* mln/transform/fft.hh: Here.
---
milena/ChangeLog | 6 +
milena/mln/transform/fft.hh | 722 ++++++++++++++++++++++++++-----------------
2 files changed, 436 insertions(+), 292 deletions(-)
diff --git a/milena/ChangeLog b/milena/ChangeLog
index 8f96157..72bfb1a 100644
--- a/milena/ChangeLog
+++ b/milena/ChangeLog
@@ -1,5 +1,11 @@
2012-10-10 Roland Levillain <roland(a)lrde.epita.fr>
+ Split the interface of the FFT off from its implementation.
+
+ * mln/transform/fft.hh: Here.
+
+2012-10-10 Roland Levillain <roland(a)lrde.epita.fr>
+
Stylistic changes in the Fast Fourier Transform.
* mln/transform/fft.hh: Here.
diff --git a/milena/mln/transform/fft.hh b/milena/mln/transform/fft.hh
index 9b70b4f..36e4b80 100644
--- a/milena/mln/transform/fft.hh
+++ b/milena/mln/transform/fft.hh
@@ -42,9 +42,11 @@ namespace mln
namespace internal
{
- /// Dispatch traits for fftw
+ /// Dispatch tags for FFT traits.
enum fft_dispatch { fft_cplx, fft_real };
+
+ /// \brief FFT traits.
template <typename T>
struct fft_trait;
@@ -68,6 +70,7 @@ namespace mln
typedef std::complex<T> fftw_input;
};
+
/// \brief Internal structure containining packing data and
/// instructions for the (forward) and inverse (backward)
/// transforms.
@@ -78,16 +81,10 @@ namespace mln
{
public:
/// \brief Accessor to transformed image (const version).
- const image2d< std::complex<T> >& transformed_image() const
- {
- return trans_im;
- }
+ const image2d< std::complex<T> >& transformed_image() const;
/// \brief Accessor to transformed image (non const version).
- image2d< std::complex<T> >& transformed_image()
- {
- return trans_im;
- }
+ image2d< std::complex<T> >& transformed_image();
/// \brief Accessor to the transformed image (magnitude).
///
@@ -98,28 +95,7 @@ namespace mln
///
/// \param ordered Kind of traversal.
template <class R>
- image2d<R> transformed_image_magn(bool ordered = true) const
- {
- // FIXME: Ensure R is real.
-
- const unsigned nrows = trans_im.nrows();
- const unsigned ncols = trans_im.ncols();
- 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 + nrows / 2) % nrows,
- (col + ncols / 2) % 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;
- }
+ image2d<R> transformed_image_magn(bool ordered = true) const;
/// \brief Accessor to the transformed image (magnitude).
///
@@ -127,10 +103,7 @@ namespace mln
/// an image containing <tt>|T[p]|</tt> is returned.
///
/// \param ordered Kind of traversal.
- image2d<T> transformed_image_magn(bool ordered = true) const
- {
- return transformed_image_magn<T>(ordered);
- }
+ image2d<T> transformed_image_magn(bool ordered = true) const;
/// \brief Accessor to the transformed image (clipped
/// magnitude).
@@ -144,43 +117,7 @@ namespace mln
/// \param ordered Kind of traversal.
template <class R>
image2d<R> transformed_image_clipped_magn(double clip,
- bool ordered = true) const
- {
- // FIXME: Ensure R is real.
- // FIXME: Ensure `clip' is between 0 and 1?
-
- double max = mln_min(double);
- mln_piter(image2d<T>) it(trans_im.domain());
- for_all(it)
- if (std::norm(trans_im(it)) > max)
- max = std::norm(trans_im(it));
-
- const unsigned nrows = trans_im.nrows();
- const unsigned ncols = trans_im.ncols();
- 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)
- if (std::norm(opt::at(trans_im,
- (row + nrows / 2) % nrows,
- (col + ncols / 2) % 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 + nrows / 2) % nrows,
- (col + ncols / 2) % 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;
- }
+ bool ordered = true) const;
/// \brief Accessor to the transformed image (clipped
/// magnitude).
