cornerdetection.hxx

/************************************************************************/
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/*               Copyright 1998-2004 by Ullrich Koethe                  */
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/************************************************************************/
 
 
#ifndef VIGRA_CORNERDETECTION_HXX
#define VIGRA_CORNERDETECTION_HXX

#include "utilities.hxx"
#include "numerictraits.hxx"
#include "stdimage.hxx"
#include "combineimages.hxx"
#include "convolution.hxx"
#include "functortraits.hxx"
#include "multi_shape.hxx"

namespace vigra {

template <class SrcType>
struct CornerResponseFunctor
{
    typedef typename NumericTraits<SrcType>::RealPromote argument_type;
    typedef argument_type result_type;
    
    result_type operator()(argument_type a1, 
                        argument_type a2, argument_type a3) const
    {
      return detail::RequiresExplicitCast<result_type>::cast((a1*a2 - a3*a3) - 0.04 * (a1 + a2) * (a1 + a2));
    }
};

template <class T>
class FunctorTraits<CornerResponseFunctor<T> >
: public FunctorTraitsBase<CornerResponseFunctor<T> >
{
  public:
    typedef VigraTrueType isTernaryFunctor;
};

template <class SrcType>
struct FoerstnerCornerFunctor
{
    typedef typename NumericTraits<SrcType>::RealPromote argument_type;
    typedef argument_type result_type;
    
    result_type operator()(argument_type a1, 
                           argument_type a2, argument_type a3) const
    {
        return (a1*a2 - a3*a3) / (a1 + a2);
    }
};

template <class T>
class FunctorTraits<FoerstnerCornerFunctor<T> >
: public FunctorTraitsBase<FoerstnerCornerFunctor<T> >
{
  public:
    typedef VigraTrueType isTernaryFunctor;
};

template <class SrcType>
struct RohrCornerFunctor
{
    typedef typename NumericTraits<SrcType>::RealPromote argument_type;
    typedef argument_type result_type;
    
    result_type operator()(argument_type a1, 
                        argument_type a2, argument_type a3) const
    {
        return (a1*a2 - a3*a3);
    }
};

template <class T>
class FunctorTraits<RohrCornerFunctor<T> >
: public FunctorTraitsBase<RohrCornerFunctor<T> >
{
  public:
    typedef VigraTrueType isTernaryFunctor;
};

template <class SrcType>
struct BeaudetCornerFunctor
{
    typedef typename NumericTraits<SrcType>::RealPromote argument_type;
    typedef argument_type result_type;
    
    result_type operator()(argument_type a1, 
                        argument_type a2, argument_type a3) const
    {
        return (a3*a3 - a1*a2);
    }
};

template <class T>
class FunctorTraits<BeaudetCornerFunctor<T> >
: public FunctorTraitsBase<BeaudetCornerFunctor<T> >
{
  public:
    typedef VigraTrueType isTernaryFunctor;
};

/** \addtogroup CornerDetection Corner Detection
    Measure the 'cornerness' at each pixel.
    Note: The Kitchen-Rosenfeld detector is not implemented because of its
    inferior performance. The SUSAN detector is missing because it's patented.
*/
//@{ 
                                    
/********************************************************/
/*                                                      */
/*                 cornerResponseFunction               */
/*                                                      */
/********************************************************/

/** \brief Find corners in an image (1).

    This algorithm implements the so called 'corner response function'
    to measure the 'cornerness' of each pixel in the image, according to
    [C.G. Harris and M.J. Stevens: <em> "A Combined Corner and Edge Detector"</em>,
    Proc. of 4th Alvey Vision Conference, 1988]. Several studies have found this to be a
    very robust corner detector, although it moves the corners somewhat into one
    region, depending on the scale.
    
    The algorithm first determines the structure tensor at each pixel by calling
    \ref structureTensor(). Then the entries of the structure tensor are combined as 
    
    \f[
        \mbox{\rm CornerResponse} = \mbox{\rm det(StructureTensor)} - 0.04 \mbox{\rm tr(StructureTensor)}^2
        = A B - C^2 - 0.04 (A + B)^2
    \f]
    
    The local maxima of the corner response denote the corners in the gray level 
    image.
    
    The source value type must be a linear algebra, i.e. addition, subtraction, and
    multiplication with itself, multiplication with doubles and 
    \ref NumericTraits "NumericTraits" must 
    be defined. 
    
