    // Copyright (C) 2006  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_PIXEl_
    #define DLIB_PIXEl_

    #include <iostream>
    #include "serialize.h"
    #include <cmath>
    #include "algs.h"
    #include "uintn.h"
    #include <limits>
    #include <complex>
    #include "enable_if.h"

    namespace dlib
    {

    // ----------------------------------------------------------------------------------------

        /*!
            This file contains definitions of pixel objects and related classes and
            functionality.
        !*/

    // ----------------------------------------------------------------------------------------

        template <typename T>
        struct pixel_traits;
        /*!
            WHAT THIS OBJECT REPRESENTS
                As the name implies, this is a traits class for pixel types.
                It defines the properties of a pixel.

            This traits class will define the following public static members:
                - bool grayscale
                - bool rgb
                - bool rgb_alpha
                - bool hsi
                - bool lab

                - bool has_alpha

                - long num

                - basic_pixel_type
                - basic_pixel_type min()
                - basic_pixel_type max()
                - is_unsigned

            The above public constants are subject to the following constraints:
                - only one of grayscale, rgb, rgb_alpha, hsi or lab is true
                - if (rgb == true) then
                    - The type T will be a struct with 3 public members of type
                      unsigned char named "red" "green" and "blue".
                    - This type of pixel represents the RGB color space.
                    - num == 3
                    - has_alpha == false
                    - basic_pixel_type == unsigned char
                    - min() == 0
                    - max() == 255
                    - is_unsigned == true
                - if (rgb_alpha == true) then
                    - The type T will be a struct with 4 public members of type
                      unsigned char named "red" "green" "blue" and "alpha".
                    - This type of pixel represents the RGB color space with
                      an alpha channel where an alpha of 0 represents a pixel
                      that is totally transparent and 255 represents a pixel
                      with maximum opacity.
                    - num == 4
                    - has_alpha == true
                    - basic_pixel_type == unsigned char
                    - min() == 0
                    - max() == 255
                    - is_unsigned == true
                - else if (hsi == true) then
                    - The type T will be a struct with 3 public members of type
                      unsigned char named "h" "s" and "i".
                    - This type of pixel represents the HSI color space.
                    - num == 3
                    - has_alpha == false
                    - basic_pixel_type == unsigned char
                    - min() == 0
                    - max() == 255
                    - is_unsigned == true
                 - else if (lab == true) then
                    - The type T will be a struct with 3 public members of type
                      unsigned char named "l" "a" and "b".
                    - This type of pixel represents the Lab color space.
                    - num == 3
                    - has_alpha == false
                    - basic_pixel_type == unsigned char
                    - min() == 0
                    - max() == 255
                    - is_unsigned == true
                - else
                    - grayscale == true
                    - This type of pixel represents a grayscale color space.  T
                      will be some kind of basic scalar type such as unsigned int.
                    - num == 1
                    - has_alpha == false
                    - basic_pixel_type == T
                    - min() == the minimum obtainable value of objects of type T
                    - max() == the maximum obtainable value of objects of type T
                    - is_unsigned is true if min() == 0 and false otherwise
        !*/

    // ----------------------------------------------------------------------------------------

        struct rgb_pixel
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is a simple struct that represents an RGB colored graphical pixel.
            !*/

            rgb_pixel (
            ) {}

            rgb_pixel (
                unsigned char red_,
                unsigned char green_,
                unsigned char blue_
            ) : red(red_), green(green_), blue(blue_) {}

            unsigned char red;
            unsigned char green;
            unsigned char blue;
        };

    // ----------------------------------------------------------------------------------------

        struct bgr_pixel
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is a simple struct that represents an BGR colored graphical pixel.
                    (the reason it exists in addition to the rgb_pixel is so you can lay
                    it down on top of a memory region that organizes its color data in the
                    BGR format and still be able to read it)
            !*/

            bgr_pixel (
            ) {}

            bgr_pixel (
                unsigned char blue_,
                unsigned char green_,
                unsigned char red_
            ) : blue(blue_), green(green_), red(red_) {}

            unsigned char blue;
            unsigned char green;
            unsigned char red;
        };

    // ----------------------------------------------------------------------------------------

        struct rgb_alpha_pixel
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is a simple struct that represents an RGB colored graphical pixel
                    with an alpha channel.
            !*/

            rgb_alpha_pixel (
            ) {}

            rgb_alpha_pixel (
                unsigned char red_,
                unsigned char green_,
                unsigned char blue_,
                unsigned char alpha_
            ) : red(red_), green(green_), blue(blue_), alpha(alpha_) {}

            unsigned char red;
            unsigned char green;
            unsigned char blue;
            unsigned char alpha;
        };

    // ----------------------------------------------------------------------------------------

        struct hsi_pixel
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is a simple struct that represents an HSI colored graphical pixel.
            !*/

            hsi_pixel (
            ) {}

            hsi_pixel (
                unsigned char h_,
                unsigned char s_,
                unsigned char i_
            ) : h(h_), s(s_), i(i_) {}

            unsigned char h;
            unsigned char s;
            unsigned char i;
        };
        // ----------------------------------------------------------------------------------------

        struct lab_pixel
        {
            /*!
                WHAT THIS OBJECT REPRESENTS
                    This is a simple struct that represents an Lab colored graphical pixel.
            !*/

            lab_pixel (
            ) {}

            lab_pixel (
                    unsigned char l_,
                    unsigned char a_,
                    unsigned char b_
            ) : l(l_), a(a_), b(b_) {}

            unsigned char l;
            unsigned char a;
            unsigned char b;
        };

