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details Recursive convolution functions VIGRA

Functions

template<... >
void recursiveFilterLine (...)
 Performs a 1-dimensional recursive convolution of the source signal.
template<... >
void recursiveFilterX (...)
 Performs 1 dimensional recursive filtering (1st and 2nd order) in x direction.
template<... >
void recursiveFilterY (...)
 Performs 1 dimensional recursive filtering (1st and 2nd order) in y direction.
template<... >
void recursiveFirstDerivativeLine (...)
 Performs a 1 dimensional recursive convolution of the source signal.
template<... >
void recursiveFirstDerivativeX (...)
 Recursively calculates the 1 dimensional first derivative in x direction.
template<... >
void recursiveFirstDerivativeY (...)
 Recursively calculates the 1 dimensional first derivative in y direction.
template<... >
void recursiveSecondDerivativeLine (...)
 Performs a 1 dimensional recursive convolution of the source signal.
template<... >
void recursiveSecondDerivativeX (...)
 Recursively calculates the 1 dimensional second derivative in x direction.
template<... >
void recursiveSecondDerivativeY (...)
 Recursively calculates the 1 dimensional second derivative in y direction.
template<... >
void recursiveSmoothLine (...)
 Convolves the image with a 1-dimensional exponential filter.
template<... >
void recursiveSmoothX (...)
 Performs 1 dimensional recursive smoothing in x direction.
template<... >
void recursiveSmoothY (...)
 Performs 1 dimensional recursive smoothing in y direction.


Detailed Description

First order recursive filters and their specialization for the exponential filter and its derivatives (1D and separable 2D). These filters are very fast, and the speed does not depend on the filter size.


Function Documentation

void vigra::recursiveFilterLine (   ...  ) 

Performs a 1-dimensional recursive convolution of the source signal.

The function performs a causal and an anti-causal first or second order recursive filtering with the given filter parameter b1 and border treatment border (first order filter, b2 = 0) or parameters b1, b2 and BORDER_TREATMENT_REFLECT (second order filter). Thus, the result is always a filtering with linear phase.

\[ \begin{array}{rcl} a_{i, causal} & = & source_i + b1 * a_{i-1, causal} + b2 * a_{i-2, causal} \\ a_{i, anticausal} & = & source_i + b1 * a_{i+1, anticausal} + b2 * a_{i+2, anticausal} \\ dest_i & = & \frac{1 - b1 - b2}{1 + b1 + b2}(a_{i, causal} + a_{i, anticausal} - source_i) \end{array} \]

The signal's value_type (SrcAccessor::value_type) must be a linear space over double, i.e. addition of source values, multiplication with double, and NumericTraits must be defined.

Declaration:

First order recursive filter:

    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
              class DestIterator, class DestAccessor>
        void recursiveFilterLine(SrcIterator is, SrcIterator isend, SrcAccessor as,
                     DestIterator id, DestAccessor ad, 
                     double b1, BorderTreatmentMode border)
    }

Second order recursive filter:

    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
              class DestIterator, class DestAccessor>
        void recursiveFilterLine(SrcIterator is, SrcIterator isend, SrcAccessor as,
                     DestIterator id, DestAccessor ad, 
                     double b1, double b2)
    }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vector<float> src, dest;    
    ...
    
    vigra::DefaultAccessor<vector<float>::iterator, float> FAccessor;
    
    
    vigra::recursiveFilterLine(src.begin(), src.end(), FAccessor(), 
                               dest.begin(), FAccessor(), 
                               0.5, BORDER_TREATMENT_REFLECT);

Required Interface:

    RandomAccessIterator is, isend;
    RandomAccessIterator id;
    
    SrcAccessor src_accessor;
    DestAccessor dest_accessor;
    
    NumericTraits<SrcAccessor::value_type>::RealPromote s = src_accessor(is);
    double d;
    
    s = s + s;
    s = d * s;

    dest_accessor.set(
        NumericTraits<DestAccessor::value_type>::fromRealPromote(s), id);

Preconditions:

    -1 < b  < 1
void vigra::recursiveSmoothLine (   ...  ) 

Convolves the image with a 1-dimensional exponential filter.

This function calls recursiveFilterLine() with b = exp(-1.0/scale) and border = BORDER_TREATMENT_REPEAT. See recursiveFilterLine() for more documentation.

