    // Copyright (C) 2013  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_fHOG_Hh_
    #define DLIB_fHOG_Hh_

    #include "fhog_abstract.h"
    #include "../matrix.h"
    #include "../array2d.h"
    #include "../array.h"
    #include "../geometry.h"
    #include "assign_image.h"
    #include "draw.h"
    #include "interpolation.h"
    #include "../simd/simd4i.h"
    #include "../simd/simd4f.h"

    namespace dlib
    {

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

        namespace impl_fhog
        {
            template <typename image_type>
            inline typename dlib::enable_if_c<pixel_traits<typename image_type::pixel_type>::rgb>::type get_gradient (
                const int r,
                const int c,
                const image_type& img,
                matrix<double,2,1>& grad,
                double& len
            )
            {
                matrix<double,2,1> grad2, grad3;
                // get the red gradient
                grad(0) = (int)img[r][c+1].red-(int)img[r][c-1].red;
                grad(1) = (int)img[r+1][c].red-(int)img[r-1][c].red;
                len = length_squared(grad);

                // get the green gradient
                grad2(0) = (int)img[r][c+1].green-(int)img[r][c-1].green;
                grad2(1) = (int)img[r+1][c].green-(int)img[r-1][c].green;
                double v2 = length_squared(grad2);

                // get the blue gradient
                grad3(0) = (int)img[r][c+1].blue-(int)img[r][c-1].blue;
                grad3(1) = (int)img[r+1][c].blue-(int)img[r-1][c].blue;
                double v3 = length_squared(grad3);

                // pick color with strongest gradient
                if (v2 > len)
                {
                    len = v2;
                    grad = grad2;
                }
                if (v3 > len)
                {
                    len = v3;
                    grad = grad3;
                }
            }

            template <typename image_type>
            inline typename dlib::enable_if_c<pixel_traits<typename image_type::pixel_type>::rgb>::type get_gradient (
                const int r,
                const int c,
                const image_type& img,
                simd4f& grad_x,
                simd4f& grad_y,
                simd4f& len
            )
            {
                simd4i rleft((int)img[r][c-1].red,
                            (int)img[r][c].red,
                            (int)img[r][c+1].red,
                            (int)img[r][c+2].red);
                simd4i rright((int)img[r][c+1].red,
                             (int)img[r][c+2].red,
                             (int)img[r][c+3].red,
                             (int)img[r][c+4].red);
                simd4i rtop((int)img[r-1][c].red,
                           (int)img[r-1][c+1].red,
                           (int)img[r-1][c+2].red,
                           (int)img[r-1][c+3].red);
                simd4i rbottom((int)img[r+1][c].red,
                              (int)img[r+1][c+1].red,
                              (int)img[r+1][c+2].red,
                              (int)img[r+1][c+3].red);

                simd4i gleft((int)img[r][c-1].green,
                            (int)img[r][c].green,
                            (int)img[r][c+1].green,
                            (int)img[r][c+2].green);
                simd4i gright((int)img[r][c+1].green,
                             (int)img[r][c+2].green,
                             (int)img[r][c+3].green,
                             (int)img[r][c+4].green);
                simd4i gtop((int)img[r-1][c].green,
                           (int)img[r-1][c+1].green,
                           (int)img[r-1][c+2].green,
                           (int)img[r-1][c+3].green);
                simd4i gbottom((int)img[r+1][c].green,
                              (int)img[r+1][c+1].green,
                              (int)img[r+1][c+2].green,
                              (int)img[r+1][c+3].green);

                simd4i bleft((int)img[r][c-1].blue,
                            (int)img[r][c].blue,
                            (int)img[r][c+1].blue,
                            (int)img[r][c+2].blue);
                simd4i bright((int)img[r][c+1].blue,
                             (int)img[r][c+2].blue,
                             (int)img[r][c+3].blue,
                             (int)img[r][c+4].blue);
                simd4i btop((int)img[r-1][c].blue,
                           (int)img[r-1][c+1].blue,
                           (int)img[r-1][c+2].blue,
                           (int)img[r-1][c+3].blue);
                simd4i bbottom((int)img[r+1][c].blue,
                              (int)img[r+1][c+1].blue,
                              (int)img[r+1][c+2].blue,
                              (int)img[r+1][c+3].blue);