    // ----------------------------------------------------------------------------------------

        template <
            typename P1,
            typename P2
            >
        inline void assign_pixel (
            P1& dest,
            const P2& src
        );
        /*!
            requires
                - pixel_traits<P1> must be defined
                - pixel_traits<P2> must be defined
            ensures
                - if (P1 and P2 are the same type of pixel) then
                    - simply copies the value of src into dest.  In other words,
                      dest will be identical to src after this function returns.
                - else if (P1 and P2 are not the same type of pixel) then
                    - assigns pixel src to pixel dest and does any necessary color space
                      conversions.
                    - When converting from a grayscale color space with more than 255 values the
                      pixel intensity is saturated at pixel_traits<P1>::max() or pixel_traits<P1>::min()
                      as appropriate.
                    - if (the dest pixel has an alpha channel and the src pixel doesn't) then
                        - #dest.alpha == 255
                    - else if (the src pixel has an alpha channel but the dest pixel doesn't) then
                        - #dest == the original dest value blended with the src value according
                          to the alpha channel in src.
                          (i.e.  #dest == src*(alpha/255) + dest*(1-alpha/255))
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            typename P
            >
        inline typename pixel_traits<P>::basic_pixel_type get_pixel_intensity (
            const P& src
        );
        /*!
            requires
                - pixel_traits<P> must be defined
            ensures
                - if (pixel_traits<P>::grayscale == true) then
                    - returns src
                - else
                    - converts src to grayscale and returns the resulting value.
        !*/

    // ----------------------------------------------------------------------------------------

        template <
            typename P,
            typename T
            >
        inline void assign_pixel_intensity (
            P& dest,
            const T& new_intensity
        );
        /*!
            requires
                - pixel_traits<P> must be defined
                - pixel_traits<T> must be defined
            ensures
                - This function changes the intensity of the dest pixel. So if the pixel in
                  question is a grayscale pixel then it simply assigns that pixel with the
                  value of get_pixel_intensity(new_intensity).  However, if the pixel is not
                  a grayscale pixel then it converts the pixel to the HSI color space and sets
                  the I channel to the given intensity and then converts this HSI value back to
                  the original pixel's color space.
                - Note that we don't necessarily have #get_pixel_intensity(dest) == get_pixel_intensity(new_intensity)
                  due to vagaries of how converting to and from HSI works out.
                - if (the dest pixel has an alpha channel) then
                    - #dest.alpha == dest.alpha
        !*/

    // ----------------------------------------------------------------------------------------

        inline void serialize (
            const rgb_pixel& item,
            std::ostream& out
        );
        /*!
            provides serialization support for the rgb_pixel struct
        !*/

    // ----------------------------------------------------------------------------------------

        inline void deserialize (
            rgb_pixel& item,
            std::istream& in
        );
        /*!
            provides deserialization support for the rgb_pixel struct
        !*/

    // ----------------------------------------------------------------------------------------

        inline void serialize (
            const bgr_pixel& item,
            std::ostream& out
        );
        /*!
            provides serialization support for the bgr_pixel struct
        !*/

    // ----------------------------------------------------------------------------------------

        inline void deserialize (
            bgr_pixel& item,
            std::istream& in
        );
        /*!
            provides deserialization support for the bgr_pixel struct
        !*/

    // ----------------------------------------------------------------------------------------

        inline void serialize (
            const rgb_alpha_pixel& item,
            std::ostream& out
        );
        /*!
            provides serialization support for the rgb_alpha_pixel struct
        !*/

    // ----------------------------------------------------------------------------------------

        inline void deserialize (
            rgb_alpha_pixel& item,
            std::istream& in
        );
        /*!
            provides deserialization support for the rgb_alpha_pixel struct
        !*/

    // ----------------------------------------------------------------------------------------

        inline void serialize (
            const hsi_pixel& item,
            std::ostream& out
        );
        /*!
            provides serialization support for the hsi_pixel struct
        !*/

    // ----------------------------------------------------------------------------------------

        inline void serialize (
                const lab_pixel& item,
                std::ostream& out
        );
        /*!
            provides serialization support for the lab_pixel struct
        !*/

    // ----------------------------------------------------------------------------------------

        inline void deserialize (
            hsi_pixel& item,
            std::istream& in
        );
        /*!
            provides deserialization support for the hsi_pixel struct
        !*/
    // ----------------------------------------------------------------------------------------

        inline void deserialize (
                lab_pixel& item,
                std::istream& in
        );
        /*!
            provides deserialization support for the lab_pixel struct
        !*/

    // ----------------------------------------------------------------------------------------

        template <>
        struct pixel_traits<rgb_pixel>
        {
            const static bool rgb  = true;
            const static bool rgb_alpha  = false;
            const static bool grayscale = false;
            const static bool hsi = false;
            const static bool lab = false;
            enum {num = 3};
            typedef unsigned char basic_pixel_type;
            static basic_pixel_type min() { return 0;}
            static basic_pixel_type max() { return 255;}
            const static bool is_unsigned = true;
            const static bool has_alpha = false;
        };

    // ----------------------------------------------------------------------------------------

        template <>
        struct pixel_traits<bgr_pixel>
        {
            const static bool rgb  = true;
            const static bool rgb_alpha  = false;
            const static bool grayscale = false;
            const static bool hsi = false;
            const static bool lab = false;
            enum {num = 3};
            typedef unsigned char basic_pixel_type;
            static basic_pixel_type min() { return 0;}
            static basic_pixel_type max() { return 255;}
            const static bool is_unsigned = true;
            const static bool has_alpha = false;
        };