@@ -191,10 +128,7 @@ namespace mln
/// \param clip Value used for clipping.
/// \param ordered Kind of traversal.
image2d<T> transformed_image_clipped_magn(double clip,
- bool ordered = true) const
- {
- return transformed_image_clipped_magn<T>(clip, ordered);
- }
+ bool ordered = true) const;
/// \brief Accessor to the transformed image (clipped
/// magnitude).
@@ -206,10 +140,7 @@ namespace mln
///
/// \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);
- }
+ image2d<R> transformed_image_clipped_magn(bool ordered = true) const;
/// \brief Accessor to the transformed image (clipped
/// magnitude).
@@ -218,10 +149,7 @@ namespace mln
/// containing a clipped value of <tt>|T[p]|</tt> is returned.
///
/// \param ordered Kind of traversal.
- image2d<T> transformed_image_clipped_magn(bool ordered = true) const
- {
- return transformed_image_clipped_magn<T>(1, ordered);
- }
+ image2d<T> transformed_image_clipped_magn(bool ordered = true) const;
/// \brief Accessor to the transformed image (log of the
/// magnitude).
@@ -237,43 +165,7 @@ namespace mln
/// \param ordered Kind of traversal.
template <class R>
image2d<R> transformed_image_log_magn(double a, double b,
- bool ordered = true) const
- {
- /* FIXME: Find a more elegant way to fix range interval on a
- and b (Note from Roland: what does it mean?). */
-
- // FIXME: Ensure R is real.
- // FIXME: Ensure 0 <= a <= 1000.
- // FIXME: Ensure 0 <= b <= 1000.
-
- image2d<R> new_im(trans_im.domain());
-
- double max = mln_min(double);
- mln_piter(image2d<R>) it(trans_im.domain());
- for_all(it)
- if (std::norm(trans_im(it)) > max)
- max = std::norm(trans_im(it));
-
- const unsigned nrows = trans_im.nrows();
- const unsigned ncols = trans_im.ncols();
- 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 + nrows / 2) % nrows,
- (col + ncols / 2) % 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;
- }
+ bool ordered = true) const;
/// \brief Accessor to the transformed image (log of the
/// magnitude).
@@ -286,10 +178,7 @@ namespace mln
/// \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);
- }
+ bool ordered = true) const;
/// \brief Accessor to the transformed image (log of the
/// magnitude).
@@ -302,10 +191,7 @@ namespace mln
///
/// \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);
- }
+ image2d<R> transformed_image_log_magn(bool ordered = true) const;
/// \brief Accessor to the transformed image (log of the
/// magnitude).
@@ -315,18 +201,9 @@ namespace mln
/// interval [1, 100].
///
/// \param ordered Kind of traversal.
- image2d<T> transformed_image_log_magn(bool ordered = true) const
- {
- return transformed_image_log_magn<T>(1, 100, ordered);
- }
-
- ~fft()
- {
- fftw_free(in);
- fftw_free(out);
- fftw_destroy_plan(p);
- fftw_destroy_plan(p_inv);
- }
+ image2d<T> transformed_image_log_magn(bool ordered = true) const;
+
+ ~fft();
protected:
/// Input image (used internally by FFTW).
@@ -359,7 +236,7 @@ namespace mln
class fft;
- /// \brief FFT engine (specialization for images of real values).
+ /// \brief oFFT engine (specialization for images of real values).
