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| Point operators for multi-dimensional arrays. |

## Functions
template<... >
void | combineThreeMultiArrays (...)
| Combine three multi-dimensional arrays into one using a ternary function or functor.
template<... >
void | combineTwoMultiArrays (...)
| Combine two multi-dimensional arrays into one using a binary function or functor.
template<... >
void | copyMultiArray (...)
| Copy a multi-dimensional array.
template<... >
void | initMultiArray (...)
| Write a value to every pixel in a multi-dimensional array.
template<class Iterator , class Diff_type , class Accessor , class VALUETYPE >
void | initMultiArrayBorder (Iterator upperleft, Diff_type shape, Accessor a, int border_width, VALUETYPE v)
| Write value to the specified border values in the array.
template<... >
void | inspectMultiArray (...)
| Call an analyzing functor at every element of a multi-dimensional array.
template<... >
void | inspectTwoMultiArrays (...)
| Call an analyzing functor at all corresponding elements of two multi-dimensional arrays.
template<... >
void | tensorDeterminantMultiArray (...)
| Calculate the tensor determinant for every element of a ND tensor array.
template<... >
void | tensorEigenvaluesMultiArray (...)
| Calculate the tensor eigenvalues for every element of a N-D tensor array.
template<... >
void | tensorTraceMultiArray (...)
| Calculate the tensor trace for every element of a N-D tensor array.
template<... >
void | transformMultiArray (...)
| Transform a multi-dimensional array with a unary function or functor.
template<... >
void | vectorToTensorMultiArray (...)
| Calculate the tensor (outer) product of a N-D vector with itself.

## Detailed Description

Copy, transform, and inspect arbitrary dimensional arrays which are represented by iterators compatible to Multi-dimensional Array Iterators. Note that are range is here specified by a pair: an iterator referring to the first point of the array and a shape object specifying the size of the (rectangular) ROI.

#include <vigra/multi_pointoperators.hxx>

## Function Documentation

void vigra::initMultiArray | ( |  | ... | ) |

Write a value to every pixel in a multi-dimensional array.

This function can be used to init the array which must be represented by a pair of iterators compatible to vigra::MultiIterator. It uses an accessor to access the data elements. Note that the iterator range must be specified by a shape object, because otherwise we could not control the range simultaneously in all dimensions (this is a necessary consequence of the vigra::MultiIterator design).

The initial value can either be a constant of appropriate type (compatible with the destination's value_type), or a functor with compatible result_type. These two cases are automatically distinguished when `FunctorTraits<FUNCTOR>::isInitializer` yields `VigraTrueType`. Since the functor is passed by `const` reference, its `operator()` must be const, and its internal state may need to be `mutable`.

Declarations:

pass arguments explicitly:

        namespace vigra {
            template <class Iterator, class Shape, class Accessor, class VALUETYPE>
            void
            initMultiArray(Iterator s, Shape const & shape, Accessor a,  VALUETYPE const & v);

            template <class Iterator, class Shape, class Accessor, class FUNCTOR>
            void
            initMultiArray(Iterator s, Shape const & shape, Accessor a,  FUNCTOR const & f);
        }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class Iterator, class Shape, class Accessor, class VALUETYPE>
            void
            initMultiArray(triple<Iterator, Shape, Accessor> const & s, VALUETYPE const & v);

            template <class Iterator, class Shape, class Accessor, class FUNCTOR>
            void
            initMultiArray(triple<Iterator, Shape, Accessor> const & s, FUNCTOR const & f);
        }

Usage:

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

        typedef vigra::MultiArray<3, int> Array;
        Array array(Array::size_type(100, 200, 50));

        // zero the array
        vigra::initMultiArray(destMultiArrayRange(array), 0);

Required Interface:

The function accepts either a value that is copied into every destination element:

        MultiIterator begin;

        Accessor accessor;
        VALUETYPE v;

        accessor.set(v, begin);

or a functor that is called (without argument) at every location, and the result is written into the current element. Internally, functors are recognized by the meta function `FunctorTraits<FUNCTOR>::isInitializer` yielding `VigraTrueType`. Make sure that your functor correctly defines `FunctorTraits` because otherwise the code will not compile.