    <b> Declarations:</b>
    
    pass 2D array views:
    \code
    namespace vigra {
        template <class T1, class S1,
                  class T2, class S2>
        void 
        cornerResponseFunction(MultiArrayView<2, T1, S1> const & src,
                               MultiArrayView<2, T2, S2> dest,
                               double scale);
    }
    \endcode
    
    \deprecatedAPI{cornerResponseFunction}
    pass \ref ImageIterators and \ref DataAccessors :
    \code
    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
                  class DestIterator, class DestAccessor>
        void
        cornerResponseFunction(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                               DestIterator dul, DestAccessor ad,
                               double scale)
    }
    \endcode
    use argument objects in conjunction with \ref ArgumentObjectFactories :
    \code
    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
                  class DestIterator, class DestAccessor>
        void cornerResponseFunction(
                   triple<SrcIterator, SrcIterator, SrcAccessor> src,
                   pair<DestIterator, DestAccessor> dest,
                   double scale)
    }
    \endcode
    \deprecatedEnd
    
    <b> Usage:</b>
    
    <b>\#include</b> <vigra/cornerdetection.hxx><br>
    Namespace: vigra

    \code
    MultiArray<2, unsigned char> src(w,h), corners(w,h);
    MultiArray<2, float>         corner_response(w,h);
    ...
    
    // find corner response at scale 1.0
    cornerResponseFunction(src, corner_response, 1.0);
    
    // find local maxima of corner response, mark with 1
    localMaxima(corner_response, corners);
    
    // threshold corner response to keep only strong corners (above 400.0)
    transformImage(corner_response, corner_response,
                   Threshold<double, double>(400.0, std::numeric_limits<double>::max(), 0.0, 1.0)); 

    // combine thresholding and local maxima
    combineTwoImages(corners, corner_response,
                     corners, std::multiplies<float>());
    \endcode

    \deprecatedUsage{cornerResponseFunction}
    \code
    vigra::BImage src(w,h), corners(w,h);
    vigra::FImage corner_response(w,h);
    
    // empty corner image
    corners.init(0.0);
    ...
    
    // find corner response at scale 1.0
    vigra::cornerResponseFunction(srcImageRange(src), destImage(corner_response), 
                           1.0);
    
    // find local maxima of corner response, mark with 1
    vigra::localMaxima(srcImageRange(corner_response), destImage(corners));
    
    // threshold corner response to keep only strong corners (above 400.0)
    transformImage(srcImageRange(corner_response), destImage(corner_response),
          vigra::Threshold<double, double>(
               400.0, std::numeric_limits<double>::max(), 0.0, 1.0)); 

    // combine thresholding and local maxima
    vigra::combineTwoImages(srcImageRange(corners), srcImage(corner_response),
                     destImage(corners), std::multiplies<float>());
    \endcode
    <b> Required Interface:</b>
    \code
    SrcImageIterator src_upperleft, src_lowerright;
    DestImageIterator dest_upperleft;
    
    SrcAccessor src_accessor;
    DestAccessor dest_accessor;
    
    SrcAccessor::value_type u = src_accessor(src_upperleft);
    double d;
    
    u = u + u
    u = u - u
    u = u * u
    u = d * u
    
    dest_accessor.set(u, dest_upperleft);
    \endcode
    \deprecatedEnd
*/
doxygen_overloaded_function(template <...> void cornerResponseFunction)

template <class SrcIterator, class SrcAccessor,
          class DestIterator, class DestAccessor>
void
cornerResponseFunction(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                       DestIterator dul, DestAccessor ad,
                       double scale)
{
    vigra_precondition(scale > 0.0,
                 "cornerResponseFunction(): Scale must be > 0");
                 
    int w = slr.x - sul.x;
    int h = slr.y - sul.y;
    
    if(w <= 0 || h <= 0) return;
    
    typedef typename 
        NumericTraits<typename SrcAccessor::value_type>::RealPromote TmpType;
        
    typedef BasicImage<TmpType> TmpImage;
    
    TmpImage gx(w,h);
    TmpImage gy(w,h);
    TmpImage gxy(w,h);

    structureTensor(srcIterRange(sul, slr, as), 
                    destImage(gx), destImage(gxy), destImage(gy), 
                    scale, scale);
    CornerResponseFunctor<typename SrcAccessor::value_type > cf;
                    
    combineThreeImages(srcImageRange(gx), srcImage(gy), srcImage(gxy), 
                       destIter(dul, ad), cf );
}