    // ----------------------------------------------------------------------------------------

        template <>
        struct pixel_traits<rgb_alpha_pixel>
        {
            const static bool rgb  = false;
            const static bool rgb_alpha  = true;
            const static bool grayscale = false;
            const static bool hsi = false;
            const static bool lab = false;
            enum {num = 4};
            typedef unsigned char basic_pixel_type;
            static basic_pixel_type min() { return 0;}
            static basic_pixel_type max() { return 255;}
            const static bool is_unsigned = true;
            const static bool has_alpha = true;
        };

    // ----------------------------------------------------------------------------------------

        template <>
        struct pixel_traits<hsi_pixel>
        {
            const static bool rgb  = false;
            const static bool rgb_alpha  = false;
            const static bool grayscale = false;
            const static bool hsi = true;
            const static bool lab = false;
            enum {num = 3};
            typedef unsigned char basic_pixel_type;
            static basic_pixel_type min() { return 0;}
            static basic_pixel_type max() { return 255;}
            const static bool is_unsigned = true;
            const static bool has_alpha = false;
        };

    // ----------------------------------------------------------------------------------------

        template <>
        struct pixel_traits<lab_pixel>
        {
            const static bool rgb  = false;
            const static bool rgb_alpha  = false;
            const static bool grayscale = false;
            const static bool hsi = false;
            const static bool lab = true;
            const static long num = 3;
            typedef unsigned char basic_pixel_type;
            static basic_pixel_type min() { return 0;}
            static basic_pixel_type max() { return 255;}
            const static bool is_unsigned = true;
            const static bool has_alpha = false;
        };

    // ----------------------------------------------------------------------------------------

        template <typename T>
        struct grayscale_pixel_traits
        {
            const static bool rgb  = false;
            const static bool rgb_alpha  = false;
            const static bool grayscale = true;
            const static bool hsi = false;
            const static bool lab = false;
            enum {num = 1};
            const static bool has_alpha = false;
            typedef T basic_pixel_type;
            static basic_pixel_type min() { return std::numeric_limits<T>::min();}
            static basic_pixel_type max() { return std::numeric_limits<T>::max();}
            const static bool is_unsigned = is_unsigned_type<T>::value;
        };

        template <> struct pixel_traits<unsigned char>  : public grayscale_pixel_traits<unsigned char> {};
        template <> struct pixel_traits<unsigned short> : public grayscale_pixel_traits<unsigned short> {};
        template <> struct pixel_traits<unsigned int>   : public grayscale_pixel_traits<unsigned int> {};
        template <> struct pixel_traits<unsigned long>  : public grayscale_pixel_traits<unsigned long> {};

        template <> struct pixel_traits<char>           : public grayscale_pixel_traits<char> {};
        template <> struct pixel_traits<signed char>    : public grayscale_pixel_traits<signed char> {};
        template <> struct pixel_traits<short>          : public grayscale_pixel_traits<short> {};
        template <> struct pixel_traits<int>            : public grayscale_pixel_traits<int> {};
        template <> struct pixel_traits<long>           : public grayscale_pixel_traits<long> {};

        template <> struct pixel_traits<int64>          : public grayscale_pixel_traits<int64> {};
        template <> struct pixel_traits<uint64>         : public grayscale_pixel_traits<uint64> {};

    // ----------------------------------------------------------------------------------------

        template <typename T>
        struct float_grayscale_pixel_traits
        {
            const static bool rgb  = false;
            const static bool rgb_alpha  = false;
            const static bool grayscale = true;
            const static bool hsi = false;
            const static bool lab = false;
            enum {num = 1};
            const static bool has_alpha = false;
            typedef T basic_pixel_type;
            static basic_pixel_type min() { return -std::numeric_limits<T>::max();}
            static basic_pixel_type max() { return std::numeric_limits<T>::max();}
            const static bool is_unsigned = false;
        };

        template <> struct pixel_traits<float>          : public float_grayscale_pixel_traits<float> {};
        template <> struct pixel_traits<double>         : public float_grayscale_pixel_traits<double> {};
        template <> struct pixel_traits<long double>    : public float_grayscale_pixel_traits<long double> {};

        // These are here mainly so you can easily copy images into complex arrays.  This is
        // useful when you want to do a FFT on an image or some similar operation.
        template <> struct pixel_traits<std::complex<float> > :       public float_grayscale_pixel_traits<float> {};
        template <> struct pixel_traits<std::complex<double> > :      public float_grayscale_pixel_traits<double> {};
        template <> struct pixel_traits<std::complex<long double> > : public float_grayscale_pixel_traits<long double> {};

    // ----------------------------------------------------------------------------------------

        // The following is a bunch of conversion stuff for the assign_pixel function.

        namespace assign_pixel_helpers
        {

        // -----------------------------
            // all the same kind

            template < typename P >
            typename enable_if_c<pixel_traits<P>::grayscale>::type
            assign(P& dest, const P& src)
            {
                dest = src;
            }

        // -----------------------------

            template <typename T>
            typename unsigned_type<T>::type make_unsigned (
                const T& val
            ) { return static_cast<typename unsigned_type<T>::type>(val); }

            inline float make_unsigned(const float& val) { return val; }
            inline double make_unsigned(const double& val) { return val; }
            inline long double make_unsigned(const long double& val) { return val; }

            template <typename T, typename P>
            typename enable_if_c<pixel_traits<T>::is_unsigned == pixel_traits<P>::is_unsigned, bool>::type less_or_equal_to_max (
                const P& p
            )
            /*!
                ensures
                    - returns true if p is <= max value of T
            !*/
            {
                return p <= pixel_traits<T>::max();
            }

            template <typename T, typename P>
            typename enable_if_c<pixel_traits<T>::is_unsigned && !pixel_traits<P>::is_unsigned, bool>::type less_or_equal_to_max (
                const P& p
            )
            {
                if (p <= 0)
                    return true;
                else if (make_unsigned(p) <= pixel_traits<T>::max())
                    return true;
                else
                    return false;
            }

            template <typename T, typename P>
            typename enable_if_c<!pixel_traits<T>::is_unsigned && pixel_traits<P>::is_unsigned, bool>::type less_or_equal_to_max (
                const P& p
            )
            {
                return p <= make_unsigned(pixel_traits<T>::max());
            }