///
/// \tparam T Data type.
template <class T>
@@ -372,96 +249,20 @@ namespace mln
///
/// \param original_im Image to process.
template <typename D>
- fft(const image2d<D>& original_im)
- {
- const unsigned nrows = original_im.nrows();
- const unsigned ncols = original_im.ncols();
-
- this->in = (T*) fftw_malloc(nrows * ncols * sizeof(T));
- this->out = (std::complex<T>*) fftw_malloc(nrows
- * (ncols / 2 + 1)
- * sizeof(std::complex<T>));
-
- for (unsigned row = 0; row < nrows; ++row)
- for (unsigned col = 0; col < ncols; ++col)
- this->in[row * ncols + col] =
- opt::at(original_im, row, col);
-
- this->p =
- fftw_plan_dft_r2c_2d (nrows, ncols,
- this->in,
- reinterpret_cast<fftw_complex*>(this->out),
- FFTW_ESTIMATE);
- this->p_inv =
- fftw_plan_dft_c2r_2d (nrows, ncols,
- reinterpret_cast<fftw_complex*>(this->out),
- this->in,
- FFTW_ESTIMATE);
- this->trans_im = image2d< std::complex<T> >(original_im.domain());
- }
+ fft(const image2d<D>& original_im);
/// \brief Compute and return the transform (as a complex image).
- image2d< std::complex<T> > transform()
- {
- fftw_execute(this->p);
-
- const unsigned nrows = this->trans_im.nrows();
- const unsigned ncols = this->trans_im.ncols();
- unsigned denom = nrows * ncols;
- int i = 0;
- for (unsigned row = 0; row < nrows; ++row)
- for (unsigned col = 0; col <= 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 < nrows; ++row)
- for (unsigned col = ncols - 1; col > ncols / 2; --col)
- opt::at(this->trans_im, row, col) =
- opt::at(this->trans_im, nrows - row - 1, ncols - col - 1);
- return this->trans_im;
- }
+ image2d< std::complex<T> > transform();
/// \brief Compute and return the inverse transform (as a real
/// image) of the FFT.
///
/// \tparam R Value type of output image.
template <class R>
- image2d<R> transform_inv()
- {
- // FIXME: Ensure R is real.
-
- const unsigned nrows = this->trans_im.nrows();
- const unsigned ncols = this->trans_im.ncols();
- for (unsigned row = 0; row < nrows; ++row)
- for (unsigned col = 0; col <= ncols / 2; ++col)
- this->out[row * (ncols / 2 + 1) + col] =
- opt::at(this->trans_im, row, col);
-
- fftw_execute(this->p_inv);
-
- image2d<R> new_im(this->trans_im.domain());
- int i = 0;
- for (unsigned row = 0; row < nrows; ++row)
- for (unsigned col = 0; col < 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;
- }
+ image2d<R> transform_inv();
/// \brief Compute and return the inverse transform of the FFT.
- image2d<T> transform_inv()
- {
- return transform_inv<T>();
- }
+ image2d<T> transform_inv();
};
@@ -477,48 +278,10 @@ namespace mln
/// Initialization of data for the computation of the FFT.
///
/// \param original_im Image to process.
- fft(const image2d< std::complex<T> >& original_im)
- {
- const unsigned nrows = original_im.nrows();
- const unsigned ncols = original_im.ncols();
-
- this->in = fftw_malloc(sizeof(std::complex<T>) * nrows * ncols);
- this->out = fftw_malloc(sizeof(std::complex<T>) * nrows * ncols);
-
- for (unsigned row = 0; row < nrows; ++row)
- for (unsigned col = 0; col < ncols; ++col)
- {
- this->in[row * ncols + col].re = original_im(row, col).real();
- this->in[row * ncols + col].im = original_im(row, col).imag();
- }
-
- this->p = fftw_plan_dft_2d(nrows, ncols, this->in, this->out,
- FFTW_FORWARD, FFTW_ESTIMATE);
- this->p_inv = fftw_plan_dft_2d(nrows, ncols, this->out, this->in,
- FFTW_BACKWARD, FFTW_ESTIMATE);
- this->trans_im = image2d< std::complex<T> >(original_im.domain());
- }
+ fft(const image2d< std::complex<T> >& original_im);
/// \brief Compute and return the transform (as a complex image).