        MultiIterator begin;
        Accessor accessor;

        FUNCTOR f;
        assert(typeid(FunctorTraits<FUNCTOR>::isInitializer) == typeid(VigraTrueType));

        accessor.set(f(), begin);

void vigra::initMultiArrayBorder | ( | Iterator | upperleft,
|  | Diff_type | shape,
|  | Accessor | a,
|  | int | border_width,
|  | VALUETYPE | v
| ) |  |

Write value to the specified border values in the array.

void vigra::copyMultiArray | ( |  | ... | ) |

Copy a multi-dimensional array.

This function can be applied in two modes:

Standard Mode:
  If the source and destination arrays have the same size, the corresponding array elements are simply copied. If necessary, type conversion takes place.
Expanding Mode:
  If the source array has length 1 along some (or even all) dimensions, the source value at index 0 is used for all destination elements in those dimensions. For example, if we have single row of data (column length is 1), we can copy it into a 2D image of the same width: The given row is automatically repeated for every row of the destination image. Again, type conversion os performed if necessary.

The arrays must be represented by iterators compatible with vigra::MultiIterator, and the iteration range is specified by means of shape objects. If only the source shape is given the destination array is assumed to have the same shape, and standard mode is applied. If two shapes are given, the size of corresponding dimensions must be either equal (standard copy), or the source length must be 1 (expanding copy). The function uses accessors to access the data elements.

Declarations:

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

pass arguments explicitly:

        namespace vigra {
            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestAccessor>
            void
            copyMultiArray(SrcIterator s,
                           SrcShape const & shape, SrcAccessor src,
                           DestIterator d, DestAccessor dest);

            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestShape, class DestAccessor>
            void
            copyMultiArray(SrcIterator s, SrcShape const & sshape, SrcAccessor src,
                           DestIterator d, DestShape const & dshape, DestAccessor dest);
        }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestAccessor>
            void
            copyMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> const & src,
                           pair<DestIterator, DestAccessor> const & dest);

            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestShape, class DestAccessor>
            void
            copyMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> const & src,
                           triple<DestIterator, DestShape, DestAccessor> const & dest);
        }

Usage - Standard Mode:

        typedef vigra::MultiArray<3, int> Array;
        Array src(Array::size_type(100, 200, 50)),
              dest(Array::size_type(100, 200, 50));
        ...

        vigra::copyMultiArray(srcMultiArrayRange(src), destMultiArray(dest));

Usage - Expanding Mode:

The source array is only 2D (it has depth 1). Thus, the destination will contain 50 identical copies of this image. Note that the destination shape must be passed to the algorithm for the expansion to work, so we use `destMultiArrayRange()` rather than `destMultiArray()`.

        typedef vigra::MultiArray<3, int> Array;
        Array src(Array::size_type(100, 200, 1)),
              dest(Array::size_type(100, 200, 50));
        ...

        vigra::copyMultiArray(srcMultiArrayRange(src), destMultiArrayRange(dest));

Required Interface:

        MultiIterator src_begin, dest_begin;

        SrcAccessor src_accessor;
        DestAccessor dest_accessor;

        dest_accessor.set(src_accessor(src_begin), dest_begin);

void vigra::transformMultiArray | ( |  | ... | ) |

Transform a multi-dimensional array with a unary function or functor.

This function can be applied in three modes:

Standard Mode:
  If the source and destination arrays have the same size, the transformation given by the functor is applied to every source element and the result written into the corresponding destination element. Unary functions, unary functors from the STL and the functors specifically defined in Functors to Transform Images can be used in standard mode. Creation of new functors is easiest by using Functor Expressions.
Expanding Mode:
  If the source array has length 1 along some (or even all) dimensions, the source value at index 0 is used for all destination elements in those dimensions. In other words, the source index is not incremented along these dimensions, but the transformation functor is applied as usual. So, we can expand a small array (e.g. a single row of data, column length is 1), into a larger one (e.g. a 2D image with the same width): the given values are simply reused as necessary (e.g. for every row of the destination image). The same functors as in standard mode can be applied.
Reducing Mode:
  If the destination array has length 1 along some (or even all) dimensions, the source values in these dimensions are reduced to single values by means of a suitable functor (e.g. vigra::ReduceFunctor), which supports two function call operators: one with a single argument to collect the values, and without argument to obtain the final (reduced) result. This behavior is a multi-dimensional generalization of the C++ standard function `std::accumulate()`.

