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

    #include "../pixel.h"
    #include "spatial_filtering_abstract.h"
    #include "../algs.h"
    #include "../assert.h"
    #include "../array2d.h"
    #include "../matrix.h"
    #include "../geometry/border_enumerator.h"
    #include "../simd.h"
    #include <limits>
    #include "assign_image.h"

    namespace dlib
    {

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

        namespace impl
        {
            template <
                typename in_image_type,
                typename out_image_type,
                typename EXP,
                typename T
                >
            rectangle grayscale_spatially_filter_image (
                const in_image_type& in_img_,
                out_image_type& out_img_,
                const matrix_exp<EXP>& filter_,
                T scale,
                bool use_abs,
                bool add_to
            )
            {
                const_temp_matrix<EXP> filter(filter_);
                COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<in_image_type>::pixel_type>::has_alpha == false );
                COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<out_image_type>::pixel_type>::has_alpha == false );

                DLIB_ASSERT(scale != 0 && filter.size() != 0,
                    "\trectangle spatially_filter_image()"
                    << "\n\t You can't give a scale of zero or an empty filter."
                    << "\n\t scale: "<< scale
                    << "\n\t filter.nr(): "<< filter.nr()
                    << "\n\t filter.nc(): "<< filter.nc()
                );
                DLIB_ASSERT(is_same_object(in_img_, out_img_) == false,
                    "\trectangle spatially_filter_image()"
                    << "\n\tYou must give two different image objects"
                );

                const_image_view<in_image_type> in_img(in_img_);
                image_view<out_image_type> out_img(out_img_);

                // if there isn't any input image then don't do anything
                if (in_img.size() == 0)
                {
                    out_img.clear();
                    return rectangle();
                }

                out_img.set_size(in_img.nr(),in_img.nc());

                // figure out the range that we should apply the filter to
                const long first_row = filter.nr()/2;
                const long first_col = filter.nc()/2;
                const long last_row = in_img.nr() - ((filter.nr()-1)/2);
                const long last_col = in_img.nc() - ((filter.nc()-1)/2);

                const rectangle non_border = rectangle(first_col, first_row, last_col-1, last_row-1);
                if (!add_to)
                    zero_border_pixels(out_img_, non_border);

                // apply the filter to the image
                for (long r = first_row; r < last_row; ++r)
                {
                    for (long c = first_col; c < last_col; ++c)
                    {
                        typedef typename EXP::type ptype;
                        ptype p;
                        ptype temp = 0;
                        for (long m = 0; m < filter.nr(); ++m)
                        {
                            for (long n = 0; n < filter.nc(); ++n)
                            {
                                // pull out the current pixel and put it into p
                                p = get_pixel_intensity(in_img[r-first_row+m][c-first_col+n]);
                                temp += p*filter(m,n);
                            }
                        }

                        temp /= scale;

                        if (use_abs && temp < 0)
                        {
                            temp = -temp;
                        }

                        // save this pixel to the output image
                        if (add_to == false)
                        {
                            assign_pixel(out_img[r][c], temp);
                        }
                        else
                        {
                            assign_pixel(out_img[r][c], temp + out_img[r][c]);
                        }
                    }
                }

                return non_border;
            }

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

            template <
                typename in_image_type,
                typename out_image_type,
                typename EXP
                >
            rectangle float_spatially_filter_image (
                const in_image_type& in_img_,
                out_image_type& out_img_,
                const matrix_exp<EXP>& filter_,
                bool add_to
            )
            {

                const_temp_matrix<EXP> filter(filter_);
                DLIB_ASSERT(filter.size() != 0,
                    "\trectangle spatially_filter_image()"
                    << "\n\t You can't give an empty filter."
                    << "\n\t filter.nr(): "<< filter.nr()
                    << "\n\t filter.nc(): "<< filter.nc()
                );
                DLIB_ASSERT(is_same_object(in_img_, out_img_) == false,
                    "\trectangle spatially_filter_image()"
                    << "\n\tYou must give two different image objects"
                );

                const_image_view<in_image_type> in_img(in_img_);
                image_view<out_image_type> out_img(out_img_);

                // if there isn't any input image then don't do anything
                if (in_img.size() == 0)
                {
                    out_img.clear();
                    return rectangle();
                }

                out_img.set_size(in_img.nr(),in_img.nc());

                // figure out the range that we should apply the filter to
                const long first_row = filter.nr()/2;
                const long first_col = filter.nc()/2;
                const long last_row = in_img.nr() - ((filter.nr()-1)/2);
                const long last_col = in_img.nc() - ((filter.nc()-1)/2);

                const rectangle non_border = rectangle(first_col, first_row, last_col-1, last_row-1);
                if (!add_to)
                    zero_border_pixels(out_img_, non_border);

                // apply the filter to the image
                for (long r = first_row; r < last_row; ++r)
                {
                    long c = first_col;
                    for (; c < last_col-7; c+=8)
                    {
                        simd8f p,p2,p3;
                        simd8f temp = 0, temp2=0, temp3=0;
                        for (long m = 0; m < filter.nr(); ++m)
                        {
                            long n = 0;
                            for (; n < filter.nc()-2; n+=3)
                            {
                                // pull out the current pixel and put it into p
                                p.load(&in_img[r-first_row+m][c-first_col+n]);
                                p2.load(&in_img[r-first_row+m][c-first_col+n+1]);
                                p3.load(&in_img[r-first_row+m][c-first_col+n+2]);
                                temp += p*filter(m,n);
                                temp2 += p2*filter(m,n+1);
                                temp3 += p3*filter(m,n+2);
                            }
                            for (; n < filter.nc(); ++n)
                            {
                                // pull out the current pixel and put it into p
                                p.load(&in_img[r-first_row+m][c-first_col+n]);
                                temp += p*filter(m,n);
                            }
                        }
                        temp += temp2+temp3;