- image2d< std::complex<T> > transform()
- {
- fftw_execute(this->p);
-
- const unsigned nrows = this->trans_im.nrows();
- const unsigned ncols = this->trans_im.ncols();
- unsigned denom = nrows * ncols;
- int i = 0;
- for (unsigned row = 0; row < nrows; ++row)
- for (unsigned col = 0; col < 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;
- }
+ image2d< std::complex<T> > transform();
/// \brief Compute and return the inverse transform (as a
/// complex image).
@@ -526,42 +289,417 @@ namespace mln
/// \tparam R Component type of the value type of the output
/// image.
template <class R>
- image2d< std::complex<R> > transform_inv()
- {
- const unsigned nrows = this->trans_im.nrows();
- const unsigned ncols = this->trans_im.ncols();
- for (unsigned row = 0; row < nrows; ++row)
- for (unsigned col = 0; col < ncols; ++col)
- {
- this->out[row * ncols + col].re =
- this->trans_im(row, col).real();
- this->out[row * 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 < nrows; ++row)
- for (unsigned col = 0; col < ncols; ++col)
- {
- new_im(row, col) = this->in[i];
- ++i;
- }
- return new_im;
- }
+ image2d< std::complex<R> > transform_inv();
/// \brief Compute and return the inverse transform of the FFT.
- image2d< std::complex<T> > transform_inv()
- {
- return transform_inv<T>();
- }
-
+ image2d< std::complex<T> > transform_inv();
};
} // end of namespace mln::transform
+
+
+# ifndef MLN_INCLUDE_ONLY
+
+ namespace internal
+ {
+
+ template <class T>
+ inline
+ const image2d< std::complex<T> >&
+ fft<T>::transformed_image() const
+ {
+ return trans_im;
+ }
+
+ template <class T>
+ inline
+ image2d< std::complex<T> >&
+ fft<T>::transformed_image()
+ {
+ return trans_im;
+ }
+
+ template <class T>
+ template <class R>
+ inline
+ image2d<R>
+ fft<T>::transformed_image_magn(bool ordered) const
+ {
+ // FIXME: Ensure R is real.
+
+ const unsigned nrows = trans_im.nrows();
+ const unsigned ncols = trans_im.ncols();
+ 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 + nrows / 2) % nrows,
+ (col + ncols / 2) % 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;
+ }
+
+ template <class T>
+ inline
+ image2d<T>
+ fft<T>::transformed_image_magn(bool ordered) const
+ {
+ return transformed_image_magn<T>(ordered);
+ }
+
+ template <class T>
+ template <class R>
+ inline
+ image2d<R>
+ fft<T>::transformed_image_clipped_magn(double clip, bool ordered) const
+ {
+ // FIXME: Ensure R is real.
+ // FIXME: Ensure `clip' is between 0 and 1?
+
+ double max = mln_min(double);
+ mln_piter(image2d<T>) it(trans_im.domain());
+ for_all(it)
+ if (std::norm(trans_im(it)) > max)
+ max = std::norm(trans_im(it));
+
+ const unsigned nrows = trans_im.nrows();
+ const unsigned ncols = trans_im.ncols();
+ 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)
+ if (std::norm(opt::at(trans_im,
+ (row + nrows / 2) % nrows,
+ (col + ncols / 2) % 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 + nrows / 2) % nrows,
+ (col + ncols / 2) % 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;
+ }
+
+ template <class T>
+ inline
+ image2d<T>
+ fft<T>::transformed_image_clipped_magn(double clip, bool ordered) const
+ {
+ return transformed_image_clipped_magn<T>(clip, ordered);
+ }
+
+ template <class T>
+ template <class R>
+ inline
+ image2d<R>
+ fft<T>::transformed_image_clipped_magn(bool ordered) const
+ {
+ return transformed_image_clipped_magn<R>(1, ordered);
+ }
+
+ template <class T>
+ inline
+ image2d<T>
+ fft<T>::transformed_image_clipped_magn(bool ordered) const
+ {
+ return transformed_image_clipped_magn<T>(1, ordered);
+ }
+
+ template <class T>
+ template <class R>
+ inline
+ image2d<R>
+ fft<T>::transformed_image_log_magn(double a, double b, bool ordered) const
+ {
+ /* FIXME: Find a more elegant way to fix range interval on a
+ and b (Note from Roland: what does it mean?). */
+
+ // FIXME: Ensure R is real.