The arrays must be represented by iterators compatible with vigra::MultiIterator, and the iteration range is specified by means of shape objects. If only the source shape is given the destination array is assumed to have the same shape, and standard mode is applied. If two shapes are given, the size of corresponding dimensions must be either equal (standard copy), or the source length must be 1 (expand mode), or the destination length must be 1 (reduce mode). However, reduction and expansion cannot be executed at the same time, so the latter conditions are mutual exclusive, even if they apply to different dimensions.

The function uses accessors to access the data elements.

Declarations:

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

pass arguments explicitly:

        namespace vigra {
            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestAccessor,
                      class Functor>
            void
            transformMultiArray(SrcIterator s, SrcShape const & shape, SrcAccessor src,
                                DestIterator d, DestAccessor dest, Functor const & f);

            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestShape, class DestAccessor,
                      class Functor>
            void
            transformMultiArray(SrcIterator s, SrcShape const & sshape, SrcAccessor src,
                                DestIterator d, DestShape const & dshape, DestAccessor dest,
                                Functor const & f);
        }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestAccessor,
                      class Functor>
            void
            transformMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> const & src,
                                pair<DestIterator, DestAccessor> const & dest, Functor const & f);

            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestShape, class DestAccessor,
                      class Functor>
            void
            transformMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> const & src,
                                triple<DestIterator, DestShape, DestAccessor> const & dest,
                                Functor const & f)
        }

Usage - Standard Mode:

Source and destination array have the same size.

        #include <cmath>         // for sqrt()

        typedef vigra::MultiArray<3, float> Array;
        Array src(Array::size_type(100, 200, 50)),
              dest(Array::size_type(100, 200, 50));
        ...

        vigra::transformMultiArray(srcMultiArrayRange(src),
                                   destMultiArray(dest),
                                   (float(*)(float))&std::sqrt );

Usage - Expand Mode:

The source array is only 2D (it has depth 1). Thus, the destination will contain 50 identical copies of the transformed source array. Note that the destination shape must be passed to the algorithm for the expansion to work, so we use `destMultiArrayRange()` rather than `destMultiArray()`.

        #include <cmath>         // for sqrt()

        typedef vigra::MultiArray<3, float> Array;
        Array src(Array::size_type(100, 200, 1)),
              dest(Array::size_type(100, 200, 50));
        ...

        vigra::transformMultiArray(srcMultiArrayRange(src),
                                   destMultiArrayRange(dest),
                                   (float(*)(float))&std::sqrt );

Usage - Reduce Mode:

The destination array is only 1D (it's width and height are 1). Thus, it will contain accumulated data for every slice of the source volume (or for every frame, if the source is interpreted as an image sequence). In the example, we use the functor vigra::FindAverage to calculate the average gray value of every slice. Note that the destination shape must also be passed for the reduction to work, so we use `destMultiArrayRange()` rather than `destMultiArray()`.

        typedef vigra::MultiArray<3, float> Array;
        Array src(Array::size_type(100, 200, 50)),
              dest(Array::size_type(1, 1, 50));
        ...

        vigra::transformMultiArray(srcMultiArrayRange(src),
                                   destMultiArrayRange(dest),
                                   vigra::FindAverage<float>() );

Note that the functor must define the appropriate traits described below in order to be recognized as a reduce functor. This is most easily achieved by deriving from `UnaryReduceFunctorTag` (see vigra::FunctorTraits).

Required Interface:

In standard and expand mode, the functor must be a model of UnaryFunction (i.e. support function call with one argument and a return value `res = functor(arg)`):

        MultiIterator src_begin, src_end, dest_begin;

        SrcAccessor src_accessor;
        DestAccessor dest_accessor;
        Functor functor;

        dest_accessor.set(functor(src_accessor(src_begin)), dest_begin);

In reduce mode, it must be a model of UnaryAnalyser (i.e. support function call with one argument and no return value `functor(arg)`) and Initializer (i.e. support function call with no argument, but return value `res = functor()`). Internally, such functors are recognized by the meta functions `FunctorTraits<FUNCTOR>::isUnaryAnalyser` and `FunctorTraits<FUNCTOR>::isInitializer` which must both yield `VigraTrueType`. Make sure that your functor correctly defines `FunctorTraits` because otherwise reduce mode will not work. This is most easily achieved by deriving the functor from `UnaryReduceFunctorTag` (see vigra::FunctorTraits). In addition, the functor must be copy constructible in order to start each reduction with a fresh functor.