Declaration:

    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
              class DestIterator, class DestAccessor>
        void recursiveSmoothLine(SrcIterator is, SrcIterator isend, SrcAccessor as,
                     DestIterator id, DestAccessor ad, double scale)
    }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vector<float> src, dest;    
    ...
    
    vigra::DefaultAccessor<vector<float>::iterator, float> FAccessor;
    
    
    vigra::recursiveSmoothLine(src.begin(), src.end(), FAccessor(), 
                        dest.begin(), FAccessor(), 3.0);

Required Interface:

    RandomAccessIterator is, isend;
    RandomAccessIterator id;
    
    SrcAccessor src_accessor;
    DestAccessor dest_accessor;
    
    NumericTraits<SrcAccessor::value_type>::RealPromote s = src_accessor(is);
    double d;
    
    s = s + s;
    s = d * s;

    dest_accessor.set(
        NumericTraits<DestAccessor::value_type>::fromRealPromote(s), id);

Preconditions:

    scale > 0
void vigra::recursiveFirstDerivativeLine (   ...  ) 

Performs a 1 dimensional recursive convolution of the source signal.

It uses the first derivative an exponential d/dx exp(-abs(x)/scale) as a kernel. The signal's value_type (SrcAccessor::value_type) must be a linear space over double, i.e. addition and subtraction of source values, multiplication with double, and NumericTraits must be defined. Border treatment is always BORDER_TREATMENT_REPEAT.

Declaration:

    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
              class DestIterator, class DestAccessor>
        void recursiveFirstDerivativeLine(SrcIterator is, SrcIterator isend, SrcAccessor as,
                     DestIterator id, DestAccessor ad, double scale)
    }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vector<float> src, dest;    
    ...
    
    vigra::DefaultAccessor<vector<float>::iterator, float> FAccessor;
    
    
    vigra::recursiveFirstDerivativeLine(src.begin(), src.end(), FAccessor(), 
                        dest.begin(), FAccessor(), 3.0);

Required Interface:

    RandomAccessIterator is, isend;
    RandomAccessIterator id;
    
    SrcAccessor src_accessor;
    DestAccessor dest_accessor;
    
    NumericTraits<SrcAccessor::value_type>::RealPromote s = src_accessor(is);
    double d;
    
    s = s + s;
    s = -s;
    s = d * s;

    dest_accessor.set(
        NumericTraits<DestAccessor::value_type>::fromRealPromote(s), id);

Preconditions:

    scale > 0
void vigra::recursiveSecondDerivativeLine (   ...  ) 

Performs a 1 dimensional recursive convolution of the source signal.

It uses the second derivative an exponential d2/dx2 exp(-abs(x)/scale) as a kernel. The signal's value_type (SrcAccessor::value_type) must be a linear space over double, i.e. addition and subtraction of source values, multiplication with double, and NumericTraits must be defined. Border treatment is always BORDER_TREATMENT_REPEAT.

Declaration:

    namespace vigra {
        template <class SrcIterator, class SrcAccessor,
              class DestIterator, class DestAccessor>
        void recursiveSecondDerivativeLine(SrcIterator is, SrcIterator isend, SrcAccessor as,
                     DestIterator id, DestAccessor ad, double scale)
    }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vector<float> src, dest;    
    ...
    
    vigra::DefaultAccessor<vector<float>::iterator, float> FAccessor;
    
    
    vigra::recursiveSecondDerivativeLine(src.begin(), src.end(), FAccessor(), 
                        dest.begin(), FAccessor(), 3.0);

Required Interface:

    RandomAccessIterator is, isend;
    RandomAccessIterator id;
    
    SrcAccessor src_accessor;
    DestAccessor dest_accessor;
    
    NumericTraits<SrcAccessor::value_type>::RealPromote s = src_accessor(is);
    double d;
    
    s = s + s;
    s = s - s;
    s = d * s;

    dest_accessor.set(
        NumericTraits<DestAccessor::value_type>::fromRealPromote(s), id);

Preconditions:

    scale > 0
void vigra::recursiveFilterX (   ...  ) 

Performs 1 dimensional recursive filtering (1st and 2nd order) in x direction.

It calls recursiveFilterLine() for every row of the image. See recursiveFilterLine() for more information about required interfaces and vigra_preconditions.

