GteImage3.h

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// David Eberly, Geometric Tools, Redmond WA 98052
// Copyright (c) 1998-2017
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
// File Version: 3.0.0 (2016/06/19)

#pragma once

#include <Imagics/GteImage.h>
#include <array>

namespace gte
{

template <typename PixelType>
class Image3 : public Image<PixelType>
{
public:
    // Construction and destruction.  The last constructor must have positive
    // dimensions; otherwise, the image is empty.
    virtual ~Image3();
    Image3();
    Image3(int dimension0, int dimension1, int dimension2);

    // Support for copy semantics.
    Image3(Image3 const& image);
    Image3& operator= (Image3 const& image);

    // Support for move semantics.
    Image3(Image3&& image);
    Image3& operator= (Image3&& image);

    // Support for changing the image dimensions.  All pixel data is lost by
    // this operation.
    void Reconstruct(int dimension0, int dimension1, int dimension2);

    // Conversion between 1-dimensional indices and 3-dimensional coordinates.
    inline size_t GetIndex(int x, int y, int z) const;
    inline size_t GetIndex(std::array<int, 3> const& coord) const;
    inline void GetCoordinates(size_t index, int& x, int& y, int& z) const;
    inline std::array<int, 3> GetCoordinates(size_t index) const;

    // Access the data as a 3-dimensional array.  The operator() functions
    // test for valid (x,y,z) when iterator checking is enabled and assert on
    // invalid (x,y,z).  The Get() functions test for valid (x,y,z) and clamp
    // when invalid; these functions cannot fail.
    inline PixelType& operator() (int x, int y, int z);
    inline PixelType const& operator() (int x, int y, int z) const;
    inline PixelType& operator() (std::array<int, 3> const& coord);
    inline PixelType const& operator() (std::array<int,3> const& coord) const;
    inline PixelType& Get(int x, int y, int z);
    inline PixelType const& Get(int x, int y, int z) const;
    inline PixelType& Get(std::array<int, 3> coord);
    inline PixelType const& Get(std::array<int, 3> coord) const;

    // In the following discussion, u, v and w are in {-1,1}.  Given a voxel
    // (x,y,z), the 6-connected neighbors have relative offsets (u,0,0),
    // (0,v,0), and (0,0,w).  The 18-connected neighbors include the
    // 6-connected neighbors and have additional relative offsets (u,v,0),
    // (u,0,w), and (0,v,w).  The 26-connected neighbors include the
    // 18-connected neighbors and have additional relative offsets (u,v,w).
    // The corner neighbors have offsets (0,0,0), (1,0,0), (0,1,0), (1,1,0),
    // (0,0,1), (1,0,1), (0,1,1), and (1,1,1) in that order.  The full
    // neighborhood is the set of 3x3x3 pixels centered at (x,y).

    // The neighborhoods can be accessed as 1-dimensional indices using these
    // functions.  The first five functions provide 1-dimensional indices
    // relative to any voxel location; these depend only on the image
    // dimensions.  The last five functions provide 1-dimensional indices
    // for the actual voxels in the neighborhood; no clamping is used when
    // (x,y,z) is on the boundary.
    void GetNeighborhood(std::array<int, 6>& nbr) const;
    void GetNeighborhood(std::array<int, 18>& nbr) const;
    void GetNeighborhood(std::array<int, 26>& nbr) const;
    void GetCorners(std::array<int, 8>& nbr) const;
    void GetFull(std::array<int, 27>& nbr) const;
    void GetNeighborhood(int x, int y, int z, std::array<size_t, 6>& nbr) const;
    void GetNeighborhood(int x, int y, int z, std::array<size_t, 18>& nbr) const;
    void GetNeighborhood(int x, int y, int z, std::array<size_t, 26>& nbr) const;
    void GetCorners(int x, int y, int z, std::array<size_t, 8>& nbr) const;
    void GetFull(int x, int y, int z, std::array<size_t, 27>& nbr) const;