                        // save this pixel to the output image
                        if (add_to == false)
                        {
                            temp.store(&out_img[r][c]);
                        }
                        else
                        {
                            p.load(&out_img[r][c]);
                            temp += p;
                            temp.store(&out_img[r][c]);
                        }
                    }
                    for (; c < last_col; ++c)
                    {
                        float p;
                        float temp = 0;
                        for (long m = 0; m < filter.nr(); ++m)
                        {
                            for (long n = 0; n < filter.nc(); ++n)
                            {
                                // pull out the current pixel and put it into p
                                p = in_img[r-first_row+m][c-first_col+n];
                                temp += p*filter(m,n);
                            }
                        }

                        // save this pixel to the output image
                        if (add_to == false)
                        {
                            out_img[r][c] = temp;
                        }
                        else
                        {
                            out_img[r][c] += temp;
                        }
                    }
                }

                return non_border;
            }
        }

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP
            >
        struct is_float_filtering2
        {
            const static bool value = is_same_type<typename image_traits<in_image_type>::pixel_type,float>::value &&
                                      is_same_type<typename image_traits<out_image_type>::pixel_type,float>::value &&
                                      is_same_type<typename EXP::type,float>::value;
        };

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP,
            typename T
            >
        typename enable_if_c<pixel_traits<typename image_traits<out_image_type>::pixel_type>::grayscale &&
                             is_float_filtering2<in_image_type,out_image_type,EXP>::value,rectangle>::type
        spatially_filter_image (
            const in_image_type& in_img,
            out_image_type& out_img,
            const matrix_exp<EXP>& filter,
            T scale,
            bool use_abs = false,
            bool add_to = false
        )
        {
            if (use_abs == false)
            {
                if (scale == 1)
                    return impl::float_spatially_filter_image(in_img, out_img, filter, add_to);
                else
                    return impl::float_spatially_filter_image(in_img, out_img, filter/scale, add_to);
            }
            else
            {
                return impl::grayscale_spatially_filter_image(in_img, out_img, filter, scale, true, add_to);
            }
        }

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP,
            typename T
            >
        typename enable_if_c<pixel_traits<typename image_traits<out_image_type>::pixel_type>::grayscale &&
                             !is_float_filtering2<in_image_type,out_image_type,EXP>::value,rectangle>::type
        spatially_filter_image (
            const in_image_type& in_img,
            out_image_type& out_img,
            const matrix_exp<EXP>& filter,
            T scale,
            bool use_abs = false,
            bool add_to = false
        )
        {
            return impl::grayscale_spatially_filter_image(in_img,out_img,filter,scale,use_abs,add_to);
        }

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP,
            typename T
            >
        typename disable_if_c<pixel_traits<typename image_traits<out_image_type>::pixel_type>::grayscale,rectangle>::type
        spatially_filter_image (
            const in_image_type& in_img_,
            out_image_type& out_img_,
            const matrix_exp<EXP>& filter_,
            T scale
        )
        {
            const_temp_matrix<EXP> filter(filter_);
            COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<in_image_type>::pixel_type>::has_alpha == false );
            COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<out_image_type>::pixel_type>::has_alpha == false );

            DLIB_ASSERT(scale != 0 && filter.size() != 0,
                "\trectangle spatially_filter_image()"
                << "\n\t You can't give a scale of zero or an empty filter."
                << "\n\t scale: "<< scale
                << "\n\t filter.nr(): "<< filter.nr()
                << "\n\t filter.nc(): "<< filter.nc()
                );
            DLIB_ASSERT(is_same_object(in_img_, out_img_) == false,
                "\trectangle spatially_filter_image()"
                << "\n\tYou must give two different image objects"
                );

            const_image_view<in_image_type> in_img(in_img_);
            image_view<out_image_type> out_img(out_img_);

            // if there isn't any input image then don't do anything
            if (in_img.size() == 0)
            {
                out_img.clear();
                return rectangle();
            }

            out_img.set_size(in_img.nr(),in_img.nc());

            // figure out the range that we should apply the filter to
            const long first_row = filter.nr()/2;
            const long first_col = filter.nc()/2;
            const long last_row = in_img.nr() - ((filter.nr()-1)/2);
            const long last_col = in_img.nc() - ((filter.nc()-1)/2);

            const rectangle non_border = rectangle(first_col, first_row, last_col-1, last_row-1);
            zero_border_pixels(out_img, non_border);

            // apply the filter to the image
            for (long r = first_row; r < last_row; ++r)
            {
                for (long c = first_col; c < last_col; ++c)
                {
                    typedef typename image_traits<in_image_type>::pixel_type pixel_type;
                    typedef matrix<typename EXP::type,pixel_traits<pixel_type>::num,1> ptype;
                    ptype p;
                    ptype temp;
                    temp = 0;
                    for (long m = 0; m < filter.nr(); ++m)
                    {
                        for (long n = 0; n < filter.nc(); ++n)
                        {
                            // pull out the current pixel and put it into p
                            p = pixel_to_vector<typename EXP::type>(in_img[r-first_row+m][c-first_col+n]);
                            temp += p*filter(m,n);
                        }
                    }

                    temp /= scale;

                    pixel_type pp;
                    vector_to_pixel(pp, temp);
                    assign_pixel(out_img[r][c], pp);
                }
            }

            return non_border;
        }

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP
            >
        rectangle spatially_filter_image (
            const in_image_type& in_img,
            out_image_type& out_img,
            const matrix_exp<EXP>& filter
        )
        {
            return spatially_filter_image(in_img,out_img,filter,1);
        }

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

        namespace impl
        {
            template <
                typename in_image_type,
                typename out_image_type,
                typename EXP1,
                typename EXP2,
                typename T
                >
            rectangle grayscale_spatially_filter_image_separable (
                const in_image_type& in_img_,
                out_image_type& out_img_,
                const matrix_exp<EXP1>& _row_filter,
                const matrix_exp<EXP2>& _col_filter,
                T scale,
                bool use_abs,
                bool add_to
            )
            {
                const_temp_matrix<EXP1> row_filter(_row_filter);
                const_temp_matrix<EXP2> col_filter(_col_filter);
                COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<in_image_type>::pixel_type>::has_alpha == false );
                COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<out_image_type>::pixel_type>::has_alpha == false );