        MultiIterator src_begin, src_end, dest_begin;

        SrcAccessor src_accessor;
        DestAccessor dest_accessor;

        FUNCTOR initial_functor, functor(initial_functor);
        assert(typeid(FunctorTraits<FUNCTOR>::isInitializer) == typeid(VigraTrueType));
        assert(typeid(FunctorTraits<FUNCTOR>::isUnaryAnalyser) == typeid(VigraTrueType));

        functor(src_accessor(src_begin));
        dest_accessor.set(functor(), dest_begin);

void vigra::combineTwoMultiArrays | ( |  | ... | ) |

Combine two multi-dimensional arrays into one using a binary function or functor.

This function can be applied in three modes:

Standard Mode:
  If the source and destination arrays have the same size, the transformation given by the functor is applied to every pair of corresponding source elements and the result written into the corresponding destination element. Binary functions, binary functors from the STL and the functors specifically defined in Functors to Combine Images can be used in standard mode. Creation of new functors is easiest by using Functor Expressions.
Expanding Mode:
  If the source arrays have length 1 along some (or even all) dimensions, the source values at index 0 are used for all destination elements in those dimensions. In other words, the source index is not incremented along those dimensions, but the transformation functor is applied as usual. So, we can expand small arrays (e.g. a single row of data, column length is 1), into larger ones (e.g. a 2D image with the same width): the given values are simply reused as necessary (e.g. for every row of the destination image). It is not even necessary that the source array shapes are equal. For example, we can combine a small array with one that hase the same size as the destination array. The same functors as in standard mode can be applied.
Reducing Mode:
  If the destination array has length 1 along some (or even all) dimensions, the source values in these dimensions are reduced to single values by means of a suitable functor which supports two function call operators: one with two arguments to collect the values, and one without argument to obtain the final (reduced) result. This behavior is a multi-dimensional generalization of the C++ standard function `std::accumulate()`.

The arrays must be represented by iterators compatible with vigra::MultiIterator, and the iteration range is specified by means of shape objects. If only a single source shape is given the destination array is assumed to have the same shape, and standard mode is applied. If three shapes are given, the size of corresponding dimensions must be either equal (standard copy), or the length of this dimension must be 1 in one or both source arrays (expand mode), or the destination length must be 1 (reduce mode). However, reduction and expansion cannot be executed at the same time, so the latter conditions are mutual exclusive, even if they apply to different dimensions.

The function uses accessors to access the data elements.

Declarations:

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

pass arguments explicitly:

        namespace vigra {
            template <class SrcIterator1, class SrcShape, class SrcAccessor1,
                      class SrcIterator2, class SrcAccessor2,
                      class DestIterator, class DestAccessor,
                      class Functor>
            void combineTwoMultiArrays(
                           SrcIterator1 s1, SrcShape const & shape, SrcAccessor1 src1,
                           SrcIterator2 s2, SrcAccessor2 src2,
                           DestIterator d, DestAccessor dest, Functor const & f);

            template <class SrcIterator1, class SrcShape1, class SrcAccessor1,
                      class SrcIterator2, class SrcShape2, class SrcAccessor2,
                      class DestIterator, class DestShape, class DestAccessor,
                      class Functor>
            void combineTwoMultiArrays(
                           SrcIterator1 s1, SrcShape1 const & sshape1, SrcAccessor1 src1,
                           SrcIterator2 s2, SrcShape2 const & sshape2, SrcAccessor2 src2,
                           DestIterator d, DestShape const & dshape, DestAccessor dest,
                           Functor const & f);
                }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class SrcIterator1, class SrcShape, class SrcAccessor1,
                      class SrcIterator2, class SrcAccessor2,
                      class DestIterator, class DestAccessor, class Functor>
            void combineTwoMultiArrays(
                           triple<SrcIterator1, SrcShape, SrcAccessor1> const & src1,
                           pair<SrcIterator2, SrcAccessor2> const & src2,
                           pair<DestIterator, DestAccessor> const & dest, Functor const & f);

