include/vigra/nonlineardiffusion.hxx

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/*               Copyright 1998-2002 by Ullrich Koethe                  */
/*       Cognitive Systems Group, University of Hamburg, Germany        */
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#ifndef VIGRA_NONLINEARDIFFUSION_HXX
#define VIGRA_NONLINEARDIFFUSION_HXX

#include <vector>
#include "stdimage.hxx"
#include "stdimagefunctions.hxx"
#include "imageiteratoradapter.hxx"
#include "functortraits.hxx"

namespace vigra {

template <class SrcIterator, class SrcAccessor,
          class CoeffIterator, class DestIterator>
void internalNonlinearDiffusionDiagonalSolver(
    SrcIterator sbegin, SrcIterator send, SrcAccessor sa,
    CoeffIterator diag, CoeffIterator upper, CoeffIterator lower,
    DestIterator dbegin)
{
    int w = send - sbegin - 1;

    int i;

    for(i=0; i<w; ++i)
    {
        lower[i] = lower[i] / diag[i];

        diag[i+1] = diag[i+1] - lower[i] * upper[i];
    }

    dbegin[0] = sa(sbegin);

    for(i=1; i<=w; ++i)
    {
        dbegin[i] = sa(sbegin, i) - lower[i-1] * dbegin[i-1];
    }

    dbegin[w] = dbegin[w] / diag[w];

    for(i=w-1; i>=0; --i)
    {
        dbegin[i] = (dbegin[i] - upper[i] * dbegin[i+1]) / diag[i];
    }
}


template <class SrcIterator, class SrcAccessor,
          class WeightIterator, class WeightAccessor,
          class DestIterator, class DestAccessor>
void internalNonlinearDiffusionAOSStep(
                   SrcIterator sul, SrcIterator slr, SrcAccessor as,
                   WeightIterator wul, WeightAccessor aw,
                   DestIterator dul, DestAccessor ad, double timestep)
{
    // use traits to determine SumType as to prevent possible overflow
    typedef typename
        NumericTraits<typename DestAccessor::value_type>::RealPromote
        DestType;

    typedef typename
        NumericTraits<typename WeightAccessor::value_type>::RealPromote
        WeightType;

    // calculate width and height of the image
    int w = slr.x - sul.x;
    int h = slr.y - sul.y;
    int d = (w < h) ? h : w;

    std::vector<WeightType> lower(d),
                            diag(d),
                            upper(d);

    std::vector<DestType> res(d);

    int x,y;

    WeightType one = NumericTraits<WeightType>::one();

     // create y iterators
    SrcIterator ys = sul;
    WeightIterator yw = wul;
    DestIterator yd = dul;

    // x-direction
    for(y=0; y<h; ++y, ++ys.y, ++yd.y, ++yw.y)
    {
        typename SrcIterator::row_iterator xs = ys.rowIterator();
        typename WeightIterator::row_iterator xw = yw.rowIterator();
        typename DestIterator::row_iterator xd = yd.rowIterator();

        // fill 3-diag matrix

        diag[0] = one + timestep * (aw(xw) + aw(xw, 1));
        for(x=1; x<w-1; ++x)
        {
            diag[x] = one + timestep * (2.0 * aw(xw, x) + aw(xw, x+1) + aw(xw, x-1));
        }
        diag[w-1] = one + timestep * (aw(xw, w-1) + aw(xw, w-2));

        for(x=0; x<w-1; ++x)
        {
            lower[x] = -timestep * (aw(xw, x) + aw(xw, x+1));
            upper[x] = lower[x];
        }

        internalNonlinearDiffusionDiagonalSolver(xs, xs+w, as,
                            diag.begin(), upper.begin(), lower.begin(), res.begin());

        for(x=0; x<w; ++x, ++xd)
        {
            ad.set(res[x], xd);
        }
    }

    // y-direction
    ys = sul;
    yw = wul;
    yd = dul;

    for(x=0; x<w; ++x, ++ys.x, ++yd.x, ++yw.x)
    {
        typename SrcIterator::column_iterator xs = ys.columnIterator();
        typename WeightIterator::column_iterator xw = yw.columnIterator();
        typename DestIterator::column_iterator xd = yd.columnIterator();

