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/* */
/* Copyright 2009-2010 by Ullrich Koethe */
/* */
/* This file is part of the VIGRA computer vision library. */
/* The VIGRA Website is */
/* http://hci.iwr.uni-heidelberg.de/vigra/ */
/* Please direct questions, bug reports, and contributions to */
/* ullrich.koethe@iwr.uni-heidelberg.de or */
/* vigra@informatik.uni-hamburg.de */
/* */
/* Permission is hereby granted, free of charge, to any person */
/* obtaining a copy of this software and associated documentation */
/* files (the "Software"), to deal in the Software without */
/* restriction, including without limitation the rights to use, */
/* copy, modify, merge, publish, distribute, sublicense, and/or */
/* sell copies of the Software, and to permit persons to whom the */
/* Software is furnished to do so, subject to the following */
/* conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the */
/* Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES */
/* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND */
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/* OTHER DEALINGS IN THE SOFTWARE. */
/* */
/************************************************************************/
#ifndef VIGRA_MULTI_TENSORUTILITIES_HXX
#define VIGRA_MULTI_TENSORUTILITIES_HXX
#include <cmath>
#include "utilities.hxx"
#include "mathutil.hxx"
#include "metaprogramming.hxx"
#include "multi_pointoperators.hxx"
namespace vigra {
namespace detail {
template <int N, class ArgumentVector, class ResultVector>
class OuterProductFunctor
{
public:
typedef ArgumentVector argument_type;
typedef ResultVector result_type;
typedef typename ArgumentVector::value_type ValueType;
result_type operator()(argument_type const & in) const
{
result_type res;
for(int b=0, i=0; i<N; ++i)
{
for(int j=i; j<N; ++j, ++b)
{
res[b] = detail::RequiresExplicitCast<ValueType>::cast(in[i]*in[j]);
}
}
return res;
}
};
template <int N, class ArgumentVector>
class TensorTraceFunctor
{
public:
typedef ArgumentVector argument_type;
typedef typename ArgumentVector::value_type result_type;
result_type exec(argument_type const & v, MetaInt<1>) const
{
return v[0];
}
result_type exec(argument_type const & v, MetaInt<2>) const
{
return v[0] + v[2];
}
result_type exec(argument_type const & v, MetaInt<3>) const
{
return v[0] + v[3] + v[5];
}
template <int N2>
void exec(argument_type const & v, result_type & r, MetaInt<N2>) const
{
vigra_fail("tensorTraceMultiArray(): Sorry, can only handle dimensions up to 3.");
}
result_type operator()( const argument_type & a ) const
{
return exec(a, MetaInt<N>());
}
};
template <int N, class ArgumentVector, class ResultVector>
class EigenvaluesFunctor
{
public:
typedef ArgumentVector argument_type;
typedef ResultVector result_type;
void exec(argument_type const & v, result_type & r, MetaInt<1>) const
{
symmetric2x2Eigenvalues(v[0], &r[0]);
}
void exec(argument_type const & v, result_type & r, MetaInt<2>) const
{
symmetric2x2Eigenvalues(v[0], v[1], v[2], &r[0], &r[1]);
}
void exec(argument_type const & v, result_type & r, MetaInt<3>) const
{
symmetric3x3Eigenvalues(v[0], v[1], v[2], v[3], v[4], v[5], &r[0], &r[1], &r[2]);
}
template <int N2>
void exec(argument_type const & v, result_type & r, MetaInt<N2>) const
{
vigra_fail("tensorEigenvaluesMultiArray(): Sorry, can only handle dimensions up to 3.");
}
result_type operator()( const argument_type & a ) const
{
result_type res;
exec(a, res, MetaInt<N>());
return res;
}
};
template <int N, class ArgumentVector>
class DeterminantFunctor
{
public:
typedef ArgumentVector argument_type;
typedef typename ArgumentVector::value_type result_type;
result_type exec(argument_type const & v, MetaInt<1>) const
{
return v[0];
}
result_type exec(argument_type const & v, MetaInt<2>) const
{
return v[0]*v[2] - sq(v[1]);
}
result_type exec(argument_type const & v, MetaInt<3>) const
{
result_type r0, r1, r2;
symmetric3x3Eigenvalues(v[0], v[1], v[2], v[3], v[4], v[5], &r0, &r1, &r2);
return r0*r1*r2;
}
template <int N2>
void exec(argument_type const & v, result_type & r, MetaInt<N2>) const
{
vigra_fail("tensorDeterminantMultiArray(): Sorry, can only handle dimensions up to 3.");
}
result_type operator()( const argument_type & a ) const
{
return exec(a, MetaInt<N>());
}
};
} // namespace detail
/** \addtogroup MultiPointoperators
*/
//@{
/********************************************************/
/* */
/* vectorToTensorMultiArray */
/* */
/********************************************************/
/** \brief Calculate the tensor (outer) product of a N-D vector with itself.