                DLIB_ASSERT(scale != 0 && row_filter.size() != 0 && col_filter.size() != 0 &&
                    is_vector(row_filter) &&
                    is_vector(col_filter),
                    "\trectangle spatially_filter_image_separable()"
                    << "\n\t Invalid inputs were given to this function."
                    << "\n\t scale: "<< scale
                    << "\n\t row_filter.size(): "<< row_filter.size()
                    << "\n\t col_filter.size(): "<< col_filter.size()
                    << "\n\t is_vector(row_filter): "<< is_vector(row_filter)
                    << "\n\t is_vector(col_filter): "<< is_vector(col_filter)
                );
                DLIB_ASSERT(is_same_object(in_img_, out_img_) == false,
                    "\trectangle spatially_filter_image_separable()"
                    << "\n\tYou must give two different image objects"
                );

                const_image_view<in_image_type> in_img(in_img_);
                image_view<out_image_type> out_img(out_img_);

                // if there isn't any input image then don't do anything
                if (in_img.size() == 0)
                {
                    out_img.clear();
                    return rectangle();
                }

                out_img.set_size(in_img.nr(),in_img.nc());

                // figure out the range that we should apply the filter to
                const long first_row = col_filter.size()/2;
                const long first_col = row_filter.size()/2;
                const long last_row = in_img.nr() - ((col_filter.size()-1)/2);
                const long last_col = in_img.nc() - ((row_filter.size()-1)/2);

                const rectangle non_border = rectangle(first_col, first_row, last_col-1, last_row-1);
                if (!add_to)
                    zero_border_pixels(out_img, non_border);

                typedef typename EXP1::type ptype;

                array2d<ptype> temp_img;
                temp_img.set_size(in_img.nr(), in_img.nc());

                // apply the row filter
                for (long r = 0; r < in_img.nr(); ++r)
                {
                    for (long c = first_col; c < last_col; ++c)
                    {
                        ptype p;
                        ptype temp = 0;
                        for (long n = 0; n < row_filter.size(); ++n)
                        {
                            // pull out the current pixel and put it into p
                            p = get_pixel_intensity(in_img[r][c-first_col+n]);
                            temp += p*row_filter(n);
                        }
                        temp_img[r][c] = temp;
                    }
                }

                // apply the column filter
                for (long r = first_row; r < last_row; ++r)
                {
                    for (long c = first_col; c < last_col; ++c)
                    {
                        ptype temp = 0;
                        for (long m = 0; m < col_filter.size(); ++m)
                        {
                            temp += temp_img[r-first_row+m][c]*col_filter(m);
                        }

                        temp /= scale;

                        if (use_abs && temp < 0)
                        {
                            temp = -temp;
                        }

                        // save this pixel to the output image
                        if (add_to == false)
                        {
                            assign_pixel(out_img[r][c], temp);
                        }
                        else
                        {
                            assign_pixel(out_img[r][c], temp + out_img[r][c]);
                        }
                    }
                }
                return non_border;
            }

        } // namespace impl

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP1,
            typename EXP2
            >
        struct is_float_filtering
        {
            const static bool value = is_same_type<typename image_traits<in_image_type>::pixel_type,float>::value &&
                                      is_same_type<typename image_traits<out_image_type>::pixel_type,float>::value &&
                                      is_same_type<typename EXP1::type,float>::value &&
                                      is_same_type<typename EXP2::type,float>::value;
        };

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

        // This overload is optimized to use SIMD instructions when filtering float images with
        // float filters.
        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP1,
            typename EXP2
            >
        rectangle float_spatially_filter_image_separable (
            const in_image_type& in_img_,
            out_image_type& out_img_,
            const matrix_exp<EXP1>& _row_filter,
            const matrix_exp<EXP2>& _col_filter,
            out_image_type& scratch_,
            bool add_to = false
        )
        {
            // You can only use this function with images and filters containing float
            // variables.
            COMPILE_TIME_ASSERT((is_float_filtering<in_image_type,out_image_type,EXP1,EXP2>::value == true));

            const_temp_matrix<EXP1> row_filter(_row_filter);
            const_temp_matrix<EXP2> col_filter(_col_filter);
            DLIB_ASSERT(row_filter.size() != 0 && col_filter.size() != 0 &&
                is_vector(row_filter) &&
                is_vector(col_filter),
                "\trectangle float_spatially_filter_image_separable()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t row_filter.size(): "<< row_filter.size()
                << "\n\t col_filter.size(): "<< col_filter.size()
                << "\n\t is_vector(row_filter): "<< is_vector(row_filter)
                << "\n\t is_vector(col_filter): "<< is_vector(col_filter)
            );
            DLIB_ASSERT(is_same_object(in_img_, out_img_) == false,
                "\trectangle float_spatially_filter_image_separable()"
                << "\n\tYou must give two different image objects"
            );

            const_image_view<in_image_type> in_img(in_img_);
            image_view<out_image_type> out_img(out_img_);

            // if there isn't any input image then don't do anything
            if (in_img.size() == 0)
            {
                out_img.clear();
                return rectangle();
            }

            out_img.set_size(in_img.nr(),in_img.nc());

            // figure out the range that we should apply the filter to
            const long first_row = col_filter.size()/2;
            const long first_col = row_filter.size()/2;
            const long last_row = in_img.nr() - ((col_filter.size()-1)/2);
            const long last_col = in_img.nc() - ((row_filter.size()-1)/2);

            const rectangle non_border = rectangle(first_col, first_row, last_col-1, last_row-1);
            if (!add_to)
                zero_border_pixels(out_img, non_border);

            image_view<out_image_type> scratch(scratch_);
            scratch.set_size(in_img.nr(), in_img.nc());