        // fill 3-diag matrix

        diag[0] = one + timestep * (aw(xw) + aw(xw, 1));
        for(y=1; y<h-1; ++y)
        {
            diag[y] = one + timestep * (2.0 * aw(xw, y) + aw(xw, y+1) + aw(xw, y-1));
        }
        diag[h-1] = one + timestep * (aw(xw, h-1) + aw(xw, h-2));

        for(y=0; y<h-1; ++y)
        {
            lower[y] = -timestep * (aw(xw, y) + aw(xw, y+1));
            upper[y] = lower[y];
        }

        internalNonlinearDiffusionDiagonalSolver(xs, xs+h, as,
                            diag.begin(), upper.begin(), lower.begin(), res.begin());

        for(y=0; y<h; ++y, ++xd)
        {
            ad.set(0.5 * (ad(xd) + res[y]), xd);
        }
    }
}

/** \addtogroup NonLinearDiffusion Non-linear Diffusion

    Perform edge-preserving smoothing.
*/
//@{

/********************************************************/
/*                                                      */
/*                  nonlinearDiffusion                  */
/*                                                      */
/********************************************************/

/** \brief Perform edge-preserving smoothing at the given scale.

    The algorithm solves the non-linear diffusion equation

    \f[
        \frac{\partial}{\partial t} u =
        \frac{\partial}{\partial x}
          \left( g(|\nabla u|)
                 \frac{\partial}{\partial x} u
          \right)
    \f]

    where <em> t</em> is the time, <b> x</b> is the location vector,
    <em> u(</em><b> x</b><em> , t)</em> is the smoothed image at time <em> t</em>, and
    <em> g(.)</em> is the location dependent diffusivity. At time zero, the image
    <em> u(</em><b> x</b><em> , 0)</em> is simply the original image. The time is
    propotional to the square of the scale parameter: \f$t = s^2\f$.
    The diffusion
    equation is solved iteratively according
    to the Additive Operator Splitting Scheme (AOS) from


    J. Weickert: <em>"Recursive Separable Schemes for Nonlinear Diffusion
    Filters"</em>,
    in: B. ter Haar Romeny, L. Florack, J. Koenderingk, M. Viergever (eds.):
        1st Intl. Conf. on Scale-Space Theory in Computer Vision 1997,
        Springer LNCS 1252

    <TT>DiffusivityFunctor</TT> implements the gradient dependent local diffusivity.
    It is passed
    as an argument to \ref gradientBasedTransform(). The return value must be
    between 0 and 1 and determines the weight a pixel gets when
    its neighbors are smoothed. Weickert recommends the use of the diffusivity
    implemented by class \ref DiffusivityFunctor. It's also possible to use
    other functors, for example one that always returns 1, in which case
    we obtain the solution to the linear diffusion equation, i.e.
    Gaussian convolution.

    The source value type must be a
    linear space with internal addition, scalar multiplication, and
    NumericTraits defined. The value_type of the DiffusivityFunctor must be the
    scalar field over wich the source value type's linear space is defined.

    In addition to <TT>nonlinearDiffusion()</TT>, there is an algorithm
    <TT>nonlinearDiffusionExplicit()</TT> which implements the Explicit Scheme
    described in the above article. Both algorithms have the same interface,
    but the explicit scheme gives slightly more accurate approximations of
    the diffusion process at the cost of much slower processing.