        // -----------------------------

            template <typename T, typename P>
            typename enable_if_c<pixel_traits<P>::is_unsigned, bool >::type greater_or_equal_to_min (
                const P&
            ) { return true; }
            /*!
                ensures
                    - returns true if p is >= min value of T
            !*/

            template <typename T, typename P>
            typename enable_if_c<!pixel_traits<P>::is_unsigned && pixel_traits<T>::is_unsigned, bool >::type greater_or_equal_to_min (
                const P& p
            )
            {
                return p >= 0;
            }

            template <typename T, typename P>
            typename enable_if_c<!pixel_traits<P>::is_unsigned && !pixel_traits<T>::is_unsigned, bool >::type greater_or_equal_to_min (
                const P& p
            )
            {
                return p >= pixel_traits<T>::min();
            }
        // -----------------------------

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::grayscale && pixel_traits<P2>::grayscale>::type
            assign(P1& dest, const P2& src)
            {
                /*
                    The reason for these weird comparison functions is to avoid getting compiler
                    warnings about comparing signed types to unsigned and stuff like that.
                */

                if (less_or_equal_to_max<P1>(src))
                    if (greater_or_equal_to_min<P1>(src))
                        dest = static_cast<P1>(src);
                    else
                        dest = pixel_traits<P1>::min();
                else
                    dest = pixel_traits<P1>::max();
            }

        // -----------------------------
        // -----------------------------
        // -----------------------------

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::rgb && pixel_traits<P2>::rgb>::type
            assign(P1& dest, const P2& src)
            {
                dest.red = src.red;
                dest.green = src.green;
                dest.blue = src.blue;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::rgb_alpha && pixel_traits<P2>::rgb_alpha>::type
            assign(P1& dest, const P2& src)
            {
                dest.red = src.red;
                dest.green = src.green;
                dest.blue = src.blue;
                dest.alpha = src.alpha;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::hsi && pixel_traits<P2>::hsi>::type
            assign(P1& dest, const P2& src)
            {
                dest.h = src.h;
                dest.s = src.s;
                dest.i = src.i;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::lab && pixel_traits<P2>::lab>::type
            assign(P1& dest, const P2& src)
            {
                dest.l = src.l;
                dest.a = src.a;
                dest.b = src.b;
            }

        // -----------------------------
            // dest is a grayscale

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::grayscale && pixel_traits<P2>::rgb>::type
            assign(P1& dest, const P2& src)
            {
                const unsigned int temp = ((static_cast<unsigned int>(src.red) +
                                            static_cast<unsigned int>(src.green) +
                                            static_cast<unsigned int>(src.blue))/3);
                assign_pixel(dest, temp);
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::grayscale && pixel_traits<P2>::rgb_alpha>::type
            assign(P1& dest, const P2& src)
            {

                const unsigned char avg = static_cast<unsigned char>((static_cast<unsigned int>(src.red) +
                                                                      static_cast<unsigned int>(src.green) +
                                                                      static_cast<unsigned int>(src.blue))/3);

                if (src.alpha == 255)
                {
                    assign_pixel(dest, avg);
                }
                else
                {
                    // perform this assignment using fixed point arithmetic:
                    // dest = src*(alpha/255) + dest*(1 - alpha/255);
                    // dest = src*(alpha/255) + dest*1 - dest*(alpha/255);
                    // dest = dest*1 + src*(alpha/255) - dest*(alpha/255);
                    // dest = dest*1 + (src - dest)*(alpha/255);
                    // dest += (src - dest)*(alpha/255);

                    int temp = avg;
                    // copy dest into dest_copy using assign_pixel to avoid potential
                    // warnings about implicit float to int warnings.
                    int dest_copy;
                    assign_pixel(dest_copy, dest);

                    temp -= dest_copy;

                    temp *= src.alpha;

                    temp /= 255;

                    assign_pixel(dest, temp+dest_copy);
                }
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::grayscale && pixel_traits<P2>::hsi>::type
            assign(P1& dest, const P2& src)
            {
                assign_pixel(dest, src.i);
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::grayscale && pixel_traits<P2>::lab>::type
            assign(P1& dest, const P2& src)
            {
                assign_pixel(dest, src.l);
            }

        // -----------------------------

            struct HSL
            {
                double h;
                double s;
                double l;
            };

            struct COLOUR
            {
                double r;
                double g;
                double b;
            };

            /*
                I found this excellent bit of code for dealing with HSL spaces at
                http://local.wasp.uwa.edu.au/~pbourke/colour/hsl/
            */
            /*
                Calculate HSL from RGB
                Hue is in degrees
                Lightness is between 0 and 1
                Saturation is between 0 and 1
            */
            inline HSL RGB2HSL(COLOUR c1)
            {
                double themin,themax,delta;
                HSL c2;
                using namespace std;

                themin = std::min(c1.r,std::min(c1.g,c1.b));
                themax = std::max(c1.r,std::max(c1.g,c1.b));
                delta = themax - themin;
                c2.l = (themin + themax) / 2;
                c2.s = 0;
                if (c2.l > 0 && c2.l < 1)
                    c2.s = delta / (c2.l < 0.5 ? (2*c2.l) : (2-2*c2.l));
                c2.h = 0;
                if (delta > 0) {
                    if (themax == c1.r && themax != c1.g)
                        c2.h += (c1.g - c1.b) / delta;
                    if (themax == c1.g && themax != c1.b)
                        c2.h += (2 + (c1.b - c1.r) / delta);
                    if (themax == c1.b && themax != c1.r)
                        c2.h += (4 + (c1.r - c1.g) / delta);
                    c2.h *= 60;
                }
                return(c2);
            }