    // The neighborhoods can be accessed as 3-tuples using these functions.
    // The first five functions provide 3-tuples relative to any voxel
    // location; these depend only on the image dimensions.  The last five
    // functions provide 3-tuples for the actual voxels in the neighborhood;
    // no clamping is used when (x,y,z) is on the boundary.
    void GetNeighborhood(std::array<std::array<int, 3>, 6>& nbr) const;
    void GetNeighborhood(std::array<std::array<int, 3>, 18>& nbr) const;
    void GetNeighborhood(std::array<std::array<int, 3>, 26>& nbr) const;
    void GetCorners(std::array<std::array<int, 3>, 8>& nbr) const;
    void GetFull(std::array<std::array<int, 3>, 27>& nbr) const;
    void GetNeighborhood(int x, int y, int z, std::array<std::array<size_t, 3>, 6>& nbr) const;
    void GetNeighborhood(int x, int y, int z, std::array<std::array<size_t, 3>, 18>& nbr) const;
    void GetNeighborhood(int x, int y, int z, std::array<std::array<size_t, 3>, 26>& nbr) const;
    void GetCorners(int x, int y, int z, std::array<std::array<size_t, 3>, 8>& nbr) const;
    void GetFull(int x, int y, int z, std::array<std::array<size_t, 3>, 27>& nbr) const;
};


template <typename PixelType>
Image3<PixelType>::~Image3()
{
}

template <typename PixelType>
Image3<PixelType>::Image3()
{
}

template <typename PixelType>
Image3<PixelType>::Image3(int dimension0, int dimension1, int dimension2)
    :
    Image<PixelType>(std::vector<int>{ dimension0, dimension1, dimension2 })
{
}

template <typename PixelType>
Image3<PixelType>::Image3(Image3 const& image)
    :
    Image<PixelType>(image)
{
}

template <typename PixelType>
Image3<PixelType>& Image3<PixelType>::operator= (Image3 const& image)
{
    Image<PixelType>::operator=(image);
    return *this;
}

template <typename PixelType>
Image3<PixelType>::Image3(Image3&& image)
{
    *this = std::move(image);
}

template <typename PixelType>
Image3<PixelType>& Image3<PixelType>::operator= (Image3&& image)
{
    Image<PixelType>::operator=(image);
    return *this;
}

template <typename PixelType>
void Image3<PixelType>::Reconstruct(int dimension0, int dimension1, int dimension2)
{
    Image<PixelType>::Reconstruct(std::vector<int>{ dimension0, dimension1, dimension2 });
}

template <typename PixelType> inline
size_t Image3<PixelType>::GetIndex(int x, int y, int z) const
{
#if defined(GTE_IMAGICS_ASSERT_ON_INVALID_INDEX)
    if (0 <= x && x < this->mDimensions[0]
        && 0 <= y && y < this->mDimensions[1]
        && 0 <= z && z < this->mDimensions[2])
    {
        return static_cast<size_t>(x) +
            static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(y) +
            static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(z));
    }
    LogError("Invalid coordinates (" + std::to_string(x) + "," +
        std::to_string(y) + "," + std::to_string(z) + ").");
    return 0;
#else
    return static_cast<size_t>(x) +
        static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(y) +
        static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(z));
#endif
}

template <typename PixelType> inline
size_t Image3<PixelType>::GetIndex(std::array<int, 3> const& coord) const
{
#if defined(GTE_IMAGICS_ASSERT_ON_INVALID_INDEX)
    if (0 <= coord[0] && coord[0] < this->mDimensions[0]
        && 0 <= coord[1] && coord[1] < this->mDimensions[1]
        && 0 <= coord[2] && coord[2] < this->mDimensions[2])
    {
        return static_cast<size_t>(coord[0]) +
            static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(coord[1]) +
            static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(coord[2]));
    }
    LogError("Invalid coordinates (" + std::to_string(coord[0]) + "," +
        std::to_string(coord[1]) + "," + std::to_string(coord[2]) + ").");
    return 0;
#else
    return static_cast<size_t>(coord[0]) +
        static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(coord[1]) +
        static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(coord[2]));
#endif
}