    <b> Declarations:</b>

    pass arguments explicitly:
    \code
    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
                  class DestIterator, class DestAccessor,
                  class DiffusivityFunctor>
        void nonlinearDiffusion(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                           DestIterator dul, DestAccessor ad,
                           DiffusivityFunctor const & weight, double scale);
    }
    \endcode


    use argument objects in conjunction with \ref ArgumentObjectFactories:
    \code
    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
                  class DestIterator, class DestAccessor,
                  class DiffusivityFunctor>
        void nonlinearDiffusion(
            triple<SrcIterator, SrcIterator, SrcAccessor> src,
            pair<DestIterator, DestAccessor> dest,
            DiffusivityFunctor const & weight, double scale);
    }
    \endcode

    <b> Usage:</b>

    <b>\#include</b> "<a href="nonlineardiffusion_8hxx-source.html">vigra/nonlineardiffusion.hxx</a>"


    \code
    FImage src(w,h), dest(w,h);
    float edge_threshold, scale;
    ...

    nonlinearDiffusion(srcImageRange(src), destImage(dest),
                       DiffusivityFunctor<float>(edge_threshold), scale);
    \endcode

    <b> Required Interface:</b>

    <ul>

    <li> <TT>SrcIterator</TT> and <TT>DestIterator</TT> are models of ImageIterator
    <li> <TT>SrcAccessor</TT> and <TT>DestAccessor</TT> are models of StandardAccessor
    <li> <TT>SrcAccessor::value_type</TT> is a linear space
    <li> <TT>DiffusivityFunctor</TT> conforms to the requirements of
          \ref gradientBasedTransform(). Its range is between 0 and 1.
    <li> <TT>DiffusivityFunctor::value_type</TT> is an algebraic field

    </ul>

    <b> Precondition:</b>

    <TT>scale > 0</TT>
*/
template <class SrcIterator, class SrcAccessor,
          class DestIterator, class DestAccessor,
          class DiffusivityFunc>
void nonlinearDiffusion(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                   DestIterator dul, DestAccessor ad,
                   DiffusivityFunc const & weight, double scale)
{
    vigra_precondition(scale > 0.0, "nonlinearDiffusion(): scale must be > 0");

    double total_time = scale*scale/2.0;
    static const double time_step = 5.0;
    int number_of_steps = (int)(total_time / time_step);
    double rest_time = total_time - time_step * number_of_steps;

    Size2D size(slr.x - sul.x, slr.y - sul.y);

    typedef typename
        NumericTraits<typename SrcAccessor::value_type>::RealPromote
        TmpType;
    typedef typename DiffusivityFunc::value_type WeightType;

    BasicImage<TmpType> smooth1(size);
    BasicImage<TmpType> smooth2(size);

    BasicImage<WeightType> weights(size);

    typename BasicImage<TmpType>::Iterator s1 = smooth1.upperLeft(),
                                  s2 = smooth2.upperLeft();
    typename BasicImage<TmpType>::Accessor a = smooth1.accessor();

    typename BasicImage<WeightType>::Iterator wi = weights.upperLeft();
    typename BasicImage<WeightType>::Accessor wa = weights.accessor();

    gradientBasedTransform(sul, slr, as, wi, wa, weight);

    internalNonlinearDiffusionAOSStep(sul, slr, as, wi, wa, s1, a, rest_time);

    for(int i = 0; i < number_of_steps; ++i)
    {
        gradientBasedTransform(s1, s1+size, a, wi, wa, weight);

        internalNonlinearDiffusionAOSStep(s1, s1+size, a, wi, wa, s2, a, time_step);

		std::swap(s1, s2);
    }

    copyImage(s1, s1+size, a, dul, ad);
}

template <class SrcIterator, class SrcAccessor,
          class DestIterator, class DestAccessor,
          class DiffusivityFunc>
inline
void nonlinearDiffusion(
    triple<SrcIterator, SrcIterator, SrcAccessor> src,
    pair<DestIterator, DestAccessor> dest,
    DiffusivityFunc const & weight, double scale)
{
    nonlinearDiffusion(src.first, src.second, src.third,
                           dest.first, dest.second,
                           weight, scale);
}

template <class SrcIterator, class SrcAccessor,
          class WeightIterator, class WeightAccessor,
          class DestIterator, class DestAccessor>
void internalNonlinearDiffusionExplicitStep(
                   SrcIterator sul, SrcIterator slr, SrcAccessor as,
                   WeightIterator wul, WeightAccessor aw,
                   DestIterator dul, DestAccessor ad,
                   double time_step)
{
    // use traits to determine SumType as to prevent possible overflow
    typedef typename
        NumericTraits<typename SrcAccessor::value_type>::RealPromote
        SumType;

    typedef typename
        NumericTraits<typename WeightAccessor::value_type>::RealPromote
        WeightType;