            /*
                Calculate RGB from HSL, reverse of RGB2HSL()
                Hue is in degrees
                Lightness is between 0 and 1
                Saturation is between 0 and 1
            */
            inline COLOUR HSL2RGB(HSL c1)
            {
                COLOUR c2,sat,ctmp;
                using namespace std;

                if (c1.h < 120) {
                    sat.r = (120 - c1.h) / 60.0;
                    sat.g = c1.h / 60.0;
                    sat.b = 0;
                } else if (c1.h < 240) {
                    sat.r = 0;
                    sat.g = (240 - c1.h) / 60.0;
                    sat.b = (c1.h - 120) / 60.0;
                } else {
                    sat.r = (c1.h - 240) / 60.0;
                    sat.g = 0;
                    sat.b = (360 - c1.h) / 60.0;
                }
                sat.r = std::min(sat.r,1.0);
                sat.g = std::min(sat.g,1.0);
                sat.b = std::min(sat.b,1.0);

                ctmp.r = 2 * c1.s * sat.r + (1 - c1.s);
                ctmp.g = 2 * c1.s * sat.g + (1 - c1.s);
                ctmp.b = 2 * c1.s * sat.b + (1 - c1.s);

                if (c1.l < 0.5) {
                    c2.r = c1.l * ctmp.r;
                    c2.g = c1.l * ctmp.g;
                    c2.b = c1.l * ctmp.b;
                } else {
                    c2.r = (1 - c1.l) * ctmp.r + 2 * c1.l - 1;
                    c2.g = (1 - c1.l) * ctmp.g + 2 * c1.l - 1;
                    c2.b = (1 - c1.l) * ctmp.b + 2 * c1.l - 1;
                }

                return(c2);
            }

            // -----------------------------

            struct Lab
            {
                double l;
                double a;
                double b;
            };
            /*
                Calculate Lab from RGB
                L is between 0 and 100
                a is between -128 and 127
                b is between -128 and 127
                RGB is between 0.0 and 1.0
            */
            inline Lab RGB2Lab(COLOUR c1)
            {
                Lab c2;
                using namespace std;

                double var_R = c1.r;
                double var_G = c1.g;
                double var_B = c1.b;

                if (var_R > 0.04045) {
                    var_R = pow(((var_R + 0.055) / 1.055), 2.4);
                } else {
                    var_R = var_R / 12.92;
                }

                if (var_G > 0.04045) {
                    var_G = pow(((var_G + 0.055) / 1.055), 2.4);
                } else {
                    var_G = var_G / 12.92;
                }

                if (var_B > 0.04045) {
                    var_B = pow(((var_B + 0.055) / 1.055), 2.4);
                } else {
                    var_B = var_B / 12.92;
                }

                var_R = var_R * 100;
                var_G = var_G * 100;
                var_B = var_B * 100;

    //Observer. = 2°, Illuminant = D65
                double X = var_R * 0.4124 + var_G * 0.3576 + var_B * 0.1805;
                double Y = var_R * 0.2126 + var_G * 0.7152 + var_B * 0.0722;
                double Z = var_R * 0.0193 + var_G * 0.1192 + var_B * 0.9505;

                double var_X = X / 95.047;
                double var_Y = Y / 100.000;
                double var_Z = Z / 108.883;

                if (var_X > 0.008856) {
                    var_X = pow(var_X, (1.0 / 3));
                }
                else {
                    var_X = (7.787 * var_X) + (16.0 / 116);
                }

                if (var_Y > 0.008856) {
                    var_Y = pow(var_Y, (1.0 / 3));
                }
                else {
                    var_Y = (7.787 * var_Y) + (16.0 / 116);
                }

                if (var_Z > 0.008856) {
                    var_Z = pow(var_Z, (1.0 / 3));
                }
                else {
                    var_Z = (7.787 * var_Z) + (16.0 / 116);
                }

                //clamping
                c2.l = max(0.0, (116.0 * var_Y) - 16);
                c2.a = max(-128.0, min(127.0, 500.0 * (var_X - var_Y)));
                c2.b = max(-128.0, min(127.0, 200.0 * (var_Y - var_Z)));

                return c2;
            }

            /*
                Calculate RGB from Lab, reverse of RGB2LAb()
                L is between 0 and 100
                a is between -128 and 127
                b is between -128 and 127
                RGB is between 0.0 and 1.0
            */
            inline COLOUR Lab2RGB(Lab c1) {
                COLOUR c2;
                using namespace std;

                double var_Y = (c1.l + 16) / 116.0;
                double var_X = (c1.a / 500.0) + var_Y;
                double var_Z = var_Y - (c1.b / 200);

                if (pow(var_Y, 3) > 0.008856) {
                    var_Y = pow(var_Y, 3);
                } else {
                    var_Y = (var_Y - 16.0 / 116) / 7.787;
                }

                if (pow(var_X, 3) > 0.008856) {
                    var_X = pow(var_X, 3);
                } else {
                    var_X = (var_X - 16.0 / 116) / 7.787;
                }

                if (pow(var_Z, 3) > 0.008856) {
                    var_Z = pow(var_Z, 3);
                } else {
                    var_Z = (var_Z - 16.0 / 116) / 7.787;
                }