                simd4i grad_x_red   = rright-rleft;
                simd4i grad_y_red   = rbottom-rtop;
                simd4i grad_x_green = gright-gleft;
                simd4i grad_y_green = gbottom-gtop;
                simd4i grad_x_blue  = bright-bleft;
                simd4i grad_y_blue  = bbottom-btop;

                simd4i rlen = grad_x_red*grad_x_red + grad_y_red*grad_y_red;
                simd4i glen = grad_x_green*grad_x_green + grad_y_green*grad_y_green;
                simd4i blen = grad_x_blue*grad_x_blue + grad_y_blue*grad_y_blue;

                simd4i cmp = rlen>glen;
                simd4i tgrad_x = select(cmp,grad_x_red,grad_x_green);
                simd4i tgrad_y = select(cmp,grad_y_red,grad_y_green);
                simd4i tlen = select(cmp,rlen,glen);

                cmp = tlen>blen;
                grad_x = select(cmp,tgrad_x,grad_x_blue);
                grad_y = select(cmp,tgrad_y,grad_y_blue);
                len = select(cmp,tlen,blen);
            }

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

            template <typename image_type>
            inline typename dlib::disable_if_c<pixel_traits<typename image_type::pixel_type>::rgb>::type get_gradient (
                const int r,
                const int c,
                const image_type& img,
                matrix<double,2,1>& grad,
                double& len
            )
            {
                grad(0) = (int)get_pixel_intensity(img[r][c+1])-(int)get_pixel_intensity(img[r][c-1]);
                grad(1) = (int)get_pixel_intensity(img[r+1][c])-(int)get_pixel_intensity(img[r-1][c]);
                len = length_squared(grad);
            }

            template <typename image_type>
            inline typename dlib::disable_if_c<pixel_traits<typename image_type::pixel_type>::rgb>::type get_gradient (
                int r,
                int c,
                const image_type& img,
                simd4f& grad_x,
                simd4f& grad_y,
                simd4f& len
            )
            {
                simd4i left((int)get_pixel_intensity(img[r][c-1]),
                            (int)get_pixel_intensity(img[r][c]),
                            (int)get_pixel_intensity(img[r][c+1]),
                            (int)get_pixel_intensity(img[r][c+2]));
                simd4i right((int)get_pixel_intensity(img[r][c+1]),
                             (int)get_pixel_intensity(img[r][c+2]),
                             (int)get_pixel_intensity(img[r][c+3]),
                             (int)get_pixel_intensity(img[r][c+4]));

                simd4i top((int)get_pixel_intensity(img[r-1][c]),
                           (int)get_pixel_intensity(img[r-1][c+1]),
                           (int)get_pixel_intensity(img[r-1][c+2]),
                           (int)get_pixel_intensity(img[r-1][c+3]));
                simd4i bottom((int)get_pixel_intensity(img[r+1][c]),
                              (int)get_pixel_intensity(img[r+1][c+1]),
                              (int)get_pixel_intensity(img[r+1][c+2]),
                              (int)get_pixel_intensity(img[r+1][c+3]));

                grad_x = right-left;
                grad_y = bottom-top;

                len = (grad_x*grad_x + grad_y*grad_y);
            }

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

            template <typename T, typename mm1, typename mm2>
            inline void set_hog (
                dlib::array<array2d<T,mm1>,mm2>& hog,
                int o,
                int x,
                int y,
                const double& value
            )
            {
                hog[o][y][x] = value;
            }