    // calculate width and height of the image
    int w = slr.x - sul.x;
    int h = slr.y - sul.y;

    int x,y;

    static const Diff2D left(-1, 0);
    static const Diff2D right(1, 0);
    static const Diff2D top(0, -1);
    static const Diff2D bottom(0, 1);

    WeightType gt, gb, gl, gr, g0;
    WeightType one = NumericTraits<WeightType>::one();
    SumType sum;

    time_step /= 2.0;

    // create y iterators
    SrcIterator ys = sul;
    WeightIterator yw = wul;
    DestIterator yd = dul;

    SrcIterator xs = ys;
    WeightIterator xw = yw;
    DestIterator xd = yd;

    gt = (aw(xw) + aw(xw, bottom)) * time_step;
    gb = (aw(xw) + aw(xw, bottom)) * time_step;
    gl = (aw(xw) + aw(xw, right)) * time_step;
    gr = (aw(xw) + aw(xw, right)) * time_step;
    g0 = one - gt - gb - gr - gl;

    sum = g0 * as(xs);
    sum += gt * as(xs, bottom);
    sum += gb * as(xs, bottom);
    sum += gl * as(xs, right);
    sum += gr * as(xs, right);

    ad.set(sum, xd);

    for(x=2, ++xs.x, ++xd.x, ++xw.x; x<w; ++x, ++xs.x, ++xd.x, ++xw.x)
    {
        gt = (aw(xw) + aw(xw, bottom)) * time_step;
        gb = (aw(xw) + aw(xw, bottom)) * time_step;
        gl = (aw(xw) + aw(xw, left)) * time_step;
        gr = (aw(xw) + aw(xw, right)) * time_step;
        g0 = one - gt - gb - gr - gl;

        sum = g0 * as(xs);
        sum += gt * as(xs, bottom);
        sum += gb * as(xs, bottom);
        sum += gl * as(xs, left);
        sum += gr * as(xs, right);

        ad.set(sum, xd);
    }

    gt = (aw(xw) + aw(xw, bottom)) * time_step;
    gb = (aw(xw) + aw(xw, bottom)) * time_step;
    gl = (aw(xw) + aw(xw, left)) * time_step;
    gr = (aw(xw) + aw(xw, left)) * time_step;
    g0 = one - gt - gb - gr - gl;

    sum = g0 * as(xs);
    sum += gt * as(xs, bottom);
    sum += gb * as(xs, bottom);
    sum += gl * as(xs, left);
    sum += gr * as(xs, left);

    ad.set(sum, xd);

    for(y=2, ++ys.y, ++yd.y, ++yw.y; y<h; ++y, ++ys.y, ++yd.y, ++yw.y)
    {
        xs = ys;
        xd = yd;
        xw = yw;

        gt = (aw(xw) + aw(xw, top)) * time_step;
        gb = (aw(xw) + aw(xw, bottom)) * time_step;
        gl = (aw(xw) + aw(xw, right)) * time_step;
        gr = (aw(xw) + aw(xw, right)) * time_step;
        g0 = one - gt - gb - gr - gl;

        sum = g0 * as(xs);
        sum += gt * as(xs, top);
        sum += gb * as(xs, bottom);
        sum += gl * as(xs, right);
        sum += gr * as(xs, right);

        ad.set(sum, xd);

        for(x=2, ++xs.x, ++xd.x, ++xw.x; x<w; ++x, ++xs.x, ++xd.x, ++xw.x)
        {
            gt = (aw(xw) + aw(xw, top)) * time_step;
            gb = (aw(xw) + aw(xw, bottom)) * time_step;
            gl = (aw(xw) + aw(xw, left)) * time_step;
            gr = (aw(xw) + aw(xw, right)) * time_step;
            g0 = one - gt - gb - gr - gl;