+ // FIXME: Ensure 0 <= a <= 1000.
+ // FIXME: Ensure 0 <= b <= 1000.
+
+ image2d<R> new_im(trans_im.domain());
+
+ double max = mln_min(double);
+ mln_piter(image2d<R>) it(trans_im.domain());
+ for_all(it)
+ if (std::norm(trans_im(it)) > max)
+ max = std::norm(trans_im(it));
+
+ const unsigned nrows = trans_im.nrows();
+ const unsigned ncols = trans_im.ncols();
+ 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 + nrows / 2) % nrows,
+ (col + ncols / 2) % 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;
+ }
+
+ template <class T>
+ inline
+ image2d<T>
+ fft<T>::transformed_image_log_magn(double a, double b, bool ordered) const
+ {
+ return transformed_image_log_magn<T>(a, b, ordered);
+ }
+
+ template <class T>
+ template <class R>
+ inline
+ image2d<R>
+ fft<T>::transformed_image_log_magn(bool ordered) const
+ {
+ return transformed_image_log_magn<R>(1, 100, ordered);
+ }
+
+ template <class T>
+ inline
+ image2d<T>
+ fft<T>::transformed_image_log_magn(bool ordered) const
+ {
+ return transformed_image_log_magn<T>(1, 100, ordered);
+ }
+
+ template <class T>
+ inline
+ fft<T>::~fft()
+ {
+ fftw_free(in);
+ fftw_free(out);
+ fftw_destroy_plan(p);
+ fftw_destroy_plan(p_inv);
+ }
+
+ } // end of namespace mln::internal
+
+
+ namespace transform
+ {
+
+ /*--------------------------------------------------------.
+ | FFT engine (specialization for images of real values). |
+ `--------------------------------------------------------*/
+
+ template <class T>
+ template <typename D>
+ inline
+ fft<T, internal::fft_real>::fft(const image2d<D>& original_im)
+ {
+ const unsigned nrows = original_im.nrows();
+ const unsigned ncols = original_im.ncols();
+
+ this->in = (T*) fftw_malloc(nrows * ncols * sizeof(T));
+ this->out = (std::complex<T>*) fftw_malloc(nrows
+ * (ncols / 2 + 1)
+ * sizeof(std::complex<T>));
+
+ for (unsigned row = 0; row < nrows; ++row)
+ for (unsigned col = 0; col < ncols; ++col)
+ this->in[row * ncols + col] =
+ opt::at(original_im, row, col);
+
+ this->p =
+ fftw_plan_dft_r2c_2d (nrows, ncols,
+ this->in,
+ reinterpret_cast<fftw_complex*>(this->out),
+ FFTW_ESTIMATE);
+ this->p_inv =
+ fftw_plan_dft_c2r_2d (nrows, ncols,
+ reinterpret_cast<fftw_complex*>(this->out),
+ this->in,
+ FFTW_ESTIMATE);
+ this->trans_im = image2d< std::complex<T> >(original_im.domain());
+ }
+
+ template <class T>
+ inline
+ image2d< std::complex<T> >
+ fft<T, internal::fft_real>::transform()
+ {
+ fftw_execute(this->p);
+
+ const unsigned nrows = this->trans_im.nrows();
+ const unsigned ncols = this->trans_im.ncols();
+ unsigned denom = nrows * ncols;
+ int i = 0;
+ for (unsigned row = 0; row < nrows; ++row)
+ for (unsigned col = 0; col <= 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 < nrows; ++row)
+ for (unsigned col = ncols - 1; col > ncols / 2; --col)
+ opt::at(this->trans_im, row, col) =
+ opt::at(this->trans_im, nrows - row - 1, ncols - col - 1);
+ return this->trans_im;
+ }
+
+ template <class T>
+ template <class R>
+ inline
+ image2d<R>
+ fft<T, internal::fft_real>::transform_inv()
+ {
+ // FIXME: Ensure R is real.