            template <typename T, typename mm1, typename mm2>
            void init_hog (
                dlib::array<array2d<T,mm1>,mm2>& hog,
                int hog_nr,
                int hog_nc,
                int filter_rows_padding,
                int filter_cols_padding
            )
            {
                const int num_hog_bands = 27+4;
                hog.resize(num_hog_bands);
                for (int i = 0; i < num_hog_bands; ++i)
                {
                    hog[i].set_size(hog_nr+filter_rows_padding-1, hog_nc+filter_cols_padding-1);
                    rectangle rect = get_rect(hog[i]);
                    rect.top() +=   (filter_rows_padding-1)/2;
                    rect.left() +=  (filter_cols_padding-1)/2;
                    rect.right() -= filter_cols_padding/2;
                    rect.bottom() -= filter_rows_padding/2;
                    zero_border_pixels(hog[i],rect);
                }
            }

            template <typename T, typename mm1, typename mm2>
            void init_hog_zero_everything (
                dlib::array<array2d<T,mm1>,mm2>& hog,
                int hog_nr,
                int hog_nc,
                int filter_rows_padding,
                int filter_cols_padding
            )
            {
                const int num_hog_bands = 27+4;
                hog.resize(num_hog_bands);
                for (int i = 0; i < num_hog_bands; ++i)
                {
                    hog[i].set_size(hog_nr+filter_rows_padding-1, hog_nc+filter_cols_padding-1);
                    assign_all_pixels(hog[i], 0);
                }
            }

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

            template <typename T, typename mm>
            inline void set_hog (
                array2d<matrix<T,31,1>,mm>& hog,
                int o,
                int x,
                int y,
                const double& value
            )
            {
                hog[y][x](o) = value;
            }

            template <typename T, typename mm>
            void init_hog (
                array2d<matrix<T,31,1>,mm>& hog,
                int hog_nr,
                int hog_nc,
                int filter_rows_padding,
                int filter_cols_padding
            )
            {
                hog.set_size(hog_nr+filter_rows_padding-1, hog_nc+filter_cols_padding-1);

                // now zero out the border region
                rectangle rect = get_rect(hog);
                rect.top() +=   (filter_rows_padding-1)/2;
                rect.left() +=  (filter_cols_padding-1)/2;
                rect.right() -= filter_cols_padding/2;
                rect.bottom() -= filter_rows_padding/2;
                border_enumerator be(get_rect(hog),rect);
                while (be.move_next())
                {
                    const point p = be.element();
                    set_all_elements(hog[p.y()][p.x()], 0);
                }
            }

            template <typename T, typename mm>
            void init_hog_zero_everything (
                array2d<matrix<T,31,1>,mm>& hog,
                int hog_nr,
                int hog_nc,
                int filter_rows_padding,
                int filter_cols_padding
            )
            {
                hog.set_size(hog_nr+filter_rows_padding-1, hog_nc+filter_cols_padding-1);

                for (long r = 0; r < hog.nr(); ++r)
                {
                    for (long c = 0; c < hog.nc(); ++c)
                    {
                        set_all_elements(hog[r][c], 0);
                    }
                }
            }

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

            template <
                typename image_type,
                typename out_type
                >
            void impl_extract_fhog_features_cell_size_1(
                const image_type& img_,
                out_type& hog,
                int filter_rows_padding,
                int filter_cols_padding
            )
            {
                const_image_view<image_type> img(img_);
                // make sure requires clause is not broken
                DLIB_ASSERT( filter_rows_padding > 0 &&
                             filter_cols_padding > 0 ,
                    "\t void extract_fhog_features()"
                    << "\n\t Invalid inputs were given to this function. "
                    << "\n\t filter_rows_padding: " << filter_rows_padding
                    << "\n\t filter_cols_padding: " << filter_cols_padding
                    );

                /*
                    This function is an optimized version of impl_extract_fhog_features() for
                    the case where cell_size == 1.
                */