                double X = var_X * 95.047;
                double Y = var_Y * 100.000;
                double Z = var_Z * 108.883;

                var_X = X / 100.0;
                var_Y = Y / 100.0;
                var_Z = Z / 100.0;

                double var_R = var_X * 3.2406 + var_Y * -1.5372 + var_Z * -0.4986;
                double var_G = var_X * -0.9689 + var_Y * 1.8758 + var_Z * 0.0415;
                double var_B = var_X * 0.0557 + var_Y * -0.2040 + var_Z * 1.0570;

                if (var_R > 0.0031308) {
                    var_R = 1.055 * pow(var_R, (1 / 2.4)) - 0.055;
                } else {
                    var_R = 12.92 * var_R;
                }

                if (var_G > 0.0031308) {
                    var_G = 1.055 * pow(var_G, (1 / 2.4)) - 0.055;
                } else {
                    var_G = 12.92 * var_G;
                }

                if (var_B > 0.0031308) {
                    var_B = 1.055 * pow(var_B, (1 / 2.4)) - 0.055;
                } else {
                    var_B = 12.92 * var_B;
                }

                // clamping
                c2.r = max(0.0, min(1.0, var_R));
                c2.g = max(0.0, min(1.0, var_G));
                c2.b = max(0.0, min(1.0, var_B));

                return (c2);
            }

        // -----------------------------
            // dest is a color rgb_pixel

            template < typename P1 >
            typename enable_if_c<pixel_traits<P1>::rgb>::type
            assign(P1& dest, const unsigned char& src)
            {
                dest.red = src;
                dest.green = src;
                dest.blue = src;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::rgb && pixel_traits<P2>::grayscale>::type
            assign(P1& dest, const P2& src)
            {
                unsigned char p;
                assign_pixel(p, src);
                dest.red = p;
                dest.green = p;
                dest.blue = p;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::rgb && pixel_traits<P2>::rgb_alpha>::type
            assign(P1& dest, const P2& src)
            {
                if (src.alpha == 255)
                {
                    dest.red = src.red;
                    dest.green = src.green;
                    dest.blue = src.blue;
                }
                else
                {
                    // perform this assignment using fixed point arithmetic:
                    // dest = src*(alpha/255) + dest*(1 - alpha/255);
                    // dest = src*(alpha/255) + dest*1 - dest*(alpha/255);
                    // dest = dest*1 + src*(alpha/255) - dest*(alpha/255);
                    // dest = dest*1 + (src - dest)*(alpha/255);
                    // dest += (src - dest)*(alpha/255);

                    unsigned int temp_r = src.red;
                    unsigned int temp_g = src.green;
                    unsigned int temp_b = src.blue;

                    temp_r -= dest.red;
                    temp_g -= dest.green;
                    temp_b -= dest.blue;

                    temp_r *= src.alpha;
                    temp_g *= src.alpha;
                    temp_b *= src.alpha;

                    temp_r >>= 8;
                    temp_g >>= 8;
                    temp_b >>= 8;

                    dest.red += static_cast<unsigned char>(temp_r&0xFF);
                    dest.green += static_cast<unsigned char>(temp_g&0xFF);
                    dest.blue += static_cast<unsigned char>(temp_b&0xFF);
                }
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::rgb && pixel_traits<P2>::hsi>::type
            assign(P1& dest, const P2& src)
            {
                COLOUR c;
                HSL h;
                h.h = src.h;
                h.h = h.h/255.0*360;
                h.s = src.s/255.0;
                h.l = src.i/255.0;
                c = HSL2RGB(h);

                dest.red = static_cast<unsigned char>(c.r*255.0 + 0.5);
                dest.green = static_cast<unsigned char>(c.g*255.0 + 0.5);
                dest.blue = static_cast<unsigned char>(c.b*255.0 + 0.5);
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::rgb && pixel_traits<P2>::lab>::type
            assign(P1& dest, const P2& src)
            {
                COLOUR c;
                Lab l;
                l.l = (src.l/255.0)*100;
                l.a = (src.a-128.0);
                l.b = (src.b-128.0);
                c = Lab2RGB(l);

                dest.red = static_cast<unsigned char>(c.r*255.0 + 0.5);
                dest.green = static_cast<unsigned char>(c.g*255.0 + 0.5);
                dest.blue = static_cast<unsigned char>(c.b*255.0 + 0.5);
            }

        // -----------------------------
        // dest is a color rgb_alpha_pixel

            template < typename P1 >
            typename enable_if_c<pixel_traits<P1>::rgb_alpha>::type
            assign(P1& dest, const unsigned char& src)
            {
                dest.red = src;
                dest.green = src;
                dest.blue = src;
                dest.alpha = 255;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::rgb_alpha && pixel_traits<P2>::grayscale>::type
            assign(P1& dest, const P2& src)
            {
                unsigned char p;
                assign_pixel(p, src);

                dest.red = p;
                dest.green = p;
                dest.blue = p;
                dest.alpha = 255;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::rgb_alpha && pixel_traits<P2>::rgb>::type
            assign(P1& dest, const P2& src)
            {
                dest.red = src.red;
                dest.green = src.green;
                dest.blue = src.blue;
                dest.alpha = 255;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::rgb_alpha && pixel_traits<P2>::hsi>::type
            assign(P1& dest, const P2& src)
            {
                COLOUR c;
                HSL h;
                h.h = src.h;
                h.h = h.h/255.0*360;
                h.s = src.s/255.0;
                h.l = src.i/255.0;
                c = HSL2RGB(h);