template <typename PixelType> inline
void Image3<PixelType>::GetCoordinates(size_t index, int& x, int& y, int& z) const
{
#if defined(GTE_IMAGICS_ASSERT_ON_INVALID_INDEX)
    if (index < mNumPixels)
    {
        x = static_cast<int>(index % this->mDimensions[0]);
        index /= this->mDimensions[0];
        y = static_cast<int>(index % this->mDimensions[1]);
        z = static_cast<int>(index / this->mDimensions[1]);
    }
    else
    {
        LogError("Invalid index " + std::to_string(index) + ".");
        x = 0;
        y = 0;
        z = 0;
    }
#else
    x = static_cast<int>(index % this->mDimensions[0]);
    index /= this->mDimensions[0];
    y = static_cast<int>(index % this->mDimensions[1]);
    z = static_cast<int>(index / this->mDimensions[1]);
#endif
}

template <typename PixelType> inline
std::array<int, 3> Image3<PixelType>::GetCoordinates(size_t index) const
{
    std::array<int, 3> coord;
#if defined(GTE_IMAGICS_ASSERT_ON_INVALID_INDEX)
    if (index < mNumPixels)
    {
        coord[0] = static_cast<int>(index % this->mDimensions[0]);
        index /= this->mDimensions[0];
        coord[1] = static_cast<int>(index % this->mDimensions[1]);
        coord[2] = static_cast<int>(index / this->mDimensions[1]);
    }
    else
    {
        LogError("Invalid index " + std::to_string(index) + ".");
        coord[0] = 0;
        coord[1] = 0;
        coord[2] = 0;
    }
#else
    coord[0] = static_cast<int>(index % this->mDimensions[0]);
    index /= this->mDimensions[0];
    coord[1] = static_cast<int>(index % this->mDimensions[1]);
    coord[2] = static_cast<int>(index / this->mDimensions[1]);
#endif
    return coord;
}

template <typename PixelType> inline
PixelType& Image3<PixelType>::operator() (int x, int y, int z)
{
#if defined(GTE_IMAGICS_ASSERT_ON_INVALID_INDEX)
    if (0 <= x && x < this->mDimensions[0]
        && 0 <= y && y < this->mDimensions[1]
        && 0 <= z && z < this->mDimensions[2])
    {
        size_t i = static_cast<size_t>(x) +
            static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(y) +
            static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(z));
        return this->mPixels[i];
    }
    LogError("Invalid coordinates (" + std::to_string(x) + "," +
        std::to_string(y) + "," + std::to_string(z) + ").");
    return this->mPixels[0];
#else
    size_t i = static_cast<size_t>(x) +
        static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(y) +
        static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(z));
    return this->mPixels[i];
#endif
}

template <typename PixelType> inline
PixelType const& Image3<PixelType>::operator() (int x, int y, int z) const
{
#if defined(GTE_IMAGICS_ASSERT_ON_INVALID_INDEX)
    if (0 <= x && x < this->mDimensions[0]
        && 0 <= y && y < this->mDimensions[1]
        && 0 <= z && z < this->mDimensions[2])
    {
        size_t i = static_cast<size_t>(x) +
            static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(y) +
            static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(z));
        return this->mPixels[i];
    }
    LogError("Invalid coordinates (" + std::to_string(x) + "," +
        std::to_string(y) + "," + std::to_string(z) + ").");
    return this->mPixels[0];
#else
    size_t i = static_cast<size_t>(x) +
        static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(y) +
        static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(z));
    return this->mPixels[i];
#endif
}

template <typename PixelType> inline
PixelType& Image3<PixelType>::operator() (std::array<int, 3> const& coord)
{
#if defined(GTE_IMAGICS_ASSERT_ON_INVALID_INDEX)
    if (0 <= coord[0] && coord[0] < this->mDimensions[0]
        && 0 <= coord[1] && coord[1] < this->mDimensions[1]
        && 0 <= coord[2] && coord[2] < this->mDimensions[2])
    {
        size_t i = static_cast<size_t>(coord[0]) +
            static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(coord[1]) +
            static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(coord[2]));
        return this->mPixels[i];
    }
    LogError("Invalid coordinates (" + std::to_string(coord[0]) + "," +
        std::to_string(coord[1]) + "," + std::to_string(coord[2]) + ").");
    return mPixel[0];
#else
    size_t i = static_cast<size_t>(coord[0]) +
        static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(coord[1]) +
        static_cast<size_t>(this->mDimensions[1] * coord[2]));
    return this->mPixels[i];
#endif
}