                // unit vectors used to compute gradient orientation
                matrix<double,2,1> directions[9];
                directions[0] =  1.0000, 0.0000;
                directions[1] =  0.9397, 0.3420;
                directions[2] =  0.7660, 0.6428;
                directions[3] =  0.500,  0.8660;
                directions[4] =  0.1736, 0.9848;
                directions[5] = -0.1736, 0.9848;
                directions[6] = -0.5000, 0.8660;
                directions[7] = -0.7660, 0.6428;
                directions[8] = -0.9397, 0.3420;

                if (img.nr() <= 2 || img.nc() <= 2)
                {
                    hog.clear();
                    return;
                }

                array2d<unsigned char> angle(img.nr(), img.nc());

                array2d<float> norm(img.nr(), img.nc());
                zero_border_pixels(norm,1,1);

                // memory for HOG features
                const long hog_nr = img.nr()-2;
                const long hog_nc = img.nc()-2;

                const int padding_rows_offset = (filter_rows_padding-1)/2;
                const int padding_cols_offset = (filter_cols_padding-1)/2;
                init_hog_zero_everything(hog, hog_nr, hog_nc, filter_rows_padding, filter_cols_padding);

                const int visible_nr = img.nr()-1;
                const int visible_nc = img.nc()-1;

                // First populate the gradient histograms
                for (int y = 1; y < visible_nr; y++)
                {
                    int x;
                    for (x = 1; x < visible_nc-3; x+=4)
                    {
                        // v will be the length of the gradient vectors.
                        simd4f grad_x, grad_y, v;
                        get_gradient(y,x,img,grad_x,grad_y,v);

                        float _vv[4];
                        v.store(_vv);

                        // Now snap the gradient to one of 18 orientations
                        simd4f best_dot = 0;
                        simd4f best_o = 0;
                        for (int o = 0; o < 9; o++)
                        {
                            simd4f dot = grad_x*directions[o](0) + grad_y*directions[o](1);
                            simd4f_bool cmp = dot>best_dot;
                            best_dot = select(cmp,dot,best_dot);
                            dot *= -1;
                            best_o = select(cmp,o,best_o);

                            cmp = dot>best_dot;
                            best_dot = select(cmp,dot,best_dot);
                            best_o = select(cmp,o+9,best_o);
                        }

                        int32 _best_o[4]; simd4i(best_o).store(_best_o);

                        norm[y][x+0] = _vv[0];
                        norm[y][x+1] = _vv[1];
                        norm[y][x+2] = _vv[2];
                        norm[y][x+3] = _vv[3];

                        angle[y][x+0] = _best_o[0];
                        angle[y][x+1] = _best_o[1];
                        angle[y][x+2] = _best_o[2];
                        angle[y][x+3] = _best_o[3];

                    }
                    // Now process the right columns that don't fit into simd registers.
                    for (; x < visible_nc; x++)
                    {
                        matrix<double,2,1> grad;
                        double v;
                        get_gradient(y,x,img,grad,v);

                        // snap to one of 18 orientations
                        double best_dot = 0;
                        int best_o = 0;
                        for (int o = 0; o < 9; o++)
                        {
                            const double dot = dlib::dot(directions[o], grad);
                            if (dot > best_dot)
                            {
                                best_dot = dot;
                                best_o = o;
                            }
                            else if (-dot > best_dot)
                            {
                                best_dot = -dot;
                                best_o = o+9;
                            }
                        }

                        norm[y][x] = v;
                        angle[y][x] = best_o;
                    }
                }

                const double eps = 0.0001;
                // compute features
                for (int y = 0; y < hog_nr; y++)
                {
                    const int yy = y+padding_rows_offset;
                    for (int x = 0; x < hog_nc; x++)
                    {
                        const simd4f z1(norm[y+1][x+1],
                                        norm[y][x+1],
                                        norm[y+1][x],
                                        norm[y][x]);

                        const simd4f z2(norm[y+1][x+2],
                                        norm[y][x+2],
                                        norm[y+1][x+1],
                                        norm[y][x+1]);

                        const simd4f z3(norm[y+2][x+1],
                                        norm[y+1][x+1],
                                        norm[y+2][x],
                                        norm[y+1][x]);