                dest.red = static_cast<unsigned char>(c.r*255.0 + 0.5);
                dest.green = static_cast<unsigned char>(c.g*255.0 + 0.5);
                dest.blue = static_cast<unsigned char>(c.b*255.0 + 0.5);
                dest.alpha = 255;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::rgb_alpha && pixel_traits<P2>::lab>::type
            assign(P1& dest, const P2& src)
            {
                COLOUR c;
                Lab l;
                l.l = (src.l/255.0)*100;
                l.a = (src.a-128.0);
                l.b = (src.b-128.0);
                c = Lab2RGB(l);

                dest.red = static_cast<unsigned char>(c.r * 255 + 0.5);
                dest.green = static_cast<unsigned char>(c.g * 255 + 0.5);
                dest.blue = static_cast<unsigned char>(c.b * 255 + 0.5);
                dest.alpha = 255;
            }
        // -----------------------------
            // dest is an hsi pixel

            template < typename P1>
            typename enable_if_c<pixel_traits<P1>::hsi>::type
            assign(P1& dest, const unsigned char& src)
            {
                dest.h = 0;
                dest.s = 0;
                dest.i = src;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::hsi && pixel_traits<P2>::grayscale>::type
            assign(P1& dest, const P2& src)
            {
                dest.h = 0;
                dest.s = 0;
                assign_pixel(dest.i, src);
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::hsi && pixel_traits<P2>::rgb>::type
            assign(P1& dest, const P2& src)
            {
                COLOUR c1;
                HSL c2;
                c1.r = src.red/255.0;
                c1.g = src.green/255.0;
                c1.b = src.blue/255.0;
                c2 = RGB2HSL(c1);

                dest.h = static_cast<unsigned char>(c2.h/360.0*255.0 + 0.5);
                dest.s = static_cast<unsigned char>(c2.s*255.0 + 0.5);
                dest.i = static_cast<unsigned char>(c2.l*255.0 + 0.5);
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::hsi && pixel_traits<P2>::rgb_alpha>::type
            assign(P1& dest, const P2& src)
            {
                rgb_pixel temp;
                // convert target hsi pixel to rgb
                assign_pixel_helpers::assign(temp,dest);

                // now assign the rgb_alpha value to our temp rgb pixel
                assign_pixel_helpers::assign(temp,src);

                // now we can just go assign the new rgb value to the
                // hsi pixel
                assign_pixel_helpers::assign(dest,temp);
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::hsi && pixel_traits<P2>::lab>::type
            assign(P1& dest, const P2& src)
            {
                rgb_pixel temp;
                // convert lab value to our temp rgb pixel
                assign_pixel_helpers::assign(temp,src);
                // now we can just go assign the new rgb value to the
                // hsi pixel
                assign_pixel_helpers::assign(dest,temp);
            }

        // -----------------------------
            // dest is an lab pixel
            template < typename P1>
            typename enable_if_c<pixel_traits<P1>::lab>::type
            assign(P1& dest, const unsigned char& src)
            {
                dest.a = 128;
                dest.b = 128;
                dest.l = src;
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::lab && pixel_traits<P2>::grayscale>::type
            assign(P1& dest, const P2& src)
            {
                dest.a = 128;
                dest.b = 128;
                assign_pixel(dest.l, src);
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::lab && pixel_traits<P2>::rgb>::type
            assign(P1& dest, const P2& src)
            {
                COLOUR c1;
                Lab c2;
                c1.r = src.red / 255.0;
                c1.g = src.green / 255.0;
                c1.b = src.blue / 255.0;
                c2 = RGB2Lab(c1);

                dest.l = static_cast<unsigned char>((c2.l / 100) * 255 + 0.5);
                dest.a = static_cast<unsigned char>(c2.a + 128 + 0.5);
                dest.b = static_cast<unsigned char>(c2.b + 128 + 0.5);
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::lab && pixel_traits<P2>::rgb_alpha>::type
            assign(P1& dest, const P2& src)
            {
                rgb_pixel temp;
                // convert target lab pixel to rgb
                assign_pixel_helpers::assign(temp,dest);

                // now assign the rgb_alpha value to our temp rgb pixel
                assign_pixel_helpers::assign(temp,src);

                // now we can just go assign the new rgb value to the
                // lab pixel
                assign_pixel_helpers::assign(dest,temp);
            }

            template < typename P1, typename P2 >
            typename enable_if_c<pixel_traits<P1>::lab && pixel_traits<P2>::hsi>::type
            assign(P1& dest, const P2& src)
            {
                rgb_pixel temp;

                // convert hsi value to our temp rgb pixel
                assign_pixel_helpers::assign(temp,src);

                // now we can just go assign the new rgb value to the
                // lab pixel
                assign_pixel_helpers::assign(dest,temp);
            }
        }

        // -----------------------------

        template < typename P1, typename P2 >
        inline void assign_pixel (
            P1& dest,
            const P2& src
        ) { assign_pixel_helpers::assign(dest,src); }