            // apply the row filter
            for (long r = 0; r < in_img.nr(); ++r)
            {
                long c = first_col;
                for (; c < last_col-7; c+=8)
                {
                    simd8f p,p2,p3, temp = 0, temp2=0, temp3=0;
                    long n = 0;
                    for (; n < row_filter.size()-2; n+=3)
                    {
                        // pull out the current pixel and put it into p
                        p.load(&in_img[r][c-first_col+n]);
                        p2.load(&in_img[r][c-first_col+n+1]);
                        p3.load(&in_img[r][c-first_col+n+2]);
                        temp += p*row_filter(n);
                        temp2 += p2*row_filter(n+1);
                        temp3 += p3*row_filter(n+2);
                    }
                    for (; n < row_filter.size(); ++n)
                    {
                        // pull out the current pixel and put it into p
                        p.load(&in_img[r][c-first_col+n]);
                        temp += p*row_filter(n);
                    }
                    temp += temp2 + temp3;
                    temp.store(&scratch[r][c]);
                }
                for (; c < last_col; ++c)
                {
                    float p;
                    float temp = 0;
                    for (long n = 0; n < row_filter.size(); ++n)
                    {
                        // pull out the current pixel and put it into p
                        p = in_img[r][c-first_col+n];
                        temp += p*row_filter(n);
                    }
                    scratch[r][c] = temp;
                }
            }

            // apply the column filter
            for (long r = first_row; r < last_row; ++r)
            {
                long c = first_col;
                for (; c < last_col-7; c+=8)
                {
                    simd8f p, p2, p3, temp = 0, temp2 = 0, temp3 = 0;
                    long m = 0;
                    for (; m < col_filter.size()-2; m+=3)
                    {
                        p.load(&scratch[r-first_row+m][c]);
                        p2.load(&scratch[r-first_row+m+1][c]);
                        p3.load(&scratch[r-first_row+m+2][c]);
                        temp += p*col_filter(m);
                        temp2 += p2*col_filter(m+1);
                        temp3 += p3*col_filter(m+2);
                    }
                    for (; m < col_filter.size(); ++m)
                    {
                        p.load(&scratch[r-first_row+m][c]);
                        temp += p*col_filter(m);
                    }
                    temp += temp2+temp3;

                    // save this pixel to the output image
                    if (add_to == false)
                    {
                        temp.store(&out_img[r][c]);
                    }
                    else
                    {
                        p.load(&out_img[r][c]);
                        temp += p;
                        temp.store(&out_img[r][c]);
                    }
                }
                for (; c < last_col; ++c)
                {
                    float temp = 0;
                    for (long m = 0; m < col_filter.size(); ++m)
                    {
                        temp += scratch[r-first_row+m][c]*col_filter(m);
                    }

                    // save this pixel to the output image
                    if (add_to == false)
                    {
                        out_img[r][c] = temp;
                    }
                    else
                    {
                        out_img[r][c] += temp;
                    }
                }
            }
            return non_border;
        }

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP1,
            typename EXP2,
            typename T
            >
        typename enable_if_c<pixel_traits<typename image_traits<out_image_type>::pixel_type>::grayscale &&
                             is_float_filtering<in_image_type,out_image_type,EXP1,EXP2>::value,rectangle>::type
        spatially_filter_image_separable (
            const in_image_type& in_img,
            out_image_type& out_img,
            const matrix_exp<EXP1>& row_filter,
            const matrix_exp<EXP2>& col_filter,
            T scale,
            bool use_abs = false,
            bool add_to = false
        )
        {
            if (use_abs == false)
            {
                out_image_type scratch;
                if (scale == 1)
                    return float_spatially_filter_image_separable(in_img, out_img, row_filter, col_filter, scratch, add_to);
                else
                    return float_spatially_filter_image_separable(in_img, out_img, row_filter/scale, col_filter, scratch,  add_to);
            }
            else
            {
                return impl::grayscale_spatially_filter_image_separable(in_img, out_img, row_filter, col_filter, scale, true, add_to);
            }
        }

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP1,
            typename EXP2,
            typename T
            >
        typename enable_if_c<pixel_traits<typename image_traits<out_image_type>::pixel_type>::grayscale &&
                             !is_float_filtering<in_image_type,out_image_type,EXP1,EXP2>::value,rectangle>::type
        spatially_filter_image_separable (
            const in_image_type& in_img,
            out_image_type& out_img,
            const matrix_exp<EXP1>& row_filter,
            const matrix_exp<EXP2>& col_filter,
            T scale,
            bool use_abs = false,
            bool add_to = false
        )
        {
            return impl::grayscale_spatially_filter_image_separable(in_img,out_img, row_filter, col_filter, scale, use_abs, add_to);
        }

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP1,
            typename EXP2,
            typename T
            >
        typename disable_if_c<pixel_traits<typename image_traits<out_image_type>::pixel_type>::grayscale,rectangle>::type
        spatially_filter_image_separable (
            const in_image_type& in_img_,
            out_image_type& out_img_,
            const matrix_exp<EXP1>& _row_filter,
            const matrix_exp<EXP2>& _col_filter,
            T scale
        )
        {
            const_temp_matrix<EXP1> row_filter(_row_filter);
            const_temp_matrix<EXP2> col_filter(_col_filter);
            COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<in_image_type>::pixel_type>::has_alpha == false );
            COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<out_image_type>::pixel_type>::has_alpha == false );