template <typename PixelType> inline
PixelType const& Image3<PixelType>::operator() (std::array<int, 3> const& coord) const
{
#if defined(GTE_IMAGICS_ASSERT_ON_INVALID_INDEX)
    if (0 <= coord[0] && coord[0] < this->mDimensions[0]
        && 0 <= coord[1] && coord[1] < this->mDimensions[1]
        && 0 <= coord[2] && coord[2] < this->mDimensions[2])
    {
        size_t i = static_cast<size_t>(coord[0]) +
            static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(coord[1]) +
            static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(coord[2]));
        return this->mPixels[i];
    }
    LogError("Invalid coordinates (" + std::to_string(coord[0]) + "," +
        std::to_string(coord[1]) + "," + std::to_string(coord[2]) + ").");
    return mPixel[0];
#else
    size_t i = static_cast<size_t>(coord[0]) +
        static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(coord[1]) +
        static_cast<size_t>(this->mDimensions[1] * coord[2]));
    return this->mPixels[i];
#endif
}

template <typename PixelType>
PixelType& Image3<PixelType>::Get(int x, int y, int z)
{
    // Clamp to valid (x,y,z).
    if (x < 0)
    {
        x = 0;
    }
    else if (x >= this->mDimensions[0])
    {
        x = this->mDimensions[0] - 1;
    }

    if (y < 0)
    {
        y = 0;
    }
    else if (y >= this->mDimensions[1])
    {
        y = this->mDimensions[1] - 1;
    }

    if (z < 0)
    {
        z = 0;
    }
    else if (z >= this->mDimensions[2])
    {
        z = this->mDimensions[2] - 1;
    }

    size_t i = static_cast<size_t>(x) +
        static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(y) +
        static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(z));
    return this->mPixels[i];
}

template <typename PixelType>
PixelType const& Image3<PixelType>::Get(int x, int y, int z) const
{
    // Clamp to valid (x,y,z).
    if (x < 0)
    {
        x = 0;
    }
    else if (x >= this->mDimensions[0])
    {
        x = this->mDimensions[0] - 1;
    }

    if (y < 0)
    {
        y = 0;
    }
    else if (y >= this->mDimensions[1])
    {
        y = this->mDimensions[1] - 1;
    }

    if (z < 0)
    {
        z = 0;
    }
    else if (z >= this->mDimensions[2])
    {
        z = this->mDimensions[2] - 1;
    }

    size_t i = static_cast<size_t>(x) +
        static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(y) +
        static_cast<size_t>(this->mDimensions[1]) * static_cast<size_t>(z));
    return this->mPixels[i];
}

template <typename PixelType>
PixelType& Image3<PixelType>::Get(std::array<int, 3> coord)
{
    // Clamp to valid (x,y,z).
    for (int d = 0; d < 3; ++d)
    {
        if (coord[d] < 0)
        {
            coord[d] = 0;
        }
        else if (coord[d] >= this->mDimensions[d])
        {
            coord[d] = this->mDimensions[d] - 1;
        }
    }

    size_t i = static_cast<size_t>(coord[0]) +
        static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(coord[1]) +
        static_cast<size_t>(this->mDimensions[1] * coord[2]));
    return this->mPixels[i];
}

template <typename PixelType>
PixelType const& Image3<PixelType>::Get(std::array<int, 3> coord) const
{
    // Clamp to valid (x,y,z).
    for (int d = 0; d < 3; ++d)
    {
        if (coord[d] < 0)
        {
            coord[d] = 0;
        }
        else if (coord[d] >= this->mDimensions[d])
        {
            coord[d] = this->mDimensions[d] - 1;
        }
    }