Declarations:

pass arguments explicitly:

    namespace vigra {
        // first order filter
        template <class SrcImageIterator, class SrcAccessor,
                  class DestImageIterator, class DestAccessor>
        void recursiveFilterX(SrcImageIterator supperleft, 
                               SrcImageIterator slowerright, SrcAccessor as,
                               DestImageIterator dupperleft, DestAccessor ad, 
                               double b, BorderTreatmentMode border);

        // second order filter
        template <class SrcImageIterator, class SrcAccessor,
                  class DestImageIterator, class DestAccessor>
        void recursiveFilterX(SrcImageIterator supperleft, 
                               SrcImageIterator slowerright, SrcAccessor as,
                               DestImageIterator dupperleft, DestAccessor ad, 
                               double b1, double b2);
    }

use argument objects in conjunction with Argument Object Factories :

    namespace vigra {
        // first order filter
        template <class SrcImageIterator, class SrcAccessor,
                  class DestImageIterator, class DestAccessor>
        void recursiveFilterX(
                    triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
                    pair<DestImageIterator, DestAccessor> dest, 
                    double b, BorderTreatmentMode border);

        // second order filter
        template <class SrcImageIterator, class SrcAccessor,
                  class DestImageIterator, class DestAccessor>
        void recursiveFilterX(
                    triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
                    pair<DestImageIterator, DestAccessor> dest, 
                    double b1, double b2);
            }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vigra::FImage src(w,h), dest(w,h);    
    ...
    
    vigra::recursiveSmoothX(srcImageRange(src), destImage(dest), 
           0.5, BORDER_TREATMENT_REFLECT);
void vigra::recursiveSmoothX (   ...  ) 

Performs 1 dimensional recursive smoothing in x direction.

It calls recursiveSmoothLine() for every row of the image. See recursiveSmoothLine() for more information about required interfaces and vigra_preconditions.

Declarations:

pass arguments explicitly:

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveSmoothX(SrcImageIterator supperleft, 
                  SrcImageIterator slowerright, SrcAccessor as,
                  DestImageIterator dupperleft, DestAccessor ad, 
                  double scale)
    }

use argument objects in conjunction with Argument Object Factories :

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveSmoothX(
            triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
            pair<DestImageIterator, DestAccessor> dest, 
            double scale)
    }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vigra::FImage src(w,h), dest(w,h);    
    ...
    
    vigra::recursiveSmoothX(srcImageRange(src), destImage(dest), 3.0);
Examples:
smooth.cxx, and watershed.cxx.
void vigra::recursiveFilterY (   ...  ) 

Performs 1 dimensional recursive filtering (1st and 2nd order) in y direction.

It calls recursiveFilterLine() for every column of the image. See recursiveFilterLine() for more information about required interfaces and vigra_preconditions.

Declarations:

pass arguments explicitly:

    namespace vigra {
        // first order filter
        template <class SrcImageIterator, class SrcAccessor,
                  class DestImageIterator, class DestAccessor>
        void recursiveFilterY(SrcImageIterator supperleft, 
                               SrcImageIterator slowerright, SrcAccessor as,
                               DestImageIterator dupperleft, DestAccessor ad, 
                               double b, BorderTreatmentMode border);

        // second order filter
        template <class SrcImageIterator, class SrcAccessor,
                  class DestImageIterator, class DestAccessor>
        void recursiveFilterY(SrcImageIterator supperleft, 
                               SrcImageIterator slowerright, SrcAccessor as,
                               DestImageIterator dupperleft, DestAccessor ad, 
                               double b1, double b2);
    }

use argument objects in conjunction with Argument Object Factories :

    namespace vigra {
        // first order filter
        template <class SrcImageIterator, class SrcAccessor,
                  class DestImageIterator, class DestAccessor>
        void recursiveFilterY(
                    triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
                    pair<DestImageIterator, DestAccessor> dest, 
                    double b, BorderTreatmentMode border);

        // second order filter
        template <class SrcImageIterator, class SrcAccessor,
                  class DestImageIterator, class DestAccessor>
        void recursiveFilterY(
                    triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
                    pair<DestImageIterator, DestAccessor> dest, 
                    double b1, double b2);
            }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vigra::FImage src(w,h), dest(w,h);    
    ...
    
    vigra::recursiveFilterY(srcImageRange(src), destImage(dest), -0.6, -0.06);
void vigra::recursiveSmoothY (   ...  ) 

Performs 1 dimensional recursive smoothing in y direction.

It calls recursiveSmoothLine() for every column of the image. See recursiveSmoothLine() for more information about required interfaces and vigra_preconditions.