    // ----------------------------------------------------------------------------------------

        template <
            typename P,
            typename T
            >
        inline typename enable_if_c<pixel_traits<P>::grayscale>::type assign_pixel_intensity_helper (
            P& dest,
            const T& new_intensity
        )
        {
            assign_pixel(dest, new_intensity);
        }

        template <
            typename P,
            typename T
            >
        inline typename enable_if_c<pixel_traits<P>::grayscale == false &&
                                    pixel_traits<P>::has_alpha>::type assign_pixel_intensity_helper (
            P& dest,
            const T& new_intensity
        )
        {
            hsi_pixel p;
            const unsigned long old_alpha = dest.alpha;
            dest.alpha = 255;
            rgb_pixel temp;
            assign_pixel(temp, dest); // put dest into an rgb_pixel to avoid the somewhat complicated assign_pixel(hsi,rgb_alpha).
            assign_pixel(p,temp);
            assign_pixel(p.i, new_intensity);
            assign_pixel(dest,p);
            dest.alpha = old_alpha;
        }

        template <
            typename P,
            typename T
            >
        inline typename enable_if_c<pixel_traits<P>::grayscale == false &&
                                    pixel_traits<P>::has_alpha == false>::type assign_pixel_intensity_helper (
            P& dest,
            const T& new_intensity
        )
        {
            hsi_pixel p;
            assign_pixel(p,dest);
            assign_pixel(p.i, new_intensity);
            assign_pixel(dest,p);
        }

        template <
            typename P,
            typename T
            >
        inline void assign_pixel_intensity (
            P& dest,
            const T& new_intensity
        )
        {
            assign_pixel_intensity_helper(dest, new_intensity);
        }

    // ----------------------------------------------------------------------------------------

        template <
            typename P
            >
        inline typename enable_if_c<pixel_traits<P>::grayscale, P>::type get_pixel_intensity_helper (
            const P& src
        )
        {
            return src;
        }

        template <
            typename P
            >
        inline typename enable_if_c<pixel_traits<P>::grayscale == false&&
                                    pixel_traits<P>::has_alpha,
                                    typename pixel_traits<P>::basic_pixel_type>::type get_pixel_intensity_helper (
            const P& src
        )
        {
            P temp = src;
            temp.alpha = 255;
            typename pixel_traits<P>::basic_pixel_type p;
            assign_pixel(p,temp);
            return p;
        }

        template <
            typename P
            >
        inline typename enable_if_c<pixel_traits<P>::grayscale == false&&
                                    pixel_traits<P>::has_alpha == false,
                                    typename pixel_traits<P>::basic_pixel_type>::type get_pixel_intensity_helper (
            const P& src
        )
        {
            typename pixel_traits<P>::basic_pixel_type p;
            assign_pixel(p,src);
            return p;
        }

        template <
            typename P
            >
        inline typename pixel_traits<P>::basic_pixel_type get_pixel_intensity (
            const P& src
        )
        {
            return get_pixel_intensity_helper(src);
        }

    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------
    // ----------------------------------------------------------------------------------------

        inline void serialize (
            const rgb_alpha_pixel& item,
            std::ostream& out
        )
        {
            try
            {
                serialize(item.red,out);
                serialize(item.green,out);
                serialize(item.blue,out);
                serialize(item.alpha,out);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while serializing object of type rgb_alpha_pixel");
            }
        }

    // ----------------------------------------------------------------------------------------

        inline void deserialize (
            rgb_alpha_pixel& item,
            std::istream& in
        )
        {
            try
            {
                deserialize(item.red,in);
                deserialize(item.green,in);
                deserialize(item.blue,in);
                deserialize(item.alpha,in);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while deserializing object of type rgb_alpha_pixel");
            }
        }

    // ----------------------------------------------------------------------------------------

        inline void serialize (
            const rgb_pixel& item,
            std::ostream& out
        )
        {
            try
            {
                serialize(item.red,out);
                serialize(item.green,out);
                serialize(item.blue,out);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while serializing object of type rgb_pixel");
            }
        }

    // ----------------------------------------------------------------------------------------

        inline void deserialize (
            rgb_pixel& item,
            std::istream& in
        )
        {
            try
            {
                deserialize(item.red,in);
                deserialize(item.green,in);
                deserialize(item.blue,in);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while deserializing object of type rgb_pixel");
            }
        }

    // ----------------------------------------------------------------------------------------

        inline void serialize (
            const bgr_pixel& item,
            std::ostream& out
        )
        {
            try
            {
                serialize(item.blue,out);
                serialize(item.green,out);
                serialize(item.red,out);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while serializing object of type bgr_pixel");
            }
        }

    // ----------------------------------------------------------------------------------------

        inline void deserialize (
            bgr_pixel& item,
            std::istream& in
        )
        {
            try
            {
                deserialize(item.blue,in);
                deserialize(item.green,in);
                deserialize(item.red,in);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while deserializing object of type bgr_pixel");
            }
        }

    // ----------------------------------------------------------------------------------------

        inline void serialize (
            const hsi_pixel& item,
            std::ostream& out
        )
        {
            try
            {
                serialize(item.h,out);
                serialize(item.s,out);
                serialize(item.i,out);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while serializing object of type hsi_pixel");
            }
        }

    // ----------------------------------------------------------------------------------------

        inline void deserialize (
            hsi_pixel& item,
            std::istream& in
        )
        {
            try
            {
                deserialize(item.h,in);
                deserialize(item.s,in);
                deserialize(item.i,in);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while deserializing object of type hsi_pixel");
            }
        }

    // ----------------------------------------------------------------------------------------

        inline void serialize (
                const lab_pixel& item,
                std::ostream& out
        )
        {
            try
            {
                serialize(item.l,out);
                serialize(item.a,out);
                serialize(item.b,out);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while serializing object of type lab_pixel");
            }
        }

    // ----------------------------------------------------------------------------------------

        inline void deserialize (
                lab_pixel& item,
                std::istream& in
        )
        {
            try
            {
                deserialize(item.l,in);
                deserialize(item.a,in);
                deserialize(item.b,in);
            }
            catch (serialization_error& e)
            {
                throw serialization_error(e.info + "\n   while deserializing object of type lab_pixel");
            }
        }

    // ----------------------------------------------------------------------------------------

    }

    #endif // DLIB_PIXEl_