This function is useful to transform vector arrays into a tensor representation
that can be used as input to tensor based processing and analysis functions
(e.g. tensor smoothing). When the input array has N dimensions, the input value_type
must be a vector of length N, whereas the output value_type mus be vectors of length
N*(N-1)/2 which will represent the upper triangular part of the resulting (symmetric)
tensor. That is, for 2D arrays the output contains the elements
<tt>[t11, t12 == t21, t22]</tt> in this order, whereas it contains the elements
<tt>[t11, t12, t13, t22, t23, t33]</tt> for 3D arrays.
Currently, <tt>N <= 3</tt> is required.
<b> Declarations:</b>
pass arguments explicitly:
\code
namespace vigra {
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
vectorToTensorMultiArray(SrcIterator si, SrcShape const & shape, SrcAccessor src,
DestIterator di, DestAccessor dest);
}
\endcode
use argument objects in conjunction with \ref ArgumentObjectFactories :
\code
namespace vigra {
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
vectorToTensorMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
pair<DestIterator, DestAccessor> d);
}
\endcode
<b> Usage:</b>
<b>\#include</b> \<vigra/multi_tensorutilities.hxx\>
\code
MultiArray<3, float> vol(shape);
MultiArray<3, TinyVector<float, 3> > gradient(shape);
MultiArray<3, TinyVector<float, 6> > tensor(shape);
gaussianGradientMultiArray(srcMultiArrayRange(vol), destMultiArray(gradient), 2.0);
vectorToTensorMultiArray(srcMultiArrayRange(gradient), destMultiArray(tensor));
\endcode
*/
doxygen_overloaded_function(template <...> void vectorToTensorMultiArray)
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
vectorToTensorMultiArray(SrcIterator si, SrcShape const & shape, SrcAccessor src,
DestIterator di, DestAccessor dest)
{
static const int N = SrcShape::static_size;
static const int M = N*(N+1)/2;
typedef typename SrcAccessor::value_type SrcType;
typedef typename DestAccessor::value_type DestType;
for(int k=0; k<N; ++k)
if(shape[k] <=0)
return;
vigra_precondition(N == (int)src.size(si),
"vectorToTensorMultiArray(): Wrong number of channels in input array.");
vigra_precondition(M == (int)dest.size(di),
"vectorToTensorMultiArray(): Wrong number of channels in output array.");
transformMultiArray(si, shape, src, di, dest,
detail::OuterProductFunctor<N, SrcType, DestType>());
}
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
inline void
vectorToTensorMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
pair<DestIterator, DestAccessor> d)
{
vectorToTensorMultiArray(s.first, s.second, s.third, d.first, d.second);
}
/********************************************************/
/* */
/* tensorTraceMultiArray */
/* */
/********************************************************/
/** \brief Calculate the tensor trace for every element of a N-D tensor array.
This function turns a N-D tensor (whose value_type is a vector of length N*(N+1)/2,
see \ref vectorToTensorMultiArray()) representing the upper triangular part of a
symmetric tensor into a scalar array holding the tensor trace.
Currently, <tt>N <= 3</tt> is required.
<b> Declarations:</b>
pass arguments explicitly:
\code
namespace vigra {
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
tensorTraceMultiArray(SrcIterator si, SrcShape const & shape, SrcAccessor src,
DestIterator di, DestAccessor dest);
}
\endcode
use argument objects in conjunction with \ref ArgumentObjectFactories :
\code
namespace vigra {
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
tensorTraceMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
pair<DestIterator, DestAccessor> d);
}
\endcode
<b> Usage:</b>
<b>\#include</b> \<vigra/multi_tensorutilities.hxx\>
\code
MultiArray<3, float> vol(shape);
MultiArray<3, TinyVector<float, 6> > hessian(shape);
MultiArray<3, float> trace(shape);
hessianOfGaussianMultiArray(srcMultiArrayRange(vol), destMultiArray(hessian), 2.0);
tensorTraceMultiArray(srcMultiArrayRange(hessian), destMultiArray(trace));
\endcode
*/
doxygen_overloaded_function(template <...> void tensorTraceMultiArray)
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
tensorTraceMultiArray(SrcIterator si, SrcShape const & shape, SrcAccessor src,
DestIterator di, DestAccessor dest)
{
static const int N = SrcShape::static_size;
typedef typename SrcAccessor::value_type SrcType;
transformMultiArray(si, shape, src, di, dest,
detail::TensorTraceFunctor<N, SrcType>());
}
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
inline void
tensorTraceMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
pair<DestIterator, DestAccessor> d)
{
tensorTraceMultiArray(s.first, s.second, s.third, d.first, d.second);
}
/********************************************************/
/* */
/* tensorEigenvaluesMultiArray */
/* */
/********************************************************/
/** \brief Calculate the tensor eigenvalues for every element of a N-D tensor array.
