* mln/transform/fft.hh, * tests/transform/fft.cc: New. Imported from the old directory sanbox/abraham/. Signed-off-by: Roland Levillain &lt;roland(a)lrde.epita.fr&gt; --- milena/ChangeLog | 9 + milena/mln/transform/fft.hh | 693 +++++++++++++++++++++++++++++++++++++++++ milena/tests/transform/fft.cc | 92 ++++++ 3 files changed, 794 insertions(+) create mode 100644 milena/mln/transform/fft.hh create mode 100644 milena/tests/transform/fft.cc diff --git a/milena/ChangeLog b/milena/ChangeLog index 2e0ed94..83a2c76 100644 --- a/milena/ChangeLog +++ b/milena/ChangeLog @@ -1,3 +1,12 @@ +2012-10-09 Alexandre Abraham &lt;abraham(a)lrde.epita.fr&gt; + + Import the FFTW-based Fast Fourier Transform. + + * mln/transform/fft.hh, + * tests/transform/fft.cc: + New. + Imported from the old directory sanbox/abraham/. + 2013-08-23 Roland Levillain &lt;roland(a)lrde.epita.fr&gt; Fix a couple of Milena tests. diff --git a/milena/mln/transform/fft.hh b/milena/mln/transform/fft.hh new file mode 100644 index 0000000..0dafa7b --- /dev/null +++ b/milena/mln/transform/fft.hh @@ -0,0 +1,693 @@ +// Copyright (C) 2007, 2008, 2009 EPITA Research and Development Laboratory +// +// This file is part of the Milena Library. This library is free +// software; you can redistribute it and/or modify it under the terms +// of the GNU General Public License version 2 as published by the +// Free Software Foundation. +// +// This library is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this library; see the file COPYING. If not, write to +// the Free Software Foundation, 51 Franklin Street, Fifth Floor, +// Boston, MA 02111-1307, USA. +// +// As a special exception, you may use this file as part of a free +// software library without restriction. Specifically, if other files +// instantiate templates or use macros or inline functions from this +// file, or you compile this file and link it with other files to +// produce an executable, this file does not by itself cause the +// resulting executable to be covered by the GNU General Public +// License. This exception does not however invalidate any other +// reasons why the executable file might be covered by the GNU General +// Public License. + +#ifndef MLN_TRANSFORM_FFT_HH +# define MLN_TRANSFORM_FFT_HH + +# include <mln/core/image/image2d.hh> +# include <mln/estim/min_max.hh> +# include <mln/opt/at.hh> + +# include <complex> + +# include <fftw3.h> + +namespace mln { + + namespace internal { + + /// Dispatch traits for fftw + enum fft_dispatch { fft_cplx, fft_real }; + + template <typename T> + struct fft_trait; + + /*! + ** \brief fft trait. + */ + template <> + struct fft_trait<double> + { + static const fft_dispatch which = fft_real; ///< Real dispatch. + typedef double fftw_input; ///< Type of input. + }; + + /*! + ** \brief fft trait. + ** + ** \specialization for ntg::cplx<R, T> + */ + template <typename T> + struct fft_trait< std::complex<T> > + { + static const fft_dispatch which = fft_cplx; ///< Complex dispatch. + typedef std::complex <T> fftw_input; ///< Type of input. + }; + + /*! + ** _fft<ntg::cplx_representation, T> + ** + ** \param T Data type. + */ + template <class T> + class _fft + { + public: + /*! + ** \brief Accessor to transformed image. + ** + ** Const version. + */ + const image2d< std::complex<T> > transformed_image() const + { + return trans_im; + } + + /*! + ** \brief Accessor to transformed image. + ** + ** Non const version. + */ + image2d< std::complex<T> >& transformed_image() + { + return trans_im; + } + + /*! + ** \brief Accessor to transformed image. + ** + ** For each point p of the transformed image T, you get + ** |T[p]|. + ** + ** \tparam