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

template <class T1, class S1,
          class T2, class S2>
inline void 
cornerResponseFunction(MultiArrayView<2, T1, S1> const & src,
                       MultiArrayView<2, T2, S2> dest,
                       double scale)
{
    vigra_precondition(src.shape() == dest.shape(),
        "cornerResponseFunction(): shape mismatch between input and output.");
    cornerResponseFunction(srcImageRange(src), destImage(dest), scale);
}

/********************************************************/
/*                                                      */
/*               foerstnerCornerDetector                */
/*                                                      */
/********************************************************/

/** \brief Find corners in an image (2).

    This algorithm implements the so called 'Foerstner Corner Detector'
    to measure the 'cornerness' of each pixel in the image, according to
    [W. F&ouml;rstner: <em> "A feature based correspondence algorithms for image
    matching"</em>, Intl. Arch. Photogrammetry and Remote Sensing, vol. 24, pp 160-166, 
    1986]. It is also known as the "Plessey Detector" by Harris. However, it should not 
    be confused with the
    "\link cornerResponseFunction Corner Response Function\endlink ",
    another detector invented by Harris.
    
    The algorithm first determines the structure tensor at each pixel by calling
    \ref structureTensor(), where the given scale is used for both the inner and outer scales. 
    Then the entries of the structure tensor are combined as 
    
    \f[
        \mbox{\rm FoerstnerCornerStrength} = \frac{\mbox{\rm det(StructureTensor)}}{\mbox{\rm tr(StructureTensor)}} = 
        \frac{A B - C^2}{A + B}
    \f]
    
    The local maxima of the corner strength denote the corners in the gray level 
    image. Its performance is similar to the \ref cornerResponseFunction().
    
    The source value type must be a division algebra, i.e. addition, subtraction,
    multiplication, and division with itself, multiplication with doubles and 
    \ref NumericTraits "NumericTraits" must 
    be defined.
    
    <b> Declarations:</b>
    
    pass 2D array views:
    \code
    namespace vigra {
        template <class T1, class S1,
                  class T2, class S2>
        void
        foerstnerCornerDetector(MultiArrayView<2, T1, S1> const & src,
                                MultiArrayView<2, T2, S2> dest,
                                double scale);
    }
    \endcode
    
    \deprecatedAPI{foerstnerCornerDetector}
    pass \ref ImageIterators and \ref DataAccessors :
    \code
    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
                  class DestIterator, class DestAccessor>
        void
        foerstnerCornerDetector(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                               DestIterator dul, DestAccessor ad,
                               double scale)
    }
    \endcode
    use argument objects in conjunction with \ref ArgumentObjectFactories :
    \code
    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
                  class DestIterator, class DestAccessor>
         void foerstnerCornerDetector(
                   triple<SrcIterator, SrcIterator, SrcAccessor> src,
                   pair<DestIterator, DestAccessor> dest,
                   double scale)
    }
    \endcode
    \deprecatedEnd
    
    <b> Usage:</b>
    
    <b>\#include</b> <vigra/cornerdetection.hxx><br>
    Namespace: vigra

    \code
    MultiArray<2, unsigned char> src(w,h), corners(w,h);
    MultiArray<2, float>         foerstner_corner_strength(w,h);
    ...
    
    // find corner response at scale 1.0
    foerstnerCornerDetector(src, foerstner_corner_strength, 1.0);
    
    // find local maxima of corner response, mark with 1
    localMaxima(foerstner_corner_strength, corners);
    \endcode

    \deprecatedUsage{foerstnerCornerDetector}
    \code
    vigra::BImage src(w,h), corners(w,h);
    vigra::FImage foerstner_corner_strength(w,h);
    
    // empty corner image
    corners.init(0.0);
    ...
    