    size_t i = static_cast<size_t>(coord[0]) +
        static_cast<size_t>(this->mDimensions[0]) * (static_cast<size_t>(coord[1]) +
        static_cast<size_t>(this->mDimensions[1] * coord[2]));
    return this->mPixels[i];
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(std::array<int, 6>& nbr) const
{
    int dim0 = this->mDimensions[0];
    int dim01 = this->mDimensions[0] * this->mDimensions[1];
    nbr[0] = -1;        // (x-1,y,z)
    nbr[1] = +1;        // (x+1,y,z)
    nbr[2] = -dim0;     // (x,y-1,z)
    nbr[3] = +dim0;     // (x,y+1,z)
    nbr[4] = -dim01;    // (x,y,z-1)
    nbr[5] = +dim01;    // (x,y,z+1)
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(std::array<int, 18>& nbr) const
{
    int dim0 = this->mDimensions[0];
    int dim01 = this->mDimensions[0] * this->mDimensions[1];
    nbr[0] = -1;                // (x-1,y,z)
    nbr[1] = +1;                // (x+1,y,z)
    nbr[2] = -dim0;             // (x,y-1,z)
    nbr[3] = +dim0;             // (x,y+1,z)
    nbr[4] = -dim01;            // (x,y,z-1)
    nbr[5] = +dim01;            // (x,y,z+1)
    nbr[6] = -1 - dim0;         // (x-1,y-1,z)
    nbr[7] = +1 - dim0;         // (x+1,y-1,z)
    nbr[8] = -1 + dim0;         // (x-1,y+1,z)
    nbr[9] = +1 + dim0;         // (x+1,y+1,z)
    nbr[10] = -1 + dim01;       // (x-1,y,z+1)
    nbr[11] = +1 + dim01;       // (x+1,y,z+1)
    nbr[12] = -dim0 + dim01;    // (x,y-1,z+1)
    nbr[13] = +dim0 + dim01;    // (x,y+1,z+1)
    nbr[14] = -1 - dim01;       // (x-1,y,z-1)
    nbr[15] = +1 - dim01;       // (x+1,y,z-1)
    nbr[16] = -dim0 - dim01;    // (x,y-1,z-1)
    nbr[17] = +dim0 - dim01;    // (x,y+1,z-1)
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(std::array<int, 26>& nbr) const
{
    int dim0 = this->mDimensions[0];
    int dim01 = this->mDimensions[0] * this->mDimensions[1];
    nbr[0] = -1;                    // (x-1,y,z)
    nbr[1] = +1;                    // (x+1,y,z)
    nbr[2] = -dim0;                 // (x,y-1,z)
    nbr[3] = +dim0;                 // (x,y+1,z)
    nbr[4] = -dim01;                // (x,y,z-1)
    nbr[5] = +dim01;                // (x,y,z+1)
    nbr[6] = -1 - dim0;             // (x-1,y-1,z)
    nbr[7] = +1 - dim0;             // (x+1,y-1,z)
    nbr[8] = -1 + dim0;             // (x-1,y+1,z)
    nbr[9] = +1 + dim0;             // (x+1,y+1,z)
    nbr[10] = -1 + dim01;           // (x-1,y,z+1)
    nbr[11] = +1 + dim01;           // (x+1,y,z+1)
    nbr[12] = -dim0 + dim01;        // (x,y-1,z+1)
    nbr[13] = +dim0 + dim01;        // (x,y+1,z+1)
    nbr[14] = -1 - dim01;           // (x-1,y,z-1)
    nbr[15] = +1 - dim01;           // (x+1,y,z-1)
    nbr[16] = -dim0 - dim01;        // (x,y-1,z-1)
    nbr[17] = +dim0 - dim01;        // (x,y+1,z-1)
    nbr[18] = -1 - dim0 - dim01;    // (x-1,y-1,z-1)
    nbr[19] = +1 - dim0 - dim01;    // (x+1,y-1,z-1)
    nbr[20] = -1 + dim0 - dim01;    // (x-1,y+1,z-1)
    nbr[21] = +1 + dim0 - dim01;    // (x+1,y+1,z-1)
    nbr[22] = -1 - dim0 + dim01;    // (x-1,y-1,z+1)
    nbr[23] = +1 - dim0 + dim01;    // (x+1,y-1,z+1)
    nbr[24] = -1 + dim0 + dim01;    // (x-1,y+1,z+1)
    nbr[25] = +1 + dim0 + dim01;    // (x+1,y+1,z+1)
}