R Data type of the resulting image. + ** + ** \param ordered Kind of traversal. + */ + template <class R> + image2d<R> transformed_image_magn(bool ordered = true) const + { + // FIXME : check that R is real + + image2d<R> new_im(trans_im.domain()); + + if (ordered) + for (unsigned row = 0; row < new_im.nrows(); ++row) + for (unsigned col = 0; col < new_im.ncols(); ++col) + opt::at(new_im, row, col) = + std::norm(opt::at(trans_im, (row + trans_im.nrows() / 2) % trans_im.nrows(), + (col + trans_im.ncols() / 2) % trans_im.ncols())); + else + { + mln_piter(image2d< std::complex<T> >) it(trans_im.domain()); + + for_all(it) + new_im(it) = std::norm(trans_im(it)); + } + + return new_im; + } + + /*! + ** \brief Accessor to transformed image. + ** + ** For each point p of the transformed image T, you get + ** |T[p]|. + ** + ** \param ordered Kind of traversal. + */ + image2d<T> transformed_image_magn(bool ordered = true) const + { + return transformed_image_magn<T>(ordered); + } + + /*! + ** \brief Accessor to transformed image. + ** + ** For each point p of the transformed image T, you get + ** a clipped value of |T[p]|.\n + ** + ** \param R Data type of the resulting image. + ** + ** \param clip Value used for clipping. + ** \param ordered Kind of traversal. + */ + + template <class R> + image2d<R> transformed_image_clipped_magn(const double clip, + bool ordered = true) const + { + // Check that R is real + + image2d<R> new_im(trans_im.domain()); + // check that clip is >=0 and <=1 ? + double max; + mln_piter(image2d<T>) it(trans_im.domain()); + + for_all(it) + if (std::norm(trans_im(it)) > max) + max = std::norm(trans_im(it)); + + if (ordered) + for (unsigned row = 0; row < new_im.nrows(); ++row) + for (unsigned col = 0; col < new_im.ncols(); ++col) + { + if (std::norm(opt::at(trans_im, (row + trans_im.nrows() / 2) % trans_im.nrows(), + (col + trans_im.ncols() / 2) % + trans_im.ncols())) >= max * clip) + opt::at(new_im, row, col) = mln_max(R); + else + opt::at(new_im, row, col) = + (double) mln_max(R) * + std::norm(opt::at(trans_im, (row + trans_im.nrows() / 2) % trans_im.nrows(), + (col + trans_im.ncols() / 2) % + trans_im.ncols())) / (max * clip); + } + else + { + for_all(it) + { + if (std::norm(trans_im(it)) >= max * clip) + new_im(it) = mln_max(R); + else + new_im(it) = (double) mln_max(R) * + std::norm(trans_im(it)) / (max * clip); + } + } + + return new_im; + } + + /*! + ** \brief Accessor to transformed image. + ** + ** For each point p of the transformed image T, you get + ** a clipped value of |T[p]|.\n + ** + ** \param clip Value used for clipping. + ** \param ordered Kind of traversal. + */ + image2d<T> transformed_image_clipped_magn(const double clip, + bool ordered = true) const + { + return transformed_image_clipped_magn<T>(clip, ordered); + } + + /*! + ** \brief Accessor to transformed image. + ** + ** For each point p of the transformed image T, you get + ** a clipped value of |T[p]|.\n + ** + ** \param R Data type of the resulting image. + ** + ** \param ordered Kind of traversal. + */ + + image2d<T> transformed_image_clipped_magn(bool ordered = true) const + { + return transformed_image_clipped_magn<T>(1, ordered); + } + + /*! + ** \brief Accessor to transformed image. + ** + ** For each point p of the transformed image T, you get + ** a clipped value of |T[p]|.\n + ** + ** \param R Data type of the resulting image. + ** + ** \param ordered Kind of traversal. + */ + + template <class R> + image2d<R> transformed_image_clipped_magn(bool ordered = true) const + { + return transformed_image_clipped_magn<R>(1, ordered); + } + + // FIXME: Find a more elegant way to fix range interval on a and b. + /*! + ** \brief Accessor to transformed image. + ** + ** For each point p of the transformed image T, you get + ** a log translated value of |T[p]| on interval [a; b].