    // find corner response at scale 1.0
    vigra::foerstnerCornerDetector(srcImageRange(src), destImage(foerstner_corner_strength), 
                                   1.0);
    
    // find local maxima of corner response, mark with 1
    vigra::localMaxima(srcImageRange(foerstner_corner_strength), destImage(corners));
    \endcode
    <b> Required Interface:</b>
    \code
    SrcImageIterator src_upperleft, src_lowerright;
    DestImageIterator dest_upperleft;
    
    SrcAccessor src_accessor;
    DestAccessor dest_accessor;
    
    SrcAccessor::value_type u = src_accessor(src_upperleft);
    double d;
    
    u = u + u
    u = u - u
    u = u * u
    u = u / u
    u = d * u
    
    dest_accessor.set(u, dest_upperleft);
    \endcode
    \deprecatedEnd
*/
doxygen_overloaded_function(template <...> void foerstnerCornerDetector)

template <class SrcIterator, class SrcAccessor,
          class DestIterator, class DestAccessor>
void
foerstnerCornerDetector(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                       DestIterator dul, DestAccessor ad,
                       double scale)
{
    vigra_precondition(scale > 0.0,
                 "foerstnerCornerDetector(): Scale must be > 0");
                 
    int w = slr.x - sul.x;
    int h = slr.y - sul.y;
    
    if(w <= 0 || h <= 0) return;
    
    typedef typename 
        NumericTraits<typename SrcAccessor::value_type>::RealPromote TmpType;
        
    typedef BasicImage<TmpType> TmpImage;
    
    TmpImage gx(w,h);
    TmpImage gy(w,h);
    TmpImage gxy(w,h);

    structureTensor(srcIterRange(sul, slr, as), 
                    destImage(gx), destImage(gxy), destImage(gy), 
                    scale, scale);
    FoerstnerCornerFunctor<typename SrcAccessor::value_type > cf;
                    
    combineThreeImages(srcImageRange(gx), srcImage(gy), srcImage(gxy), 
                       destIter(dul, ad), cf );
}

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

template <class T1, class S1,
          class T2, class S2>
inline void
foerstnerCornerDetector(MultiArrayView<2, T1, S1> const & src,
                        MultiArrayView<2, T2, S2> dest,
                        double scale)
{
    vigra_precondition(src.shape() == dest.shape(),
        "foerstnerCornerDetector(): shape mismatch between input and output.");
    foerstnerCornerDetector(srcImageRange(src),
                            destImage(dest),
                            scale);
}

/********************************************************/
/*                                                      */
/*                   rohrCornerDetector                 */
/*                                                      */
/********************************************************/

/** \brief Find corners in an image (3).

    This algorithm implements yet another structure tensor-based corner detector, 
    according to [K. Rohr: <em>"Untersuchung von grauwertabh&auml;ngigen 
    Transformationen zur Ermittlung der optischen Flusses in Bildfolgen"</em>, 
    Diploma thesis, Inst. f&uuml;r Nachrichtensysteme, Univ. Karlsruhe, 1987, see also
    K. Rohr: <em>"Modelling and Identification of Characteristic Intensity Variations"</em>,
    Image and Vision Computing 10:2 (1992) 66-76 and K. Rohr: <em>"Localization Properties of 
    Direct Corner Detectors"</em>, J. of Mathematical Imaging and Vision 4:2 (1994) 139-150]. 
    
    The algorithm first determines the structure tensor at each pixel by calling
    \ref structureTensor(), where the given scale is used for both the inner and outer scales. 
    Then the entries of the structure tensor are combined as 
    
    \f[
        \mbox{\rm RohrCornerStrength} = \mbox{\rm det(StructureTensor)} = A B - C^2
    \f]
    
    The local maxima of the corner strength denote the corners in the gray level 
    image. Its performance is similar to the \ref cornerResponseFunction().
    
    The source value type must be a linear algebra, i.e. addition, subtraction, and
    multiplication with itself, multiplication with doubles and 
    \ref NumericTraits "NumericTraits" must be defined.
    
    <b> Declarations:</b>
    
    pass 2D array views:
    \code
    namespace vigra {
        template <class T1, class S1,
                  class T2, class S2>
        void
        rohrCornerDetector(MultiArrayView<2, T1, S1> const & src,
                           MultiArrayView<2, T2, S2> dest,
                           double scale);
    }
    \endcode
    
    \deprecatedAPI{rohrCornerDetector}
    pass \ref ImageIterators and \ref DataAccessors :
    \code
    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
                  class DestIterator, class DestAccessor>
        void
        rohrCornerDetector(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                           DestIterator dul, DestAccessor ad,
                           double scale)
    }
    \endcode
    use argument objects in conjunction with \ref ArgumentObjectFactories :
    \code
    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
                  class DestIterator, class DestAccessor>
        void rohrCornerDetector(
                   triple<SrcIterator, SrcIterator, SrcAccessor> src,
                   pair<DestIterator, DestAccessor> dest,
                   double scale)
    }
    \endcode
    \deprecatedEnd
    
    <b> Usage:</b>
    
    <b>\#include</b> <vigra/cornerdetection.hxx><br>
    Namespace: vigra

    \code
    MultiArray<2, unsigned char> src(w,h), corners(w,h);
    MultiArray<2, float>         rohr_corner_strength(w,h);
    ...
    
