1572864000, 1574640000, 1582031250, 1592524800, 1594323000, 1600000000, 1610612736, 1612431360, 1620000000, 1632586752, 1638400000, 1640250000, 1658880000, 1660753125, 1677721600, 1679616000, 1687500000, 1698693120, 1700611200, 1708593750, 1719926784, 1728000000, 1749600000, 1757812500, 1769472000, 1771470000, 1791590400, 1800000000, 1811939328, 1813985280, 1822500000, 1843200000, 1845281250, 1866240000, 1875000000, 1887436800, 1889568000, 1898437500, 1911029760, 1913187600, 1920000000, 1934917632, 1944000000, 1953125000, 1966080000, 1968300000, 1990656000, 1992903750, 2000000000, 2013265920, 2015539200, 2025000000, 2038431744, 2040733440, 2048000000, 2050312500, 2073600000, 2097152000, 2099520000, 2109375000, 2123366400, 2125764000 }; } int cv::getOptimalDFTSize( int size0 ) { int a = 0, b = sizeof(optimalDFTSizeTab)/sizeof(optimalDFTSizeTab[0]) - 1; if( (unsigned)size0 >= (unsigned)optimalDFTSizeTab[b] ) return -1; while( a < b ) { int c = (a + b) >> 1; if( size0 <= optimalDFTSizeTab[c] ) b = c; else a = c+1; } return optimalDFTSizeTab[b]; } CV_IMPL void cvDFT( const CvArr* srcarr, CvArr* dstarr, int flags, int nonzero_rows ) { cv::Mat src = cv::cvarrToMat(srcarr), dst0 = cv::cvarrToMat(dstarr), dst = dst0; int _flags = ((flags & CV_DXT_INVERSE) ? cv::DFT_INVERSE : 0) | ((flags & CV_DXT_SCALE) ? cv::DFT_SCALE : 0) | ((flags & CV_DXT_ROWS) ? cv::DFT_ROWS : 0); CV_Assert( src.size == dst.size ); if( src.type() != dst.type() ) { if( dst.channels() == 2 ) _flags |= cv::DFT_COMPLEX_OUTPUT; else _flags |= cv::DFT_REAL_OUTPUT; } cv::dft( src, dst, _flags, nonzero_rows ); CV_Assert( dst.data == dst0.data ); // otherwise it means that the destination size or type was incorrect } CV_IMPL void cvMulSpectrums( const CvArr* srcAarr, const CvArr* srcBarr, CvArr* dstarr, int flags ) { cv::Mat srcA = cv::cvarrToMat(srcAarr), srcB = cv::cvarrToMat(srcBarr), dst = cv::cvarrToMat(dstarr); CV_Assert( srcA.size == dst.size && srcA.type() == dst.type() ); cv::mulSpectrums(srcA, srcB, dst, (flags & CV_DXT_ROWS) ? cv::DFT_ROWS : 0, (flags & CV_DXT_MUL_CONJ) != 0 ); } CV_IMPL void cvDCT( const CvArr* srcarr, CvArr* dstarr, int flags ) { cv::Mat src = cv::cvarrToMat(srcarr), dst = cv::cvarrToMat(dstarr); CV_Assert( src.size == dst.size && src.type() == dst.type() ); int _flags = ((flags & CV_DXT_INVERSE) ? cv::DCT_INVERSE : 0) | ((flags & CV_DXT_ROWS) ? cv::DCT_ROWS : 0); cv::dct( src, dst, _flags ); } CV_IMPL int cvGetOptimalDFTSize( int size0 ) { return cv::getOptimalDFTSize(size0); } /* End of file. */