\n + ** + ** \param a Lower bound. + ** \param b Upper bound. + ** \param ordered Kind of traversal. + */ + + template <class R> + image2d<R> transformed_image_log_magn(double a, + double b, + bool ordered = true) const + { + // Check that R is real + // 0 <= a <= 1000 + // 0 <= b <= 1000 + + image2d<R> new_im(trans_im.domain()); + + double max = 0; + mln_piter(image2d<R>) it(trans_im.domain()); + + for_all(it) + if (std::norm(trans_im(it)) > max) + max = std::norm(trans_im(it)); + + + if (ordered) + for (unsigned row = 0; row < new_im.nrows(); ++row) + for (unsigned col = 0; col < new_im.ncols(); ++col) + opt::at(new_im, row, col) = + log(a + b * std::norm(opt::at(trans_im, (row + trans_im.nrows() / 2) % trans_im.nrows(), + (col + trans_im.ncols() / 2) % trans_im.ncols()))) / + log (a + b * max) * mln_max(R); + else + { + mln_piter(image2d< std::complex<T> >) it(trans_im.domain()); + + for_all(it) + new_im(it) = log(a + b * std::norm(trans_im(it))) / + log (a + b * max) * mln_max(R); + } + + return new_im; + } + + // FIXME: Find a more elegant way to fix boundaries of a and b. + /*! + ** \brief Accessor to transformed image. + ** + ** For each point p of the transformed image T, you get + ** a log translated value of |T[p]| on interval [a; b].\n + ** + ** \param a Lower bound. + ** \param b Upper bound. + ** \param ordered Kind of traversal. + */ + + image2d<T> transformed_image_log_magn(double a, + double b, + bool ordered = true) const + { + return transformed_image_log_magn<T>(a, b, ordered); + } + + /*! + ** \brief Accessor to transformed image. + ** + ** For each point p of the transformed image T, you get + ** a log translated value of |T[p]| on interval [1; 100].\n + ** + ** \param R Data type of the resulting image. + ** + ** \param ordered Kind of traversal. + */ + + template <class R> + image2d<R> transformed_image_log_magn(bool ordered = true) const + { + return transformed_image_log_magn<R>(1, 100, ordered); + } + + /*! + ** \brief Accessor to transformed image. + ** + ** For each point p of the transformed image T, you get + ** a log translated value of |T[p]| on interval [1; 100].\n + ** + ** \param ordered Kind of traversal. + */ + + image2d<T> transformed_image_log_magn(bool ordered = true) const + { + return transformed_image_log_magn<T>(1, 100, ordered); + } + + + /*! + ** \brief Destructor. + ** + ** Let memory free for other big images !!! + */ + ~_fft() + { + fftw_free(in); + fftw_free(out); + fftw_destroy_plan(p); + fftw_destroy_plan(p_inv); + } + + protected: + + typename fft_trait<T>::fftw_input *in; ///< Input image. + std::complex<T> *out; ///< Complex image. + fftw_plan p; ///< Plan. + fftw_plan p_inv; ///< inverted plan. + image2d< std::complex<T> > trans_im; ///< Transformed image. + + }; + + } // end of namespace internal + + namespace transform { + + /*! + ** \brief fft class declaration. + ** + ** \param T Data type. + ** \param which Dispatch. + */ + template <class T, + internal::fft_dispatch which = internal::fft_trait<T>::which > + class fft; + + /*! + ** \brief fft specialization for fft real dispatch. + ** + ** \param T Data type. + */ + template <class T> + class fft<T, internal::fft_real> : public internal::_fft<T> + { + + public: + + /*! + ** \brief Constructor. + ** + ** Initialization of data in order to compute the fft. + ** + ** \param original_im Image to process. + */ + template <typename D> + fft(const image2d<D>& original_im) + { + this->in = (T*) fftw_malloc(original_im.nrows() * original_im.ncols() * sizeof(T)); + this->out = (std::complex<T>*) + fftw_malloc(original_im.nrows() * (original_im.ncols() / 2 + 1) * sizeof(std::complex<T>)); + + for (unsigned row = 0; row < original_im.nrows(); ++row) + for (unsigned col = 0; col < original_im.ncols(); ++col) + this->in[row * original_im.ncols() + col] = opt::at(original_im, row, col); + + this->p = fftw_plan_dft_r2c_2d (original_im.nrows(), original_im.ncols(), + this->in, reinterpret_cast<fftw_complex*>(this->out), FFTW_ESTIMATE); + this->p_inv = fftw_plan_dft_r2c_2d (original_im.nrows(), original_im.ncols(), + this->in, reinterpret_cast<fftw_complex*>(this->out), FFTW_ESTIMATE); + + this->trans_im = image2d< std::complex<T> >(original_im.domain()); + } + + /*! + ** \brief Compute and return the transform. + */ + image2d< std::complex<T> > transform() + { + fftw_execute(this->p); + + unsigned denom = this->trans_im.nrows() * this->trans_im.ncols(); + int i = 0; + for (unsigned row = 0; row < this->trans_im.nrows(); ++row) + for (unsigned col = 0; col <= this->trans_im.ncols() / 2; ++col) + { + this->out[i] = std::complex<T> (this->out[i].real() / denom, this->out[i].imag() / denom); + opt::at(this->trans_im, row, col) = this->out[i]; + ++i; + } + for (unsigned row = 0; row < this->trans_im.nrows(); ++row) + for (unsigned col = this->trans_im.ncols() - 1; col > this->trans_im.ncols() / 2; --col) + opt::at(this->trans_im, row, col) = opt::at(this->trans_im, this->trans_im.nrows() - row - 1, + this->trans_im.ncols() - col - 1); + return this->trans_im; + } + + /*! + ** \brief Compute and return the invert transform. + ** + ** \param R Data type of output image. + */ + template <class R> + image2d<R> transform_inv() + { + // FIXME : Check that R is real + + for (unsigned row = 0; row < this->trans_im.nrows(); ++row) + for (unsigned col = 0; col <= this->trans_im.ncols() / 2; ++col) + this->out[row * (this->trans_im.ncols() / 2 + 1) + col] = + opt::at(this->trans_im, row, col).real(); + + fftw_execute(this->p_inv); + + image2d<R> new_im(this->trans_im.domain()); + int i = 0; + for (unsigned row = 0; row < this->trans_im.nrows(); ++row) + for (unsigned col = 0; col < this->trans_im.ncols(); ++col) + { + opt::at(new_im, row, col) = (this->in[i] >= mln_min(R) ? + (this->in[i] <= mln_max(R) ? + (R)this->in [i] : + mln_min(R)) : + mln_max(R)); + ++i; + } + return new_im; + } + + /*! + ** \brief Shift zero-frequency component of discrete Fourier transform + ** to center of spectrum. + ** + ** \param R The data type of the image returned. + ** + ** The zero-frequency component of discrete Fourier transform are moved + ** to center of the image : + ** + ** \htmlonly + ** <table> + ** <tr><td>1</td><td>2</td></tr> + ** <tr><td>3</td><td>4</td></tr> + ** </table> + ** becomes + ** <table> + ** <tr><td>4</td><td>3</td></tr> + ** <tr><td>2</td><td>1</td></tr> + ** </table> + ** \endhtmlonly + ** + */ + + /* + template <class R> + image2d<R> shift_transform_inv() + { + image2d<R> t = transform_inv<R>(); + image2d<R> st(t.size()); + + // We have to exchange t_1 with t_1_dest and not directly t_3 because + // they have not he same size. + typedef morpher::piece_morpher< image2d<R> > piece_t; + piece_t t_1(t, dpoint2d(0, 0), + image2d_size((t.size().nrows() - 1) / 2, + (t.size().ncols() - 1) / 2, + t.border())); + piece_t t_1_dest(st, dpoint2d(t.nrows() - t_1.nrows(), + t.ncols() - t_1.ncols()), + image2d_size(t_1.nrows(), t_1.ncols(), + t.border())); + piece_t t_2(t, dpoint2d(0, (t.size().ncols() - 1) / 2), + image2d_size((t.size().nrows() - 1) / 2, + t.size().ncols() - (t.size().ncols() - 1) / 2, + t.border())); + piece_t