Declarations:

pass arguments explicitly:

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveSmoothY(SrcImageIterator supperleft, 
                  SrcImageIterator slowerright, SrcAccessor as,
                  DestImageIterator dupperleft, DestAccessor ad, 
                  double scale)
    }

use argument objects in conjunction with Argument Object Factories :

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveSmoothY(
            triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
            pair<DestImageIterator, DestAccessor> dest, 
            double scale)
    }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vigra::FImage src(w,h), dest(w,h);    
    ...
    
    vigra::recursiveSmoothY(srcImageRange(src), destImage(dest), 3.0);
Examples:
smooth.cxx, and watershed.cxx.
void vigra::recursiveFirstDerivativeX (   ...  ) 

Recursively calculates the 1 dimensional first derivative in x direction.

It calls recursiveFirstDerivativeLine() for every row of the image. See recursiveFirstDerivativeLine() for more information about required interfaces and vigra_preconditions.

Declarations:

pass arguments explicitly:

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveFirstDerivativeX(SrcImageIterator supperleft, 
                  SrcImageIterator slowerright, SrcAccessor as,
                  DestImageIterator dupperleft, DestAccessor ad, 
                  double scale)
    }

use argument objects in conjunction with Argument Object Factories :

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveFirstDerivativeX(
            triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
            pair<DestImageIterator, DestAccessor> dest, 
            double scale)
    }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vigra::FImage src(w,h), dest(w,h);    
    ...
    
    vigra::recursiveFirstDerivativeX(srcImageRange(src), destImage(dest), 3.0);
Examples:
watershed.cxx.
void vigra::recursiveFirstDerivativeY (   ...  ) 

Recursively calculates the 1 dimensional first derivative in y direction.

It calls recursiveFirstDerivativeLine() for every column of the image. See recursiveFirstDerivativeLine() for more information about required interfaces and vigra_preconditions.

Declarations:

pass arguments explicitly:

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveFirstDerivativeY(SrcImageIterator supperleft, 
                  SrcImageIterator slowerright, SrcAccessor as,
                  DestImageIterator dupperleft, DestAccessor ad, 
                  double scale)
    }

use argument objects in conjunction with Argument Object Factories :

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveFirstDerivativeY(
            triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
            pair<DestImageIterator, DestAccessor> dest, 
            double scale)
    }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vigra::FImage src(w,h), dest(w,h);    
    ...
    
    vigra::recursiveFirstDerivativeY(srcImageRange(src), destImage(dest), 3.0);
Examples:
watershed.cxx.
void vigra::recursiveSecondDerivativeX (   ...  ) 

Recursively calculates the 1 dimensional second derivative in x direction.

It calls recursiveSecondDerivativeLine() for every row of the image. See recursiveSecondDerivativeLine() for more information about required interfaces and vigra_preconditions.

Declarations:

pass arguments explicitly:

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveSecondDerivativeX(SrcImageIterator supperleft, 
                  SrcImageIterator slowerright, SrcAccessor as,
                  DestImageIterator dupperleft, DestAccessor ad, 
                  double scale)
    }

use argument objects in conjunction with Argument Object Factories :

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveSecondDerivativeX(
            triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
            pair<DestImageIterator, DestAccessor> dest, 
            double scale)
    }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vigra::FImage src(w,h), dest(w,h);    
    ...
    
    vigra::recursiveSecondDerivativeX(srcImageRange(src), destImage(dest), 3.0);
void vigra::recursiveSecondDerivativeY (   ...  ) 

Recursively calculates the 1 dimensional second derivative in y direction.

It calls recursiveSecondDerivativeLine() for every column of the image. See recursiveSecondDerivativeLine() for more information about required interfaces and vigra_preconditions.

Declarations:

pass arguments explicitly:

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveSecondDerivativeY(SrcImageIterator supperleft, 
                  SrcImageIterator slowerright, SrcAccessor as,
                  DestImageIterator dupperleft, DestAccessor ad, 
                  double scale)
    }

use argument objects in conjunction with Argument Object Factories :

    namespace vigra {
        template <class SrcImageIterator, class SrcAccessor,
              class DestImageIterator, class DestAccessor>
        void recursiveSecondDerivativeY(
            triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
            pair<DestImageIterator, DestAccessor> dest, 
            double scale)
    }

Usage:

#include <vigra/recursiveconvolution.hxx>
Namespace: vigra

    vigra::FImage src(w,h), dest(w,h);    
    ...
    
    vigra::recursiveSecondDerivativeY(srcImageRange(src), destImage(dest), 3.0);

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de)
Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany

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VIGRA 1.6.0 (5 Nov 2009)