            template <class SrcIterator1, class SrcShape1, class SrcAccessor1,
                      class SrcIterator2, class SrcShape2, class SrcAccessor2,
                      class DestIterator, class DestShape, class DestAccessor,
                      class Functor>
            void combineTwoMultiArrays(
                           triple<SrcIterator1, SrcShape1, SrcAccessor1> const & src1,
                           triple<SrcIterator2, SrcShape2, SrcAccessor2> const & src2,
                           triple<DestIterator, DestShape, DestAccessor> const & dest,
                           Functor const & f);
        }

Usage - Standard Mode:

Source and destination arrays have the same size.

        #include <functional>     // for std::plus

        typedef vigra::MultiArray<3, int> Array;
        Array src1(Array::size_type(100, 200, 50)),
              src2(Array::size_type(100, 200, 50)),
              dest(Array::size_type(100, 200, 50));
        ...

        vigra::combineTwoMultiArrays(
                    srcMultiArrayRange(src1),
                    srcMultiArray(src2),
                    destMultiArray(dest),
                    std::plus<int>());

Usage - Expand Mode:

One source array is only 2D (it has depth 1). This image will be added to every slice of the other source array, and the result if written into the corresponding destination slice. Note that the shapes of all arrays must be passed to the algorithm, so we use `srcMultiArrayRange()` and `destMultiArrayRange()` rather than `srcMultiArray()` and `destMultiArray()`.

        #include <functional>     // for std::plus

        typedef vigra::MultiArray<3, int> Array;
        Array src1(Array::size_type(100, 200, 1)),
              src2(Array::size_type(100, 200, 50)),
              dest(Array::size_type(100, 200, 50));
        ...

        vigra::combineTwoMultiArrays(
                    srcMultiArrayRange(src1),
                    srcMultiArray(src2),
                    destMultiArray(dest),
                    std::plus<int>());

Usage - Reduce Mode:

The destination array is only 1D (it's width and height are 1). Thus, it will contain accumulated data for every slice of the source volumes (or for every frame, if the sources are interpreted as image sequences). In the example, we use vigra::ReduceFunctor together with a functor expression (see Functor Expressions) to calculate the total absolute difference of the gray values in every pair of source slices. Note that the shapes of all arrays must be passed to the algorithm in order for the reduction to work, so we use `srcMultiArrayRange()` and `destMultiArrayRange()` rather than `srcMultiArray()` and `destMultiArray()`.

        #include <vigra/functorexpression.hxx>
        using namespace vigra::functor;

        typedef vigra::MultiArray<3, int> Array;
        Array src1(Array::size_type(100, 200, 50)),
              src2(Array::size_type(100, 200, 50)),
              dest(Array::size_type(1, 1, 50));
        ...

        vigra::combineTwoMultiArrays(
                    srcMultiArrayRange(src1),
                    srcMultiArray(src2),
                    destMultiArray(dest),
                    reduceFunctor(Arg1() + abs(Arg2() - Arg3()), 0) );
                    // Arg1() is the sum accumulated so far, initialized with 0

Note that the functor must define the appropriate traits described below in order to be recognized as a reduce functor. This is most easily achieved by deriving from `BinaryReduceFunctorTag` (see vigra::FunctorTraits).

Required Interface:

In standard and expand mode, the functor must be a model of BinaryFunction (i.e. support function call with two arguments and a return value `res = functor(arg1, arg2)`):

        MultiIterator src1_begin, src2_begin, dest_begin;

        SrcAccessor1 src1_accessor;
        SrcAccessor2 src2_accessor;
        DestAccessor dest_accessor;

        Functor functor;

        dest_accessor.set(
              functor(src1_accessor(src1_begin), src2_accessor(src2_begin)),
              dest_begin);

In reduce mode, it must be a model of BinaryAnalyser (i.e. support function call with two arguments and no return value `functor(arg1, arg2)`) and Initializer (i.e. support function call with no argument, but return value `res = functor()`). Internally, such functors are recognized by the meta functions `FunctorTraits<FUNCTOR>::isBinaryAnalyser` and `FunctorTraits<FUNCTOR>::isInitializer` which must both yield `VigraTrueType`. Make sure that your functor correctly defines `FunctorTraits` because otherwise reduce mode will not work. This is most easily achieved by deriving the functor from `BinaryReduceFunctorTag` (see vigra::FunctorTraits). In addition, the functor must be copy constructible in order to start each reduction with a fresh functor.