    // find corner response at scale 1.0
    rohrCornerDetector(src, rohr_corner_strength, 1.0);
    
    // find local maxima of corner response, mark with 1
    localMaxima(rohr_corner_strength, corners);
    \endcode

    \deprecatedUsage{rohrCornerDetector}
    \code
    vigra::BImage src(w,h), corners(w,h);
    vigra::FImage rohr_corner_strength(w,h);
    
    // empty corner image
    corners.init(0.0);
    ...
    
    // find corner response at scale 1.0
    vigra::rohrCornerDetector(srcImageRange(src), destImage(rohr_corner_strength), 
                              1.0);
    
    // find local maxima of corner response, mark with 1
    vigra::localMaxima(srcImageRange(rohr_corner_strength), destImage(corners));
    \endcode
    <b> Required Interface:</b>
    \code
    SrcImageIterator src_upperleft, src_lowerright;
    DestImageIterator dest_upperleft;
    
    SrcAccessor src_accessor;
    DestAccessor dest_accessor;
    
    SrcAccessor::value_type u = src_accessor(src_upperleft);
    double d;
    
    u = u + u
    u = u - u
    u = u * u
    u = d * u
    
    dest_accessor.set(u, dest_upperleft);
    \endcode
    \deprecatedEnd
*/
doxygen_overloaded_function(template <...> void rohrCornerDetector)

template <class SrcIterator, class SrcAccessor,
          class DestIterator, class DestAccessor>
void
rohrCornerDetector(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                       DestIterator dul, DestAccessor ad,
                       double scale)
{
    vigra_precondition(scale > 0.0,
                 "rohrCornerDetector(): Scale must be > 0");
                 
    int w = slr.x - sul.x;
    int h = slr.y - sul.y;
    
    if(w <= 0 || h <= 0) return;
    
    typedef typename 
        NumericTraits<typename SrcAccessor::value_type>::RealPromote TmpType;
        
    typedef BasicImage<TmpType> TmpImage;
    
    TmpImage gx(w,h);
    TmpImage gy(w,h);
    TmpImage gxy(w,h);

    structureTensor(srcIterRange(sul, slr, as), 
                    destImage(gx), destImage(gxy), destImage(gy), 
                    scale, scale);
    RohrCornerFunctor<typename SrcAccessor::value_type > cf;
                    
    combineThreeImages(srcImageRange(gx), srcImage(gy), srcImage(gxy), 
                       destIter(dul, ad), cf );
}

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

template <class T1, class S1,
          class T2, class S2>
inline void
rohrCornerDetector(MultiArrayView<2, T1, S1> const & src,
                   MultiArrayView<2, T2, S2> dest,
                   double scale)
{
    vigra_precondition(src.shape() == dest.shape(),
        "rohrCornerDetector(): shape mismatch between input and output.");
    rohrCornerDetector(srcImageRange(src),
                       destImage(dest),
                       scale);
}

/********************************************************/
/*                                                      */
/*                 beaudetCornerDetector                */
/*                                                      */
/********************************************************/

/** \brief Find corners in an image (4).

    This algorithm implements a corner detector  
    according to [P.R. Beaudet: <em> "Rotationally Invariant Image Operators"</em>, 
    Proc. Intl. Joint Conf. on Pattern Recognition, Kyoto, Japan, 1978, pp. 579-583]. 
    
    The algorithm calculates the corner strength as the negative determinant of the 
    \link hessianMatrixOfGaussian() Hessian Matrix\endlink. 
    The local maxima of the corner strength denote the corners in the gray level 
    image. 
    
    The source value type must be a linear algebra, i.e. addition, subtraction, and
    multiplication with itself, multiplication with doubles and 
    \ref NumericTraits "NumericTraits" must 
    be defined.
    