            DLIB_ASSERT(scale != 0 && row_filter.size() != 0 && col_filter.size() != 0 &&
                        is_vector(row_filter) &&
                        is_vector(col_filter),
                "\trectangle spatially_filter_image_separable()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t scale: "<< scale
                << "\n\t row_filter.size(): "<< row_filter.size()
                << "\n\t col_filter.size(): "<< col_filter.size()
                << "\n\t is_vector(row_filter): "<< is_vector(row_filter)
                << "\n\t is_vector(col_filter): "<< is_vector(col_filter)
                );
            DLIB_ASSERT(is_same_object(in_img_, out_img_) == false,
                "\trectangle spatially_filter_image_separable()"
                << "\n\tYou must give two different image objects"
                );

            const_image_view<in_image_type> in_img(in_img_);
            image_view<out_image_type> out_img(out_img_);

            // if there isn't any input image then don't do anything
            if (in_img.size() == 0)
            {
                out_img.clear();
                return rectangle();
            }

            out_img.set_size(in_img.nr(),in_img.nc());

            // figure out the range that we should apply the filter to
            const long first_row = col_filter.size()/2;
            const long first_col = row_filter.size()/2;
            const long last_row = in_img.nr() - ((col_filter.size()-1)/2);
            const long last_col = in_img.nc() - ((row_filter.size()-1)/2);

            const rectangle non_border = rectangle(first_col, first_row, last_col-1, last_row-1);
            zero_border_pixels(out_img, non_border);

            typedef typename image_traits<in_image_type>::pixel_type pixel_type;
            typedef matrix<typename EXP1::type,pixel_traits<pixel_type>::num,1> ptype;

            array2d<ptype> temp_img;
            temp_img.set_size(in_img.nr(), in_img.nc());

            // apply the row filter
            for (long r = 0; r < in_img.nr(); ++r)
            {
                for (long c = first_col; c < last_col; ++c)
                {
                    ptype p;
                    ptype temp;
                    temp = 0;
                    for (long n = 0; n < row_filter.size(); ++n)
                    {
                        // pull out the current pixel and put it into p
                        p = pixel_to_vector<typename EXP1::type>(in_img[r][c-first_col+n]);
                        temp += p*row_filter(n);
                    }
                    temp_img[r][c] = temp;
                }
            }

            // apply the column filter
            for (long r = first_row; r < last_row; ++r)
            {
                for (long c = first_col; c < last_col; ++c)
                {
                    ptype temp;
                    temp = 0;
                    for (long m = 0; m < col_filter.size(); ++m)
                    {
                        temp += temp_img[r-first_row+m][c]*col_filter(m);
                    }

                    temp /= scale;

                    // save this pixel to the output image
                    pixel_type p;
                    vector_to_pixel(p, temp);
                    assign_pixel(out_img[r][c], p);
                }
            }
            return non_border;
        }

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP1,
            typename EXP2
            >
        rectangle spatially_filter_image_separable (
            const in_image_type& in_img,
            out_image_type& out_img,
            const matrix_exp<EXP1>& row_filter,
            const matrix_exp<EXP2>& col_filter
        )
        {
            return spatially_filter_image_separable(in_img,out_img,row_filter,col_filter,1);
        }

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

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP1,
            typename EXP2,
            typename T
            >
        rectangle spatially_filter_image_separable_down (
            const unsigned long downsample,
            const in_image_type& in_img_,
            out_image_type& out_img_,
            const matrix_exp<EXP1>& row_filter,
            const matrix_exp<EXP2>& col_filter,
            T scale,
            bool use_abs = false,
            bool add_to = false
        )
        {
            COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<in_image_type>::pixel_type>::has_alpha == false );
            COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<out_image_type>::pixel_type>::has_alpha == false );
            COMPILE_TIME_ASSERT( pixel_traits<typename image_traits<out_image_type>::pixel_type>::grayscale == true );

            DLIB_ASSERT(downsample > 0 &&
                        scale != 0 &&
                        row_filter.size()%2 == 1 &&
                        col_filter.size()%2 == 1 &&
                        is_vector(row_filter) &&
                        is_vector(col_filter),
                "\trectangle spatially_filter_image_separable_down()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t downsample: "<< downsample
                << "\n\t scale: "<< scale
                << "\n\t row_filter.size(): "<< row_filter.size()
                << "\n\t col_filter.size(): "<< col_filter.size()
                << "\n\t is_vector(row_filter): "<< is_vector(row_filter)
                << "\n\t is_vector(col_filter): "<< is_vector(col_filter)
                );
            DLIB_ASSERT(is_same_object(in_img_, out_img_) == false,
                "\trectangle spatially_filter_image_separable_down()"
                << "\n\tYou must give two different image objects"
                );

            const_image_view<in_image_type> in_img(in_img_);
            image_view<out_image_type> out_img(out_img_);

            // if there isn't any input image then don't do anything
            if (in_img.size() == 0)
            {
                out_img.clear();
                return rectangle();
            }

            out_img.set_size((long)(std::ceil((double)in_img.nr()/downsample)),
                             (long)(std::ceil((double)in_img.nc()/downsample)));

            const double col_border = std::floor(col_filter.size()/2.0);
            const double row_border = std::floor(row_filter.size()/2.0);

            // figure out the range that we should apply the filter to
            const long first_row = (long)std::ceil(col_border/downsample);
            const long first_col = (long)std::ceil(row_border/downsample);
            const long last_row  = (long)std::ceil((in_img.nr() - col_border)/downsample) - 1;
            const long last_col  = (long)std::ceil((in_img.nc() - row_border)/downsample) - 1;

            // zero border pixels
            const rectangle non_border = rectangle(first_col, first_row, last_col, last_row);
            zero_border_pixels(out_img,non_border);

            typedef typename EXP1::type ptype;

            array2d<ptype> temp_img;
            temp_img.set_size(in_img.nr(), out_img.nc());

            // apply the row filter
            for (long r = 0; r < temp_img.nr(); ++r)
            {
                for (long c = non_border.left(); c <= non_border.right(); ++c)
                {
                    ptype p;
                    ptype temp = 0;
                    for (long n = 0; n < row_filter.size(); ++n)
                    {
                        // pull out the current pixel and put it into p
                        p = get_pixel_intensity(in_img[r][c*downsample-row_filter.size()/2+n]);
                        temp += p*row_filter(n);
                    }
                    temp_img[r][c] = temp;
                }
            }