        MultiIterator src1_begin, src2_begin, dest_begin;

        SrcAccessor1 src1_accessor;
        SrcAccessor2 src2_accessor;
        DestAccessor dest_accessor;

        FUNCTOR initial_functor, functor(initial_functor);
        assert(typeid(FunctorTraits<FUNCTOR>::isInitializer) == typeid(VigraTrueType));
        assert(typeid(FunctorTraits<FUNCTOR>::isBinaryAnalyser) == typeid(VigraTrueType));

        functor(src1_accessor(src1_begin), src2_accessor(src2_begin));
        dest_accessor.set(functor(), dest_begin);

void vigra::combineThreeMultiArrays | ( |  | ... | ) |

Combine three multi-dimensional arrays into one using a ternary function or functor.

Except for the fact that it operates on three input arrays, this function is identical to combineTwoMultiArrays().

Declarations:

pass arguments explicitly:

        namespace vigra {
            template <class SrcIterator1, class SrcShape, class SrcAccessor1,
                      class SrcIterator2, class SrcAccessor2,
                      class SrcIterator3, class SrcAccessor3,
                      class DestIterator, class DestAccessor,
                      class Functor>
            void
            combineThreeMultiArrays(SrcIterator1 s1, SrcShape const & shape, SrcAccessor1 src1,
                           SrcIterator2 s2, SrcAccessor2 src2,
                           SrcIterator3 s3, SrcAccessor3 src3,
                           DestIterator d, DestAccessor dest, Functor const & f);
                        }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class SrcIterator1, class SrcShape, class SrcAccessor1,
                      class SrcIterator2, class SrcAccessor2,
                      class SrcIterator3, class SrcAccessor3,
                      class DestIterator, class DestAccessor,
                      class Functor>
            inline void
            combineThreeMultiArrays(triple<SrcIterator1, SrcShape, SrcAccessor1> const & src1,
                           pair<SrcIterator2, SrcAccessor2> const & src2,
                           pair<SrcIterator3, SrcAccessor3> const & src3,
                           pair<DestIterator, DestAccessor> const & dest, Functor const & f);
        }

Usage:

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

        #include <functional>     // for plus

        typedef vigra::MultiArray<3, int> Array;
        Array src1(Array::size_type(100, 200, 50)),
              src2(Array::size_type(100, 200, 50)),
              src3(Array::size_type(100, 200, 50)),
              dest(Array::size_type(100, 200, 50));
        ...

        vigra::combineThreeMultiArrays(
                    srcMultiArrayRange(src1),
                    srcMultiArray(src2),
                    srcMultiArray(src3),
                    destMultiArray(dest),
                    SomeThreeArgumentFunctor());

void vigra::inspectMultiArray | ( |  | ... | ) |

Call an analyzing functor at every element of a multi-dimensional array.

This function can be used to collect statistics of the array etc. The results must be stored in the functor, which serves as a return value. The arrays must be represented by iterators compatible with vigra::MultiIterator. The function uses an accessor to access the pixel data. Note that the iterator range must be specified by a shape object, because otherwise we could not control the range simultaneously in all dimensions (this is a necessary consequence of the vigra::MultiIterator design).

Declarations:

pass arguments explicitly:

        namespace vigra {
            template <class Iterator, class Shape, class Accessor, class Functor>
            void
            inspectMultiArray(Iterator s, Shape const & shape, Accessor a,  Functor & f);
        }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class Iterator, class Shape, class Accessor, class Functor>
            void
            inspectMultiArray(triple<Iterator, Shape, Accessor> const & s, Functor & f);
        }

Usage:

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

        typedef vigra::MultiArray<3, int> Array;
        Array array(Array::size_type(100, 200, 50));

        // init functor
        vigra::FindMinMax<int> minmax;

        vigra::inspectMultiArray(srcMultiArrayRange(array), minmax);

        cout << "Min: " << minmax.min << " Max: " << minmax.max;

Required Interface:

        MultiIterator src_begin;

        Accessor accessor;
        Functor functor;

        functor(accessor(src_begin));

void vigra::inspectTwoMultiArrays | ( |  | ... | ) |

Call an analyzing functor at all corresponding elements of two multi-dimensional arrays.