template <typename PixelType>
void Image3<PixelType>::GetCorners(std::array<int, 8>& nbr) const
{
    int dim0 = this->mDimensions[0];
    int dim01 = this->mDimensions[0] * this->mDimensions[1];
    nbr[0] = 0;                 // (x,y,z)
    nbr[1] = 1;                 // (x+1,y,z)
    nbr[2] = dim0;              // (x,y+1,z)
    nbr[3] = dim0 + 1;          // (x+1,y+1,z)
    nbr[4] = dim01;             // (x,y,z+1)
    nbr[5] = dim01 + 1;         // (x+1,y,z+1)
    nbr[6] = dim01 + dim0;      // (x,y+1,z+1)
    nbr[7] = dim01 + dim0 + 1;  // (x+1,y+1,z+1)
}

template <typename PixelType>
void Image3<PixelType>::GetFull(std::array<int, 27>& nbr) const
{
    int dim0 = this->mDimensions[0];
    int dim01 = this->mDimensions[0] * this->mDimensions[1];
    nbr[0] = -1 - dim0 - dim01;     // (x-1,y-1,z-1)
    nbr[1] = -dim0 - dim01;         // (x,  y-1,z-1)
    nbr[2] = +1 - dim0 - dim01;     // (x+1,y-1,z-1)
    nbr[3] = -1 - dim01;            // (x-1,y,  z-1)
    nbr[4] = -dim01;                // (x,  y,  z-1)
    nbr[5] = +1 - dim01;            // (x+1,y,  z-1)
    nbr[6] = -1 + dim0 - dim01;     // (x-1,y+1,z-1)
    nbr[7] = +dim0 - dim01;         // (x,  y+1,z-1)
    nbr[8] = +1 + dim0 - dim01;     // (x+1,y+1,z-1)
    nbr[9] = -1 - dim0;             // (x-1,y-1,z)
    nbr[10] = -dim0;                // (x,  y-1,z)
    nbr[11] = +1 - dim0;            // (x+1,y-1,z)
    nbr[12] = -1;                   // (x-1,y,  z)
    nbr[13] = 0;                    // (x,  y,  z)
    nbr[14] = +1;                   // (x+1,y,  z)
    nbr[15] = -1 + dim0;            // (x-1,y+1,z)
    nbr[16] = +dim0;                // (x,  y+1,z)
    nbr[17] = +1 + dim0;            // (x+1,y+1,z)
    nbr[18] = -1 - dim0 + dim01;    // (x-1,y-1,z+1)
    nbr[19] = -dim0 + dim01;        // (x,  y-1,z+1)
    nbr[20] = +1 - dim0 + dim01;    // (x+1,y-1,z+1)
    nbr[21] = -1 + dim01;           // (x-1,y,  z+1)
    nbr[22] = +dim01;               // (x,  y,  z+1)
    nbr[23] = +1 + dim01;           // (x+1,y,  z+1)
    nbr[24] = -1 + dim0 + dim01;    // (x-1,y+1,z+1)
    nbr[25] = +dim0 + dim01;        // (x,  y+1,z+1)
    nbr[26] = +1 + dim0 + dim01;    // (x+1,y+1,z+1)
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(int x, int y, int z, std::array<size_t, 6>& nbr) const
{
    size_t index = GetIndex(x, y, z);
    std::array<int, 6> inbr;
    GetNeighborhood(inbr);
    for (int i = 0; i < 6; ++i)
    {
        nbr[i] = index + inbr[i];
    }
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(int x, int y, int z, std::array<size_t, 18>& nbr) const
{
    size_t index = GetIndex(x, y, z);
    std::array<int, 18> inbr;
    GetNeighborhood(inbr);
    for (int i = 0; i < 18; ++i)
    {
        nbr[i] = index + inbr[i];
    }
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(int x, int y, int z, std::array<size_t, 26>& nbr) const
{
    size_t index = GetIndex(x, y, z);
    std::array<int, 26> inbr;
    GetNeighborhood(inbr);
    for (int i = 0; i < 26; ++i)
    {
        nbr[i] = index + inbr[i];
    }
}

template <typename PixelType>
void Image3<PixelType>::GetCorners(int x, int y, int z, std::array<size_t, 8>& nbr) const
{
    size_t index = GetIndex(x, y, z);
    std::array<int, 8> inbr;
    GetCorners(inbr);
    for (int i = 0; i < 8; ++i)
    {
        nbr[i] = index + inbr[i];
    }
}