t_2_dest(st, dpoint2d(t.nrows() - t_2.nrows(), 0), + image2d_size(t_2.nrows(), t_2.ncols(), + t.border())); + piece_t t_3(t, dpoint2d((t.size().nrows() - 1) / 2, 0), + image2d_size(t.size().nrows() - (t.size().nrows() - 1) / 2, + (t.size().ncols() - 1) / 2, + t.border())); + piece_t t_3_dest(st, dpoint2d(0, t.ncols() - t_3.ncols()), + image2d_size(t_3.nrows(), t_3.ncols(), + t.border())); + piece_t t_4(t, dpoint2d((t.size().nrows() - 1) / 2, + (t.size().ncols() - 1) / 2), + image2d_size(t.size().nrows() - (t.size().nrows() - 1) / 2, + t.size().ncols() - (t.size().ncols() - 1) / 2, + t.border())); + piece_t t_4_dest(st, dpoint2d(0, 0), + image2d_size(t_4.nrows(), t_4.ncols(), + t.border())); + + oln_iter_type(piece_t) i1(t_1); + for_all(i1) + t_1_dest[i1] = t_1[i1]; + oln_iter_type(piece_t) i2(t_2); + for_all(i2) + t_2_dest[i2] = t_2[i2]; + oln_iter_type(piece_t) i3(t_3); + for_all(i3) + t_3_dest[i3] = t_3[i3]; + oln_iter_type(piece_t) i4(t_4); + for_all(i4) + t_4_dest[i4] = t_4[i4]; + + return st; + } + */ + + + /*! + ** \brief Compute and return the invert transform. + */ + image2d<T> transform_inv() + { + return transform_inv<T>(); + } + + /*! + ** \brief Shift zero-frequency component of discrete Fourier transform + ** to center of spectrum. + */ + /* + image2d<T> shift_transform_inv() + { + return shift_transform_inv<T>(); + } + */ + + }; + + /*! + ** \brief fft specialization for fft complex dispatch. + ** + ** \param T Data type. + ** \param R Complex representation kind. + */ + template <class T> + class fft<T, internal::fft_cplx> : public internal::_fft<T> + { + + public: + + /*! + ** \brief Constructor. + ** + ** Initialization of data in order to compute the fft. + ** + ** \param original_im Image to process. + */ + fft(const image2d< std::complex<T> >& original_im) + { + this->in = fftw_malloc(sizeof(std::complex<T>) * + original_im.nrows() * original_im.ncols()); + this->out = fftw_malloc(sizeof(std::complex<T>) * + original_im.nrows() * original_im.ncols()); + + for (unsigned row = 0; row < original_im.nrows(); ++row) + for (unsigned col = 0; col < original_im.ncols(); ++col) + { + this->in[row * original_im.ncols() + col].re = + original_im(row, col).real(); + this->in[row * original_im.ncols() + col].im = + original_im(row, col).imag(); + } + + this->p = fftw_plan_dft_2d(original_im.nrows(), original_im.ncols(), + this->in, this->out, + FFTW_FORWARD, FFTW_ESTIMATE); + this->p_inv = fftw2d_plan_dft_2d(original_im.nrows(), original_im.ncols(), + this->in, this->out, + FFTW_BACKWARD, FFTW_ESTIMATE); + + this->trans_im = image2d< std::complex<T> >(original_im.domain()); + } + + /*! + ** \brief Compute and return the transform. + */ + image2d< std::complex<T> > transform() + { + fftw_execute(this->p); + + unsigned denom = this->trans_im.nrows() * this->trans_im.ncols(); + int i = 0; + for (unsigned row = 0; row < this->trans_im.nrows(); ++row) + for (unsigned col = 0; col < this->trans_im.ncols(); ++col) + { + this->out[i].re /= denom; + this->out[i].im /= denom; + this->trans_im(row, col) = std::complex<double>(this->out[i].re, + this->out[i].im); + ++i; + } + return this->trans_im; + } + + /*! + ** \brief Compute and return the invert transform. + ** + ** \param R Data type of output image. + */ + template <class R> + image2d< std::complex<R> > transform_inv() + { + for (unsigned row = 0; row < this->trans_im.nrows(); ++row) + for (unsigned col = 0; col < this->trans_im.ncols(); ++col) + { + this->out[row * this->trans_im.ncols() + col].re = this->trans_im(row, col).real(); + this->out[row * this->trans_im.ncols() + col].im = this->trans_im(row, col).imag(); + } + + fftw_execute(this->p_inv); + + image2d< std::complex<R> > new_im(this->trans_im.size()); + int i = 0; + for (unsigned row = 0; row < this->trans_im.nrows(); ++row) + for (unsigned col = 0; col < this->trans_im.ncols(); ++col) + { + new_im(row, col) = this->in[i]; + ++i; + } + return new_im; + } + + /*! + ** \brief Compute and return the invert transform. + */ + image2d< std::complex<T> > transform_inv() + { + return transform_inv<T>(); + } + + }; + + } // end of namespace transform + +} // end of namespace oln + +#endif // ! MLN_TRANSFORM_FFT_HH diff --git a/milena/tests/transform/fft.cc b/milena/tests/transform/fft.cc new file mode 100644 index 0000000..d7f7e63 --- /dev/null +++ b/milena/tests/transform/fft.cc @@ -0,0 +1,92 @@ +// -*- c++ -*- +// Copyright (C) 2004 EPITA Research and Development Laboratory +// +// This file is part of the Milena Library. This library is free +// software; you can redistribute it and/or modify it under the terms +// of the GNU General Public License version 2 as published by the +// Free Software Foundation. +// +// This library is distributed in the hope that it will be useful, +// but WITHOUT ANY WARRANTY; without even the implied warranty of +// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +// General Public License for more details. +// +// You should have received a copy of the GNU General Public License +// along with this library; see the file COPYING. If not, write to +// the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, +// Boston, MA 02110-1301, USA. +// +// As a special exception, you may use this file as part of a free +// software library without restriction. Specifically, if other files +// instantiate templates or use macros or inline functions from this +// file, or you compile this file and link it with other files to +// produce an executable, this file does not by itself cause the +// resulting executable to be covered by the GNU General Public +// License. This exception does not however invalidate any other +// reasons why the executable file might be covered by the GNU General +// Public License. + +#include <mln/transform/fft.hh> +#include <mln/value/int_u8.hh> +#include <mln/io/pgm/load.hh> +#include <mln/io/pgm/save.hh> +#include <mln/opt/at.hh> +#include <mln/debug/println.hh> + +#define CHECK(Condition) \ + if (Condition) \ + std::cout << "OK" << std::endl; \ + else \ + { \ + std::cout << "FAIL" << std::endl; \ + status = 1; \ + } + +using namespace mln; +using namespace transform; +using namespace value; + +int main () +{ + int status = 0; + + image2d<int_u8> im1; + io::pgm::load(im1, "lena.pgm"); + + fft<double> fourier(im1); + + image2d< std::complex<double> > im2 = fourier.transform(); + + image2d<int_u8> im3 = fourier.transform_inv<int_u8>(); + + io::pgm::save(im3, "fft_copy.pgm"); + + image2d<int_u8> fft = fourier.transformed_image_log_magn<int_u8>(true); + // debug::println(fourier.transformed_image()); + io::pgm::save(fft, "fft.pgm"); + + std::cout << "Test: Image == F-1(F(Image)) ... " << std::flush; + // CHECK (im1 == im3); + + image2d<int_u8> out = fourier.transformed_image_clipped_magn<int_u8>(0.01); + + io::pgm::save(out, "fft_trans_clipped.pgm"); + + out = fourier.transformed_image_log_magn<int_u8>(1, 100); + + io::pgm::save(out, "fft_trans_log.pgm"); + + for (int row = 40; row < im2.nrows() - 40; ++row) + for (int col = 0; col < im2.ncols(); ++col) + opt::at(im2, row, col) = 0; + + for (int row = 0; row < im2.nrows(); ++row) + for (int col = 40; col < im2.ncols() - 40; ++col) + opt::at(im2, row, col) = 0; + + out = fourier.transform_inv<int_u8>(); + + io::pgm::save(out, "fft_low_pass.pgm"); + + return status; +} -- 1.7.10.4