            // apply the column filter
            for (long r = non_border.top(); r <= non_border.bottom(); ++r)
            {
                for (long c = non_border.left(); c <= non_border.right(); ++c)
                {
                    ptype temp = 0;
                    for (long m = 0; m < col_filter.size(); ++m)
                    {
                        temp += temp_img[r*downsample-col_filter.size()/2+m][c]*col_filter(m);
                    }

                    temp /= scale;

                    if (use_abs && temp < 0)
                    {
                        temp = -temp;
                    }

                    // save this pixel to the output image
                    if (add_to == false)
                    {
                        assign_pixel(out_img[r][c], temp);
                    }
                    else
                    {
                        assign_pixel(out_img[r][c], temp + out_img[r][c]);
                    }
                }
            }

            return non_border;
        }

        template <
            typename in_image_type,
            typename out_image_type,
            typename EXP1,
            typename EXP2
            >
        rectangle spatially_filter_image_separable_down (
            const unsigned long downsample,
            const in_image_type& in_img,
            out_image_type& out_img,
            const matrix_exp<EXP1>& row_filter,
            const matrix_exp<EXP2>& col_filter
        )
        {
            return spatially_filter_image_separable_down(downsample,in_img,out_img,row_filter,col_filter,1);
        }

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

        template <
            long NR,
            long NC,
            typename T,
            typename U,
            typename in_image_type
            >
        inline void separable_3x3_filter_block_grayscale (
            T (&block)[NR][NC],
            const in_image_type& img_,
            const long& r,
            const long& c,
            const U& fe1, // separable filter end
            const U& fm,  // separable filter middle
            const U& fe2 // separable filter end 2
        )
        {
            const_image_view<in_image_type> img(img_);
            // make sure requires clause is not broken
            DLIB_ASSERT(shrink_rect(get_rect(img),1).contains(c,r) &&
                        shrink_rect(get_rect(img),1).contains(c+NC-1,r+NR-1),
                "\t void separable_3x3_filter_block_grayscale()"
                << "\n\t The sub-window doesn't fit inside the given image."
                << "\n\t get_rect(img):       " << get_rect(img)
                << "\n\t (c,r):               " << point(c,r)
                << "\n\t (c+NC-1,r+NR-1): " << point(c+NC-1,r+NR-1)
                );

            T row_filt[NR+2][NC];
            for (long rr = 0; rr < NR+2; ++rr)
            {
                for (long cc = 0; cc < NC; ++cc)
                {
                    row_filt[rr][cc] = get_pixel_intensity(img[r+rr-1][c+cc-1])*fe1 +
                                       get_pixel_intensity(img[r+rr-1][c+cc])*fm +
                                       get_pixel_intensity(img[r+rr-1][c+cc+1])*fe2;
                }
            }

            for (long rr = 0; rr < NR; ++rr)
            {
                for (long cc = 0; cc < NC; ++cc)
                {
                    block[rr][cc] = (row_filt[rr][cc]*fe1 +
                                    row_filt[rr+1][cc]*fm +
                                    row_filt[rr+2][cc]*fe2);
                }
            }

        }

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

        template <
            long NR,
            long NC,
            typename T,
            typename U,
            typename in_image_type
            >
        inline void separable_3x3_filter_block_rgb (
            T (&block)[NR][NC],
            const in_image_type& img_,
            const long& r,
            const long& c,
            const U& fe1, // separable filter end
            const U& fm,  // separable filter middle
            const U& fe2  // separable filter end 2
        )
        {
            const_image_view<in_image_type> img(img_);
            // make sure requires clause is not broken
            DLIB_ASSERT(shrink_rect(get_rect(img),1).contains(c,r) &&
                        shrink_rect(get_rect(img),1).contains(c+NC-1,r+NR-1),
                "\t void separable_3x3_filter_block_rgb()"
                << "\n\t The sub-window doesn't fit inside the given image."
                << "\n\t get_rect(img):       " << get_rect(img)
                << "\n\t (c,r):               " << point(c,r)
                << "\n\t (c+NC-1,r+NR-1): " << point(c+NC-1,r+NR-1)
                );

            T row_filt[NR+2][NC];
            for (long rr = 0; rr < NR+2; ++rr)
            {
                for (long cc = 0; cc < NC; ++cc)
                {
                    row_filt[rr][cc].red   = img[r+rr-1][c+cc-1].red*fe1   + img[r+rr-1][c+cc].red*fm   + img[r+rr-1][c+cc+1].red*fe2;
                    row_filt[rr][cc].green = img[r+rr-1][c+cc-1].green*fe1 + img[r+rr-1][c+cc].green*fm + img[r+rr-1][c+cc+1].green*fe2;
                    row_filt[rr][cc].blue  = img[r+rr-1][c+cc-1].blue*fe1  + img[r+rr-1][c+cc].blue*fm  + img[r+rr-1][c+cc+1].blue*fe2;
                }
            }

            for (long rr = 0; rr < NR; ++rr)
            {
                for (long cc = 0; cc < NC; ++cc)
                {
                    block[rr][cc].red   = row_filt[rr][cc].red*fe1   + row_filt[rr+1][cc].red*fm   + row_filt[rr+2][cc].red*fe2;
                    block[rr][cc].green = row_filt[rr][cc].green*fe1 + row_filt[rr+1][cc].green*fm + row_filt[rr+2][cc].green*fe2;
                    block[rr][cc].blue  = row_filt[rr][cc].blue*fe1  + row_filt[rr+1][cc].blue*fm  + row_filt[rr+2][cc].blue*fe2;
                }
            }