template <typename PixelType>
void Image3<PixelType>::GetFull(int x, int y, int z, std::array<size_t, 27>& nbr) const
{
    size_t index = GetIndex(x, y, z);
    std::array<int, 27> inbr;
    GetFull(inbr);
    for (int i = 0; i < 27; ++i)
    {
        nbr[i] = index + inbr[i];
    }
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(std::array<std::array<int, 3>, 6>& nbr) const
{
    nbr[0] = { { -1, 0, 0 } };
    nbr[1] = { { +1, 0, 0 } };
    nbr[2] = { { 0, -1, 0 } };
    nbr[3] = { { 0, +1, 0 } };
    nbr[4] = { { 0, 0, -1 } };
    nbr[5] = { { 0, 0, +1 } };
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(std::array<std::array<int, 3>, 18>& nbr) const
{
    nbr[0] = { { -1, 0, 0 } };
    nbr[1] = { { +1, 0, 0 } };
    nbr[2] = { { 0, -1, 0 } };
    nbr[3] = { { 0, +1, 0 } };
    nbr[4] = { { 0, 0, -1 } };
    nbr[5] = { { 0, 0, +1 } };
    nbr[6] = { { -1, -1, 0 } };
    nbr[7] = { { +1, -1, 0 } };
    nbr[8] = { { -1, +1, 0 } };
    nbr[9] = { { +1, +1, 0 } };
    nbr[10] = { { -1, 0, +1 } };
    nbr[11] = { { +1, 0, +1 } };
    nbr[12] = { { 0, -1, +1 } };
    nbr[13] = { { 0, +1, +1 } };
    nbr[14] = { { -1, 0, -1 } };
    nbr[15] = { { +1, 0, -1 } };
    nbr[16] = { { 0, -1, -1 } };
    nbr[17] = { { 0, +1, -1 } };
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(std::array<std::array<int, 3>, 26>& nbr) const
{
    nbr[0] = { { -1, 0, 0 } };
    nbr[1] = { { +1, 0, 0 } };
    nbr[2] = { { 0, -1, 0 } };
    nbr[3] = { { 0, +1, 0 } };
    nbr[4] = { { 0, 0, -1 } };
    nbr[5] = { { 0, 0, +1 } };
    nbr[6] = { { -1, -1, 0 } };
    nbr[7] = { { +1, -1, 0 } };
    nbr[8] = { { -1, +1, 0 } };
    nbr[9] = { { +1, +1, 0 } };
    nbr[10] = { { -1, 0, +1 } };
    nbr[11] = { { +1, 0, +1 } };
    nbr[12] = { { 0, -1, +1 } };
    nbr[13] = { { 0, +1, +1 } };
    nbr[14] = { { -1, 0, -1 } };
    nbr[15] = { { +1, 0, -1 } };
    nbr[16] = { { 0, -1, -1 } };
    nbr[17] = { { 0, +1, -1 } };
    nbr[18] = { { -1, -1, -1 } };
    nbr[19] = { { +1, -1, -1 } };
    nbr[20] = { { -1, +1, -1 } };
    nbr[21] = { { +1, +1, -1 } };
    nbr[22] = { { -1, -1, +1 } };
    nbr[23] = { { +1, -1, +1 } };
    nbr[24] = { { -1, +1, +1 } };
    nbr[25] = { { +1, +1, +1 } };
}

template <typename PixelType>
void Image3<PixelType>::GetCorners(std::array<std::array<int, 3>, 8>& nbr) const
{
    nbr[0] = { { 0, 0, 0 } };
    nbr[1] = { { 1, 0, 0 } };
    nbr[2] = { { 0, 1, 0 } };
    nbr[3] = { { 1, 1, 0 } };
    nbr[4] = { { 0, 0, 1 } };
    nbr[5] = { { 1, 0, 1 } };
    nbr[6] = { { 0, 1, 1 } };
    nbr[7] = { { 1, 1, 1 } };
}