            sum = g0 * as(xs);
            sum += gt * as(xs, top);
            sum += gb * as(xs, bottom);
            sum += gl * as(xs, left);
            sum += gr * as(xs, right);

            ad.set(sum, xd);
        }

        gt = (aw(xw) + aw(xw, top)) * time_step;
        gb = (aw(xw) + aw(xw, bottom)) * time_step;
        gl = (aw(xw) + aw(xw, left)) * time_step;
        gr = (aw(xw) + aw(xw, left)) * time_step;
        g0 = one - gt - gb - gr - gl;

        sum = g0 * as(xs);
        sum += gt * as(xs, top);
        sum += gb * as(xs, bottom);
        sum += gl * as(xs, left);
        sum += gr * as(xs, left);

        ad.set(sum, xd);
    }

    xs = ys;
    xd = yd;
    xw = yw;

    gt = (aw(xw) + aw(xw, top)) * time_step;
    gb = (aw(xw) + aw(xw, top)) * time_step;
    gl = (aw(xw) + aw(xw, right)) * time_step;
    gr = (aw(xw) + aw(xw, right)) * time_step;
    g0 = one - gt - gb - gr - gl;

    sum = g0 * as(xs);
    sum += gt * as(xs, top);
    sum += gb * as(xs, top);
    sum += gl * as(xs, right);
    sum += gr * as(xs, right);

    ad.set(sum, xd);

    for(x=2, ++xs.x, ++xd.x, ++xw.x; x<w; ++x, ++xs.x, ++xd.x, ++xw.x)
    {
        gt = (aw(xw) + aw(xw, top)) * time_step;
        gb = (aw(xw) + aw(xw, top)) * time_step;
        gl = (aw(xw) + aw(xw, left)) * time_step;
        gr = (aw(xw) + aw(xw, right)) * time_step;
        g0 = one - gt - gb - gr - gl;

        sum = g0 * as(xs);
        sum += gt * as(xs, top);
        sum += gb * as(xs, top);
        sum += gl * as(xs, left);
        sum += gr * as(xs, right);

        ad.set(sum, xd);
    }

    gt = (aw(xw) + aw(xw, top)) * time_step;
    gb = (aw(xw) + aw(xw, top)) * time_step;
    gl = (aw(xw) + aw(xw, left)) * time_step;
    gr = (aw(xw) + aw(xw, left)) * time_step;
    g0 = one - gt - gb - gr - gl;

    sum = g0 * as(xs);
    sum += gt * as(xs, top);
    sum += gb * as(xs, top);
    sum += gl * as(xs, left);
    sum += gr * as(xs, left);

    ad.set(sum, xd);
}

template <class SrcIterator, class SrcAccessor,
          class DestIterator, class DestAccessor,
          class DiffusivityFunc>
void nonlinearDiffusionExplicit(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                   DestIterator dul, DestAccessor ad,
                   DiffusivityFunc const & weight, double scale)
{
    vigra_precondition(scale > 0.0, "nonlinearDiffusionExplicit(): scale must be > 0");

    double total_time = scale*scale/2.0;
    static const double time_step = 0.25;
    int number_of_steps = total_time / time_step;
    double rest_time = total_time - time_step * number_of_steps;

    Size2D size(slr.x - sul.x, slr.y - sul.y);

    typedef typename
        NumericTraits<typename SrcAccessor::value_type>::RealPromote
        TmpType;
    typedef typename DiffusivityFunc::value_type WeightType;

    BasicImage<TmpType> smooth1(size);
    BasicImage<TmpType> smooth2(size);