        }

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

        inline double gaussian (
            double x,
            double sigma
        )
        {
            DLIB_ASSERT(sigma > 0,
                "\tdouble gaussian(x)"
                << "\n\t sigma must be bigger than 0"
                << "\n\t sigma: " << sigma
            );
            const double sqrt_2_pi = 2.5066282746310002416123552393401041626930;
            return 1.0/(sigma*sqrt_2_pi) * std::exp( -(x*x)/(2*sigma*sigma));
        }

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

        template <
            typename T
            >
        matrix<T,0,1> create_gaussian_filter (
            double sigma,
            int max_size
        )
        {
            DLIB_ASSERT(sigma > 0 && max_size > 0 && (max_size%2)==1,
                "\t matrix<T,0,1> create_gaussian_filter()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t sigma: " << sigma
                << "\n\t max_size:  " << max_size
            );

            // Adjust the size so that the ratio of the gaussian values isn't huge.
            // This only matters when T is an integer type.  However, we do it for
            // all types so that the behavior of this function is always relatively
            // the same.
            while (gaussian(0,sigma)/gaussian(max_size/2,sigma) > 50)
                --max_size;

            matrix<double,0,1> f(max_size);
            for (long i = 0; i < f.size(); ++i)
            {
                f(i) = gaussian(i-max_size/2, sigma);
            }

            if (is_float_type<T>::value == false)
            {
                f /= f(0);
                return matrix_cast<T>(round(f));
            }
            else
            {
                return matrix_cast<T>(f);
            }
        }

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

        template <
            typename in_image_type,
            typename out_image_type
            >
        rectangle gaussian_blur (
            const in_image_type& in_img,
            out_image_type& out_img,
            double sigma = 1,
            int max_size = 1001
        )
        {
            DLIB_ASSERT(sigma > 0 && max_size > 0 && (max_size%2)==1 &&
                        is_same_object(in_img, out_img) == false,
                "\t void gaussian_blur()"
                << "\n\t Invalid inputs were given to this function."
                << "\n\t sigma: " << sigma
                << "\n\t max_size:  " << max_size
                << "\n\t is_same_object(in_img,out_img): " << is_same_object(in_img,out_img)
            );

            if (sigma < 18)
            {
                typedef typename pixel_traits<typename image_traits<out_image_type>::pixel_type>::basic_pixel_type type;
                typedef typename promote<type>::type ptype;
                const matrix<ptype,0,1>& filt = create_gaussian_filter<ptype>(sigma, max_size);
                ptype scale = sum(filt);
                scale = scale*scale;
                return spatially_filter_image_separable(in_img, out_img, filt, filt, scale);
            }
            else
            {
                // For large sigma we need to use a type with a lot of precision to avoid
                // numerical problems.  So we use double here.
                typedef double ptype;
                const matrix<ptype,0,1>& filt = create_gaussian_filter<ptype>(sigma, max_size);
                ptype scale = sum(filt);
                scale = scale*scale;
                return spatially_filter_image_separable(in_img, out_img, filt, filt, scale);
            }

        }

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

        namespace impl
        {
        template <
            bool add_to,
            typename image_type1,
            typename image_type2
            >
        void sum_filter (
            const image_type1& img_,
            image_type2& out_,
            const rectangle& rect
        )
        {
            const_image_view<image_type1> img(img_);
            image_view<image_type2> out(out_);
            DLIB_ASSERT(img.nr() == out.nr() &&
                        img.nc() == out.nc() &&
                        is_same_object(img_,out_) == false,
                "\t void sum_filter()"
                << "\n\t Invalid arguments given to this function."
                << "\n\t img.nr(): " << img.nr()
                << "\n\t img.nc(): " << img.nc()
                << "\n\t out.nr(): " << out.nr()
                << "\n\t out.nc(): " << out.nc()
                << "\n\t is_same_object(img_,out_): " << is_same_object(img_,out_)
            );

            typedef typename image_traits<image_type1>::pixel_type pixel_type;
            typedef typename promote<pixel_type>::type ptype;

            std::vector<ptype> column_sum;
            column_sum.resize(img.nc() + rect.width(),0);

            const long top    = -1 + rect.top();
            const long bottom = -1 + rect.bottom();
            long left = rect.left()-1;

            // initialize column_sum at row -1
            for (unsigned long j = 0; j < column_sum.size(); ++j)
            {
                rectangle strip(left,top,left,bottom);
                strip = strip.intersect(get_rect(img));
                if (!strip.is_empty())
                {
                    column_sum[j] = sum(matrix_cast<ptype>(subm(mat(img),strip)));
                }

                ++left;
            }

            const rectangle area = get_rect(img);

            // Save width to avoid computing it over and over.
            const long width = rect.width();

            // Now do the bulk of the filtering work.
            for (long r = 0; r < img.nr(); ++r)
            {
                // set to sum at point(-1,r). i.e. should be equal to sum(mat(img), translate_rect(rect, point(-1,r)))
                // We compute it's value in the next loop.
                ptype cur_sum = 0;

                // Update the first part of column_sum since we only work on the c+width part of column_sum
                // in the main loop.
                const long top    = r + rect.top() - 1;
                const long bottom = r + rect.bottom();
                for (long k = 0; k < width; ++k)
                {
                    const long right  = k-width + rect.right();

                    const ptype br_corner = area.contains(right,bottom) ? img[bottom][right] : 0;
                    const ptype tr_corner = area.contains(right,top)    ? img[top][right]    : 0;
                    // update the sum in this column now that we are on the next row
                    column_sum[k] = column_sum[k] + br_corner - tr_corner;
                    cur_sum += column_sum[k];
                }

                for (long c = 0; c < img.nc(); ++c)
                {
                    const long top    = r + rect.top() - 1;
                    const long bottom = r + rect.bottom();
                    const long right  = c + rect.right();

                    const ptype br_corner = area.contains(right,bottom) ? img[bottom][right] : 0;
                    const ptype tr_corner = area.contains(right,top)    ? img[top][right]    : 0;