    <b> Declarations:</b>
    
    pass 2D array views:
    \code
    namespace vigra {
        template <class T1, class S1,
                  class T2, class S2>
        void
        beaudetCornerDetector(MultiArrayView<2, T1, S1> const & src,
                              MultiArrayView<2, T2, S2> dest,
                              double scale);
    }
    \endcode
    
    \deprecatedAPI{beaudetCornerDetector}
    pass \ref ImageIterators and \ref DataAccessors :
    \code
    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
                  class DestIterator, class DestAccessor>
        void
        beaudetCornerDetector(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                           DestIterator dul, DestAccessor ad,
                           double scale)
    }
    \endcode
    use argument objects in conjunction with \ref ArgumentObjectFactories :
    \code
    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
                  class DestIterator, class DestAccessor>
        void beaudetCornerDetector(
                   triple<SrcIterator, SrcIterator, SrcAccessor> src,
                   pair<DestIterator, DestAccessor> dest,
                   double scale)
    }
    \endcode
    \deprecatedEnd
    
    <b> Usage:</b>
    
    <b>\#include</b> <vigra/cornerdetection.hxx><br>
    Namespace: vigra

    \code
    MultiArray<2, unsigned char> src(w,h), corners(w,h);
    MultiArray<2, float>         beaudet_corner_strength(w,h);
    ...
    
    // find corner response at scale 1.0
    beaudetCornerDetector(src, beaudet_corner_strength, 1.0);
    
    // find local maxima of corner response, mark with 1
    localMaxima(beaudet_corner_strength, corners);
    \endcode

    \deprecatedUsage{beaudetCornerDetector}
    \code
    vigra::BImage src(w,h), corners(w,h);
    vigra::FImage beaudet_corner_strength(w,h);
    
    // empty corner image
    corners.init(0.0);
    ...
    
    // find corner response at scale 1.0
    vigra::beaudetCornerDetector(srcImageRange(src), destImage(beaudet_corner_strength), 
                              1.0);
    
    // find local maxima of corner response, mark with 1
    vigra::localMaxima(srcImageRange(beaudet_corner_strength), destImage(corners));
    \endcode
    <b> Required Interface:</b>
    \code
    SrcImageIterator src_upperleft, src_lowerright;
    DestImageIterator dest_upperleft;
    
    SrcAccessor src_accessor;
    DestAccessor dest_accessor;
    
    SrcAccessor::value_type u = src_accessor(src_upperleft);
    double d;
    
    u = u + u
    u = u - u
    u = u * u
    u = d * u
    
    dest_accessor.set(u, dest_upperleft);
    \endcode
    \deprecatedEnd
*/
doxygen_overloaded_function(template <...> void beaudetCornerDetector)

template <class SrcIterator, class SrcAccessor,
          class DestIterator, class DestAccessor>
void
beaudetCornerDetector(SrcIterator sul, SrcIterator slr, SrcAccessor as,
                       DestIterator dul, DestAccessor ad,
                       double scale)
{
    vigra_precondition(scale > 0.0,
                 "beaudetCornerDetector(): Scale must be > 0");
                 
    int w = slr.x - sul.x;
    int h = slr.y - sul.y;
    
    if(w <= 0 || h <= 0) return;
    
    typedef typename 
        NumericTraits<typename SrcAccessor::value_type>::RealPromote TmpType;
        
    typedef BasicImage<TmpType> TmpImage;
    
    TmpImage gx(w,h);
    TmpImage gy(w,h);
    TmpImage gxy(w,h);

    hessianMatrixOfGaussian(srcIterRange(sul, slr, as), 
                    destImage(gx), destImage(gxy), destImage(gy), 
                    scale);
    BeaudetCornerFunctor<typename SrcAccessor::value_type > cf;
                    
    combineThreeImages(srcImageRange(gx), srcImage(gy), srcImage(gxy), 
                       destIter(dul, ad), cf );
}

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

template <class T1, class S1,
          class T2, class S2>
inline void
beaudetCornerDetector(MultiArrayView<2, T1, S1> const & src,
                      MultiArrayView<2, T2, S2> dest,
                      double scale)
{
    vigra_precondition(src.shape() == dest.shape(),
        "beaudetCornerDetector(): shape mismatch between input and output.");
    beaudetCornerDetector(srcImageRange(src),
                          destImage(dest),
                          scale);
}


//@}

} // namespace vigra

#endif // VIGRA_CORNERDETECTION_HXX