    BasicImage<WeightType> weights(size);

    typename BasicImage<TmpType>::Iterator s1 = smooth1.upperLeft(),
                                  s2 = smooth2.upperLeft();
    typename BasicImage<TmpType>::Accessor a = smooth1.accessor();

    typename BasicImage<WeightType>::Iterator wi = weights.upperLeft();
    typename BasicImage<WeightType>::Accessor wa = weights.accessor();

    gradientBasedTransform(sul, slr, as, wi, wa, weight);

    internalNonlinearDiffusionExplicitStep(sul, slr, as, wi, wa, s1, a, rest_time);

    for(int i = 0; i < number_of_steps; ++i)
    {
        gradientBasedTransform(s1, s1+size, a, wi, wa, weight);

        internalNonlinearDiffusionExplicitStep(s1, s1+size, a, wi, wa, s2, a, time_step);

        swap(s1, s2);
    }

    copyImage(s1, s1+size, a, dul, ad);
}

template <class SrcIterator, class SrcAccessor,
          class DestIterator, class DestAccessor,
          class DiffusivityFunc>
inline
void nonlinearDiffusionExplicit(
    triple<SrcIterator, SrcIterator, SrcAccessor> src,
    pair<DestIterator, DestAccessor> dest,
    DiffusivityFunc const & weight, double scale)
{
    nonlinearDiffusionExplicit(src.first, src.second, src.third,
                           dest.first, dest.second,
                           weight, scale);
}

/********************************************************/
/*                                                      */
/*                   DiffusivityFunctor                 */
/*                                                      */
/********************************************************/

/** \brief Diffusivity functor for non-linear diffusion.

    This functor implements the diffusivity recommended by Weickert:

    \f[
        g(|\nabla u|) = 1 -
           \exp{\left(\frac{-3.315}{(|\nabla u| / thresh)^4}\right)}
    \f]


    where <TT>thresh</TT> is a threshold that determines whether a specific gradient
    magnitude is interpreted as a significant edge (above the threshold)
    or as noise. It is meant to be used with \ref nonlinearDiffusion().
*/
template <class Value>
class DiffusivityFunctor
{
  public:
         /** the functors first argument type (must be an algebraic field with <TT>exp()</TT> defined).
             However, the functor also works with RGBValue<first_argument_type> (this hack is
             necessary since Microsoft C++ doesn't support partial specialization).
         */
    typedef Value first_argument_type;

         /** the functors second argument type (same as first).
             However, the functor also works with RGBValue<second_argument_type> (this hack is
             necessary since Microsoft C++ doesn't support partial specialization).
         */
    typedef Value second_argument_type;

         /** the functors result type
         */
    typedef typename NumericTraits<Value>::RealPromote result_type;

         /** \deprecated use first_argument_type, second_argument_type, result_type
         */
    typedef Value value_type;

         /** init functor with given edge threshold
         */
    DiffusivityFunctor(Value const & thresh)
    : weight_(thresh*thresh),
      one_(NumericTraits<result_type>::one()),
      zero_(NumericTraits<result_type>::zero())
    {}

         /** calculate diffusivity from scalar arguments
         */
    result_type operator()(first_argument_type const & gx, second_argument_type const & gy) const
    {
        Value mag = (gx*gx + gy*gy) / weight_;

        return (mag == zero_) ? one_ : one_ - VIGRA_CSTD::exp(-3.315 / mag / mag);
    }

         /** calculate diffusivity from RGB arguments
         */
    result_type operator()(RGBValue<Value> const & gx, RGBValue<Value> const & gy) const
    {
        result_type mag = (gx.red()*gx.red() +
                     gx.green()*gx.green() +
                     gx.blue()*gx.blue() +
                     gy.red()*gy.red() +
                     gy.green()*gy.green() +
                     gy.blue()*gy.blue()) / weight_;

        return (mag == zero_) ? one_ : one_ - VIGRA_CSTD::exp(-3.315 / mag / mag);
    }

    result_type weight_;
    result_type one_;
    result_type zero_;
};

template <class ValueType>
class FunctorTraits<DiffusivityFunctor<ValueType> >
: public FunctorTraitsBase<DiffusivityFunctor<ValueType> >
{
  public:
    typedef VigraTrueType isBinaryFunctor;
};


//@}

} // namespace vigra

#endif /* VIGRA_NONLINEARDIFFUSION_HXX */