+
+ const unsigned nrows = this->trans_im.nrows();
+ const unsigned ncols = this->trans_im.ncols();
+ for (unsigned row = 0; row < nrows; ++row)
+ for (unsigned col = 0; col <= ncols / 2; ++col)
+ this->out[row * (ncols / 2 + 1) + col] =
+ opt::at(this->trans_im, row, col);
+
+ fftw_execute(this->p_inv);
+
+ image2d<R> new_im(this->trans_im.domain());
+ int i = 0;
+ for (unsigned row = 0; row < nrows; ++row)
+ for (unsigned col = 0; col < 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;
+ }
+
+ template <class T>
+ inline
+ image2d<T>
+ fft<T, internal::fft_real>::transform_inv()
+ {
+ return transform_inv<T>();
+ }
+
+
+ /*-----------------------------------------------------------.
+ | FFT engine (specialization for images of complex values). |
+ `-----------------------------------------------------------*/
+
+ template <class T>
+ inline
+ fft<T, internal::fft_cplx>::fft(const image2d< std::complex<T> >& original_im)
+ {
+ const unsigned nrows = original_im.nrows();
+ const unsigned ncols = original_im.ncols();
+
+ this->in = fftw_malloc(sizeof(std::complex<T>) * nrows * ncols);
+ this->out = fftw_malloc(sizeof(std::complex<T>) * nrows * ncols);
+
+ for (unsigned row = 0; row < nrows; ++row)
+ for (unsigned col = 0; col < ncols; ++col)
+ {
+ this->in[row * ncols + col].re = original_im(row, col).real();
+ this->in[row * ncols + col].im = original_im(row, col).imag();
+ }
+
+ this->p = fftw_plan_dft_2d(nrows, ncols, this->in, this->out,
+ FFTW_FORWARD, FFTW_ESTIMATE);
+ this->p_inv = fftw_plan_dft_2d(nrows, ncols, this->out, this->in,
+ FFTW_BACKWARD, FFTW_ESTIMATE);
+ this->trans_im = image2d< std::complex<T> >(original_im.domain());
+ }
+
+ template <class T>
+ inline
+ image2d< std::complex<T> >
+ fft<T, internal::fft_cplx>::transform()
+ {
+ fftw_execute(this->p);
+
+ const unsigned nrows = this->trans_im.nrows();
+ const unsigned ncols = this->trans_im.ncols();
+ unsigned denom = nrows * ncols;
+ int i = 0;
+ for (unsigned row = 0; row < nrows; ++row)
+ for (unsigned col = 0; col < 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;
+ }
+
+ template <class T>
+ template <class R>
+ inline
+ image2d< std::complex<R> >
+ fft<T, internal::fft_cplx>::transform_inv()
+ {
+ const unsigned nrows = this->trans_im.nrows();
+ const unsigned ncols = this->trans_im.ncols();
+ for (unsigned row = 0; row < nrows; ++row)
+ for (unsigned col = 0; col < ncols; ++col)
+ {
+ this->out[row * ncols + col].re =
+ this->trans_im(row, col).real();
+ this->out[row * 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 < nrows; ++row)
+ for (unsigned col = 0; col < ncols; ++col)
+ {
+ new_im(row, col) = this->in[i];
+ ++i;
+ }
+ return new_im;
+ }
+
+ template <class T>
+ inline
+ image2d< std::complex<T> >
+ fft<T, internal::fft_cplx>::transform_inv()
+ {
+ return transform_inv<T>();
+ }
+
+ } // end of namespace mln::transform
+
+# endif // ! MLN_INCLUDE_ONLY
+
} // end of namespace mln
#endif // ! MLN_TRANSFORM_FFT_HH
--
1.7.10.4