                        const simd4f z4(norm[y+2][x+2],
                                        norm[y+1][x+2],
                                        norm[y+2][x+1],
                                        norm[y+1][x+1]);

                        const simd4f temp0 = std::sqrt(norm[y+1][x+1]);
                        const simd4f nn = 0.2*sqrt(z1+z2+z3+z4+eps);
                        const simd4f n = 0.1/nn;

                        simd4f t = 0;

                        const int xx = x+padding_cols_offset;

                        simd4f h0 = min(temp0,nn)*n;
                        const float vv = sum(h0);
                        set_hog(hog,angle[y+1][x+1],xx,yy,   vv);
                        t += h0;

                        t *= 2*0.2357;

                        // contrast-insensitive features
                        set_hog(hog,angle[y+1][x+1]%9+18,xx,yy, vv);

                        float temp[4];
                        t.store(temp);

                        // texture features
                        set_hog(hog,27,xx,yy, temp[0]);
                        set_hog(hog,28,xx,yy, temp[1]);
                        set_hog(hog,29,xx,yy, temp[2]);
                        set_hog(hog,30,xx,yy, temp[3]);
                    }
                }
            }

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

            template <
                typename image_type,
                typename out_type
                >
            void impl_extract_fhog_features(
                const image_type& img_,
                out_type& hog,
                int cell_size,
                int filter_rows_padding,
                int filter_cols_padding
            )
            {
                const_image_view<image_type> img(img_);
                // make sure requires clause is not broken
                DLIB_ASSERT( cell_size > 0 &&
                             filter_rows_padding > 0 &&
                             filter_cols_padding > 0 ,
                    "\t void extract_fhog_features()"
                    << "\n\t Invalid inputs were given to this function. "
                    << "\n\t cell_size: " << cell_size
                    << "\n\t filter_rows_padding: " << filter_rows_padding
                    << "\n\t filter_cols_padding: " << filter_cols_padding
                    );

                /*
                    This function implements the HOG feature extraction method described in
                    the paper:
                        P. Felzenszwalb, R. Girshick, D. McAllester, D. Ramanan
                        Object Detection with Discriminatively Trained Part Based Models
                        IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 32, No. 9, Sep. 2010

                    Moreover, this function is derived from the HOG feature extraction code
                    from the features.cc file in the voc-releaseX code (see
                    http://people.cs.uchicago.edu/~rbg/latent/) which is has the following
                    license (note that the code has been modified to work with grayscale and
                    color as well as planar and interlaced input and output formats):

                    Copyright (C) 2011, 2012 Ross Girshick, Pedro Felzenszwalb
                    Copyright (C) 2008, 2009, 2010 Pedro Felzenszwalb, Ross Girshick
                    Copyright (C) 2007 Pedro Felzenszwalb, Deva Ramanan

                    Permission is hereby granted, free of charge, to any person obtaining
                    a copy of this software and associated documentation files (the
                    "Software"), to deal in the Software without restriction, including
                    without limitation the rights to use, copy, modify, merge, publish,
                    distribute, sublicense, and/or sell copies of the Software, and to
                    permit persons to whom the Software is furnished to do so, subject to
                    the following conditions:

                    The above copyright notice and this permission notice shall be
                    included in all copies or substantial portions of the Software.

                    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
                    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
                    MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
                    NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
                    LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
                    OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
                    WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
                */

                if (cell_size == 1)
                {
                    impl_extract_fhog_features_cell_size_1(img_,hog,filter_rows_padding,filter_cols_padding);
                    return;
                }

                // unit vectors used to compute gradient orientation
                matrix<double,2,1> directions[9];
                directions[0] =  1.0000, 0.0000;
                directions[1] =  0.9397, 0.3420;
                directions[2] =  0.7660, 0.6428;
                directions[3] =  0.500,  0.8660;
                directions[4] =  0.1736, 0.9848;
                directions[5] = -0.1736, 0.9848;
                directions[6] = -0.5000, 0.8660;
                directions[7] = -0.7660, 0.6428;
                directions[8] = -0.9397, 0.3420;