This function turns a N-D tensor (whose value_type is a vector of length N*(N+1)/2,
see \ref vectorToTensorMultiArray()) representing the upper triangular part of a
symmetric tensor into a vector-valued array holding the tensor eigenvalues (thus,
the destination value_type must be vectors of length N).
Currently, <tt>N <= 3</tt> is required.
<b> Declarations:</b>
pass arguments explicitly:
\code
namespace vigra {
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
tensorEigenvaluesMultiArray(SrcIterator si, SrcShape const & shape, SrcAccessor src,
DestIterator di, DestAccessor dest);
}
\endcode
use argument objects in conjunction with \ref ArgumentObjectFactories :
\code
namespace vigra {
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
tensorEigenvaluesMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
pair<DestIterator, DestAccessor> d);
}
\endcode
<b> Usage:</b>
<b>\#include</b> \<vigra/multi_tensorutilities.hxx\>
\code
MultiArray<3, float> vol(shape);
MultiArray<3, TinyVector<float, 6> > hessian(shape);
MultiArray<3, TinyVector<float, 3> > eigenvalues(shape);
hessianOfGaussianMultiArray(srcMultiArrayRange(vol), destMultiArray(hessian), 2.0);
tensorEigenvaluesMultiArray(srcMultiArrayRange(hessian), destMultiArray(eigenvalues));
\endcode
*/
doxygen_overloaded_function(template <...> void tensorEigenvaluesMultiArray)
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
tensorEigenvaluesMultiArray(SrcIterator si, SrcShape const & shape, SrcAccessor src,
DestIterator di, DestAccessor dest)
{
static const int N = SrcShape::static_size;
static const int M = N*(N+1)/2;
typedef typename SrcAccessor::value_type SrcType;
typedef typename DestAccessor::value_type DestType;
for(int k=0; k<N; ++k)
if(shape[k] <=0)
return;
vigra_precondition(M == (int)src.size(si),
"tensorEigenvaluesMultiArray(): Wrong number of channels in input array.");
vigra_precondition(N == (int)dest.size(di),
"tensorEigenvaluesMultiArray(): Wrong number of channels in output array.");
transformMultiArray(si, shape, src, di, dest,
detail::EigenvaluesFunctor<N, SrcType, DestType>());
}
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
inline void
tensorEigenvaluesMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
pair<DestIterator, DestAccessor> d)
{
tensorEigenvaluesMultiArray(s.first, s.second, s.third, d.first, d.second);
}
/********************************************************/
/* */
/* tensorDeterminantMultiArray */
/* */
/********************************************************/
/** \brief Calculate the tensor determinant for every element of a ND tensor array.
This function turns a N-D tensor (whose value_type is a vector of length N*(N+1)/2,
see \ref vectorToTensorMultiArray()) representing the upper triangular part of a
symmetric tensor into the a scalar array holding the tensor determinant.
Currently, <tt>N <= 3</tt> is required.
<b> Declarations:</b>
pass arguments explicitly:
\code
namespace vigra {
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
tensorDeterminantMultiArray(SrcIterator si, SrcShape const & shape, SrcAccessor src,
DestIterator di, DestAccessor dest);
}
\endcode
use argument objects in conjunction with \ref ArgumentObjectFactories :
\code
namespace vigra {
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
tensorDeterminantMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
pair<DestIterator, DestAccessor> d);
}
\endcode
<b> Usage:</b>
<b>\#include</b> \<vigra/multi_tensorutilities.hxx\>
\code
MultiArray<3, float> vol(shape);
MultiArray<3, TinyVector<float, 6> > hessian(shape);
MultiArray<3, float> determinant(shape);
hessianOfGaussianMultiArray(srcMultiArrayRange(vol), destMultiArray(hessian), 2.0);
tensorDeterminantMultiArray(srcMultiArrayRange(hessian), destMultiArray(determinant));
\endcode
*/
doxygen_overloaded_function(template <...> void tensorDeterminantMultiArray)
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
void
tensorDeterminantMultiArray(SrcIterator si, SrcShape const & shape, SrcAccessor src,
DestIterator di, DestAccessor dest)
{
typedef typename SrcAccessor::value_type SrcType;
static const int N = SrcShape::static_size;
static const int M = N*(N+1)/2;
for(int k=0; k<N; ++k)
if(shape[k] <=0)
return;
vigra_precondition(M == (int)src.size(si),
"tensorDeterminantMultiArray(): Wrong number of channels in output array.");
transformMultiArray(si, shape, src, di, dest,
detail::DeterminantFunctor<N, SrcType>());
}
template <class SrcIterator, class SrcShape, class SrcAccessor,
class DestIterator, class DestAccessor>
inline void
tensorDeterminantMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
pair<DestIterator, DestAccessor> d)
{
tensorDeterminantMultiArray(s.first, s.second, s.third, d.first, d.second);
}
//@}
} // namespace vigra
#endif /* VIGRA_MULTI_TENSORUTILITIES_HXX */
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