                    // update the sum in this column now that we are on the next row
                    column_sum[c+width] = column_sum[c+width] + br_corner - tr_corner;

                    // add in the new right side of the rect and subtract the old right side.
                    cur_sum = cur_sum + column_sum[c+width] - column_sum[c];

                    if (add_to)
                        out[r][c] += static_cast<typename image_traits<image_type2>::pixel_type>(cur_sum);
                    else
                        out[r][c] = static_cast<typename image_traits<image_type2>::pixel_type>(cur_sum);
                }
            }
        }
        }

        template <
            typename image_type1,
            typename image_type2
            >
        void sum_filter (
            const image_type1& img,
            image_type2& out,
            const rectangle& rect
        )
        {
            impl::sum_filter<true>(img,out,rect);
        }

        template <
            typename image_type1,
            typename image_type2
            >
        void sum_filter_assign (
            const image_type1& img,
            image_type2& out,
            const rectangle& rect
        )
        {
            set_image_size(out, num_rows(img), num_columns(img));
            impl::sum_filter<false>(img,out,rect);
        }

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

        namespace impl
        {
            template <typename T>
            class fast_deque
            {
            /*
                This is a fast and minimal implementation of std::deque for
                use with the max_filter.

                This object assumes that no more than max_size elements
                will ever be pushed into it at a time.
            */
            public:

                explicit fast_deque(unsigned long max_size)
                {
                    // find a power of two that upper bounds max_size
                    mask = 2;
                    while (mask < max_size)
                        mask *= 2;

                    clear();

                    data.resize(mask);
                    --mask;  // make into bit mask
                }

                void clear()
                {
                    first = 1;
                    last = 0;
                    size = 0;
                }

                bool empty() const
                {
                    return size == 0;
                }

                void pop_back()
                {
                    last = (last-1)&mask;
                    --size;
                }

                void push_back(const T& item)
                {
                    last = (last+1)&mask;
                    ++size;
                    data[last] = item;
                }

                void pop_front()
                {
                    first = (first+1)&mask;
                    --size;
                }

                const T& front() const
                {
                    return data[first];
                }

                const T& back() const
                {
                    return data[last];
                }

            private:

                std::vector<T> data;
                unsigned long mask;
                unsigned long first;
                unsigned long last;
                unsigned long size;
            };
        }

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

        template <
            typename image_type1,
            typename image_type2
            >
        void max_filter (
            image_type1& img_,
            image_type2& out_,
            const long width,
            const long height,
            const typename image_traits<image_type1>::pixel_type& thresh
        )
        {
            image_view<image_type1> img(img_);
            image_view<image_type2> out(out_);
            DLIB_ASSERT( width > 0 &&
                         height > 0 &&
                         out.nr() == img.nr() &&
                         out.nc() == img.nc() &&
                         is_same_object(img_,out_) == false,
                    "\t void max_filter()"
                    << "\n\t Invalid arguments given to this function."
                    << "\n\t img.nr(): " << img.nr()
                    << "\n\t img.nc(): " << img.nc()
                    << "\n\t out.nr(): " << out.nr()
                    << "\n\t out.nc(): " << out.nc()
                    << "\n\t width:    " << width
                    << "\n\t height:   " << height
                    << "\n\t is_same_object(img_,out_): " << is_same_object(img_,out_)
                         );

            typedef typename image_traits<image_type1>::pixel_type pixel_type;

            dlib::impl::fast_deque<std::pair<long,pixel_type> > Q(std::max(width,height));

            const long last_col = std::max(img.nc(), ((width-1)/2));
            const long last_row = std::max(img.nr(), ((height-1)/2));

            // run max filter along rows of img
            for (long r = 0; r < img.nr(); ++r)
            {
                Q.clear();
                for (long c = 0; c < (width-1)/2 && c < img.nc(); ++c)
                {
                    while (!Q.empty() && img[r][c] >= Q.back().second)
                        Q.pop_back();
                    Q.push_back(std::make_pair(c,img[r][c]));
                }

                for (long c = (width-1)/2; c < img.nc(); ++c)
                {
                    while (!Q.empty() && img[r][c] >= Q.back().second)
                        Q.pop_back();
                    while (!Q.empty() && Q.front().first <= c-width)
                        Q.pop_front();
                    Q.push_back(std::make_pair(c,img[r][c]));

                    img[r][c-((width-1)/2)] = Q.front().second;
                }

                for (long c = last_col; c < img.nc() + ((width-1)/2); ++c)
                {
                    while (!Q.empty() && Q.front().first <= c-width)
                        Q.pop_front();

                    img[r][c-((width-1)/2)] = Q.front().second;
                }
            }

            // run max filter along columns of img.  Store result in out.
            for (long cc = 0; cc < img.nc(); ++cc)
            {
                Q.clear();
                for (long rr = 0; rr < (height-1)/2 && rr < img.nr(); ++rr)
                {
                    while (!Q.empty() && img[rr][cc] >= Q.back().second)
                        Q.pop_back();
                    Q.push_back(std::make_pair(rr,img[rr][cc]));
                }

                for (long rr = (height-1)/2; rr < img.nr(); ++rr)
                {
                    while (!Q.empty() && img[rr][cc] >= Q.back().second)
                        Q.pop_back();
                    while (!Q.empty() && Q.front().first <= rr-height)
                        Q.pop_front();
                    Q.push_back(std::make_pair(rr,img[rr][cc]));

                    out[rr-((height-1)/2)][cc] += std::max(Q.front().second, thresh);
                }

                for (long rr = last_row; rr < img.nr() + ((height-1)/2); ++rr)
                {
                    while (!Q.empty() && Q.front().first <= rr-height)
                        Q.pop_front();

                    out[rr-((height-1)/2)][cc] += std::max(Q.front().second, thresh);
                }
            }
        }

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

    }

    #endif // DLIB_SPATIAL_FILTERINg_H_