                // First we allocate memory for caching orientation histograms & their norms.
                const int cells_nr = (int)((double)img.nr()/(double)cell_size + 0.5);
                const int cells_nc = (int)((double)img.nc()/(double)cell_size + 0.5);

                if (cells_nr == 0 || cells_nc == 0)
                {
                    hog.clear();
                    return;
                }

                // We give hist extra padding around the edges (1 cell all the way around the
                // edge) so we can avoid needing to do boundary checks when indexing into it
                // later on.  So some statements assign to the boundary but those values are
                // never used.
                array2d<matrix<float,18,1> > hist(cells_nr+2, cells_nc+2);
                for (long r = 0; r < hist.nr(); ++r)
                {
                    for (long c = 0; c < hist.nc(); ++c)
                    {
                        hist[r][c] = 0;
                    }
                }

                array2d<float> norm(cells_nr, cells_nc);
                assign_all_pixels(norm, 0);

                // memory for HOG features
                const int hog_nr = std::max(cells_nr-2, 0);
                const int hog_nc = std::max(cells_nc-2, 0);
                if (hog_nr == 0 || hog_nc == 0)
                {
                    hog.clear();
                    return;
                }
                const int padding_rows_offset = (filter_rows_padding-1)/2;
                const int padding_cols_offset = (filter_cols_padding-1)/2;
                init_hog(hog, hog_nr, hog_nc, filter_rows_padding, filter_cols_padding);

                const int visible_nr = std::min((long)cells_nr*cell_size,img.nr())-1;
                const int visible_nc = std::min((long)cells_nc*cell_size,img.nc())-1;

                // First populate the gradient histograms
                for (int y = 1; y < visible_nr; y++)
                {
                    const double yp = ((double)y+0.5)/(double)cell_size - 0.5;
                    const int iyp = (int)std::floor(yp);
                    const double vy0 = yp-iyp;
                    const double vy1 = 1.0-vy0;
                    int x;
                    for (x = 1; x < visible_nc-3; x+=4)
                    {
                        simd4f xx(x,x+1,x+2,x+3);
                        // v will be the length of the gradient vectors.
                        simd4f grad_x, grad_y, v;
                        get_gradient(y,x,img,grad_x,grad_y,v);

                        // We will use bilinear interpolation to add into the histogram bins.
                        // So first we precompute the values needed to determine how much each
                        // pixel votes into each bin.
                        simd4f xp = (xx+0.5)/(float)cell_size + 0.5;
                        simd4i ixp = simd4i(xp);
                        simd4f vx0 = xp-ixp;
                        simd4f vx1 = 1.0f-vx0;

                        v = sqrt(v);

                        // Now snap the gradient to one of 18 orientations
                        simd4f best_dot = 0;
                        simd4f best_o = 0;
                        for (int o = 0; o < 9; o++)
                        {
                            simd4f dot = grad_x*directions[o](0) + grad_y*directions[o](1);
                            simd4f_bool cmp = dot>best_dot;
                            best_dot = select(cmp,dot,best_dot);
                            dot *= -1;
                            best_o = select(cmp,o,best_o);

                            cmp = dot>best_dot;
                            best_dot = select(cmp,dot,best_dot);
                            best_o = select(cmp,o+9,best_o);
                        }

                        // Add the gradient magnitude, v, to 4 histograms around pixel using
                        // bilinear interpolation.
                        vx1 *= v;
                        vx0 *= v;
                        // The amounts for each bin
                        simd4f v11 = vy1*vx1;
                        simd4f v01 = vy0*vx1;
                        simd4f v10 = vy1*vx0;
                        simd4f v00 = vy0*vx0;