This function can be used to collect statistics of the array etc. The results must be stored in the functor, which serves as a return value. The arrays must be represented by iterators compatible with vigra::MultiIterator. The function uses an accessor to access the pixel data. Note that the iterator range must be specified by a shape object, because otherwise we could not control the range simultaneously in all dimensions (this is a necessary consequence of the vigra::MultiIterator design).

Declarations:

pass arguments explicitly:

        namespace vigra {
            template <class Iterator1, class Shape, class Accessor1,
                      class Iterator2, class Accessor2,
                      class Functor>
            void
            inspectTwoMultiArrays(Iterator1 s1, Shape const & shape, Accessor1 a1,
                                  Iterator2 s2, Accessor2 a2, Functor & f);
        }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class Iterator1, class Shape1, class Accessor1,
                      class Iterator2, class Accessor2,
                      class Functor>
            void
            inspectTwoMultiArrays(triple<Iterator1, Shape1, Accessor1> const & s1,
                                  pair<Iterator2, Accessor2> const & s2, Functor & f);
        }

Usage:

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

        typedef vigra::MultiArray<3, int> Array;
        Array array1(Array::size_type(100, 200, 50)),
              array2(Array::size_type(100, 200, 50));

        // init functor
        SomeStatisticsFunctor stats(..);

        vigra::inspectTwoMultiArrays(srcMultiArrayRange(array1), srcMultiArray(array2), stats);

Required Interface:

        MultiIterator src1_begin, src2_begin;

        Accessor a1, a2;
        Functor functor;

        functor(a1(src1_begin), a2(src2_begin));

void vigra::vectorToTensorMultiArray | ( |  | ... | ) |

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 `[t11, t12 == t21, t22]` in this order, whereas it contains the elements `[t11, t12, t13, t22, t23, t33]` for 3D arrays.

Currently, `N <= 3` is required.

Declarations:

pass arguments explicitly:

        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);
        }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestAccessor>
            void
            vectorToTensorMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
                                     pair<DestIterator, DestAccessor> d);
        }

Usage:

#include <vigra/multi_tensorutilities.hxx>

        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));

void vigra::tensorTraceMultiArray | ( |  | ... | ) |

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 vectorToTensorMultiArray()) representing the upper triangular part of a symmetric tensor into a scalar array holding the tensor trace.

Currently, `N <= 3` is required.

Declarations:

pass arguments explicitly:

        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);
        }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestAccessor>
            void
            tensorTraceMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
                                  pair<DestIterator, DestAccessor> d);
        }

Usage:

#include <vigra/multi_tensorutilities.hxx>

        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));

void vigra::tensorEigenvaluesMultiArray | ( |  | ... | ) |

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 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, `N <= 3` is required.

Declarations:

pass arguments explicitly:

        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);
        }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestAccessor>
            void
            tensorEigenvaluesMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
                                        pair<DestIterator, DestAccessor> d);
        }

Usage:

#include <vigra/multi_tensorutilities.hxx>

        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));

void vigra::tensorDeterminantMultiArray | ( |  | ... | ) |

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 vectorToTensorMultiArray()) representing the upper triangular part of a symmetric tensor into the a scalar array holding the tensor determinant.

Currently, `N <= 3` is required.

Declarations:

pass arguments explicitly:

        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);
        }

use argument objects in conjunction with Argument Object Factories :

        namespace vigra {
            template <class SrcIterator, class SrcShape, class SrcAccessor,
                      class DestIterator, class DestAccessor>
            void
            tensorDeterminantMultiArray(triple<SrcIterator, SrcShape, SrcAccessor> s,
                                        pair<DestIterator, DestAccessor> d);
        }

Usage:

#include <vigra/multi_tensorutilities.hxx>

        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));

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python vigra 1.9.0 (Tue Nov 6 2012)