template <typename PixelType>
void Image3<PixelType>::GetFull(std::array<std::array<int, 3>, 27>& nbr) const
{
    nbr[0] = { { -1, -1, -1 } };
    nbr[1] = { { 0, -1, -1 } };
    nbr[2] = { { +1, -1, -1 } };
    nbr[3] = { { -1, 0, -1 } };
    nbr[4] = { { 0, 0, -1 } };
    nbr[5] = { { +1, 0, -1 } };
    nbr[6] = { { -1, +1, -1 } };
    nbr[7] = { { 0, +1, -1 } };
    nbr[8] = { { +1, +1, -1 } };
    nbr[9] = { { -1, -1, 0 } };
    nbr[10] = { { 0, -1, 0 } };
    nbr[11] = { { +1, -1, 0 } };
    nbr[12] = { { -1, 0, 0 } };
    nbr[13] = { { 0, 0, 0 } };
    nbr[14] = { { +1, 0, 0 } };
    nbr[15] = { { -1, +1, 0 } };
    nbr[16] = { { 0, +1, 0 } };
    nbr[17] = { { +1, +1, 0 } };
    nbr[18] = { { -1, -1, +1 } };
    nbr[19] = { { 0, -1, +1 } };
    nbr[20] = { { +1, -1, +1 } };
    nbr[21] = { { -1, 0, +1 } };
    nbr[22] = { { 0, 0, +1 } };
    nbr[23] = { { +1, 0, +1 } };
    nbr[24] = { { -1, +1, +1 } };
    nbr[25] = { { 0, +1, +1 } };
    nbr[26] = { { +1, +1, +1 } };
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(int x, int y, int z, std::array<std::array<size_t, 3>, 6>& nbr) const
{
    std::array<std::array<int, 3>, 6> inbr;
    GetNeighborhood(inbr);
    for (int i = 0; i < 6; ++i)
    {
        nbr[i][0] = static_cast<size_t>(x) + inbr[i][0];
        nbr[i][1] = static_cast<size_t>(y) + inbr[i][1];
        nbr[i][2] = static_cast<size_t>(z) + inbr[i][2];
    }
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(int x, int y, int z, std::array<std::array<size_t, 3>, 18>& nbr) const
{
    std::array<std::array<int, 3>, 18> inbr;
    GetNeighborhood(inbr);
    for (int i = 0; i < 18; ++i)
    {
        nbr[i][0] = static_cast<size_t>(x) + inbr[i][0];
        nbr[i][1] = static_cast<size_t>(y) + inbr[i][1];
        nbr[i][2] = static_cast<size_t>(z) + inbr[i][2];
    }
}

template <typename PixelType>
void Image3<PixelType>::GetNeighborhood(int x, int y, int z, std::array<std::array<size_t, 3>, 26>& nbr) const
{
    std::array<std::array<int, 3>, 26> inbr;
    GetNeighborhood(inbr);
    for (int i = 0; i < 26; ++i)
    {
        nbr[i][0] = static_cast<size_t>(x) + inbr[i][0];
        nbr[i][1] = static_cast<size_t>(y) + inbr[i][1];
        nbr[i][2] = static_cast<size_t>(z) + inbr[i][2];
    }
}

template <typename PixelType>
void Image3<PixelType>::GetCorners(int x, int y, int z,
    std::array<std::array<size_t, 3>, 8>& nbr) const
{
    std::array<std::array<int, 3>, 8> inbr;
    GetCorners(inbr);
    for (int i = 0; i < 8; ++i)
    {
        nbr[i][0] = static_cast<size_t>(x) + inbr[i][0];
        nbr[i][1] = static_cast<size_t>(y) + inbr[i][1];
        nbr[i][2] = static_cast<size_t>(z) + inbr[i][2];
    }
}

template <typename PixelType>
void Image3<PixelType>::GetFull(int x, int y, int z,
    std::array<std::array<size_t, 3>, 27>& nbr) const
{
    std::array<std::array<int, 3>, 27> inbr;
    GetFull(inbr);
    for (int i = 0; i < 27; ++i)
    {
        nbr[i][0] = static_cast<size_t>(x) + inbr[i][0];
        nbr[i][1] = static_cast<size_t>(y) + inbr[i][1];
        nbr[i][2] = static_cast<size_t>(z) + inbr[i][2];
    }
}

}