                        int32 _best_o[4]; simd4i(best_o).store(_best_o);
                        int32 _ixp[4];    ixp.store(_ixp);
                        float _v11[4];    v11.store(_v11);
                        float _v01[4];    v01.store(_v01);
                        float _v10[4];    v10.store(_v10);
                        float _v00[4];    v00.store(_v00);

                        hist[iyp+1]  [_ixp[0]  ](_best_o[0]) += _v11[0];
                        hist[iyp+1+1][_ixp[0]  ](_best_o[0]) += _v01[0];
                        hist[iyp+1]  [_ixp[0]+1](_best_o[0]) += _v10[0];
                        hist[iyp+1+1][_ixp[0]+1](_best_o[0]) += _v00[0];

                        hist[iyp+1]  [_ixp[1]  ](_best_o[1]) += _v11[1];
                        hist[iyp+1+1][_ixp[1]  ](_best_o[1]) += _v01[1];
                        hist[iyp+1]  [_ixp[1]+1](_best_o[1]) += _v10[1];
                        hist[iyp+1+1][_ixp[1]+1](_best_o[1]) += _v00[1];

                        hist[iyp+1]  [_ixp[2]  ](_best_o[2]) += _v11[2];
                        hist[iyp+1+1][_ixp[2]  ](_best_o[2]) += _v01[2];
                        hist[iyp+1]  [_ixp[2]+1](_best_o[2]) += _v10[2];
                        hist[iyp+1+1][_ixp[2]+1](_best_o[2]) += _v00[2];

                        hist[iyp+1]  [_ixp[3]  ](_best_o[3]) += _v11[3];
                        hist[iyp+1+1][_ixp[3]  ](_best_o[3]) += _v01[3];
                        hist[iyp+1]  [_ixp[3]+1](_best_o[3]) += _v10[3];
                        hist[iyp+1+1][_ixp[3]+1](_best_o[3]) += _v00[3];
                    }
                    // Now process the right columns that don't fit into simd registers.
                    for (; x < visible_nc; x++)
                    {
                        matrix<double,2,1> grad;
                        double v;
                        get_gradient(y,x,img,grad,v);

                        // snap to one of 18 orientations
                        double best_dot = 0;
                        int best_o = 0;
                        for (int o = 0; o < 9; o++)
                        {
                            const double dot = dlib::dot(directions[o], grad);
                            if (dot > best_dot)
                            {
                                best_dot = dot;
                                best_o = o;
                            }
                            else if (-dot > best_dot)
                            {
                                best_dot = -dot;
                                best_o = o+9;
                            }
                        }

                        v = std::sqrt(v);
                        // add to 4 histograms around pixel using bilinear interpolation
                        const double xp = ((double)x+0.5)/(double)cell_size - 0.5;
                        const int ixp = (int)std::floor(xp);
                        const double vx0 = xp-ixp;
                        const double vx1 = 1.0-vx0;

                        hist[iyp+1][ixp+1](best_o) += vy1*vx1*v;
                        hist[iyp+1+1][ixp+1](best_o) += vy0*vx1*v;
                        hist[iyp+1][ixp+1+1](best_o) += vy1*vx0*v;
                        hist[iyp+1+1][ixp+1+1](best_o) += vy0*vx0*v;
                    }
                }

                // compute energy in each block by summing over orientations
                for (int r = 0; r < cells_nr; ++r)
                {
                    for (int c = 0; c < cells_nc; ++c)
                    {
                        for (int o = 0; o < 9; o++)
                        {
                            norm[r][c] += (hist[r+1][c+1](o) + hist[r+1][c+1](o+9)) * (hist[r+1][c+1](o) + hist[r+1][c+1](o+9));
                        }
                    }
                }

                const double eps = 0.0001;
                // compute features
                for (int y = 0; y < hog_nr; y++)
                {
                    const int yy = y+padding_rows_offset;
                    for (int x = 0; x < hog_nc; x++)
                    {
                        const simd4f z1(norm[y+1][x+1],
                                        norm[y][x+1],
                                        norm[y+1][x],
                                        norm[y][x]);

                        const simd4f z2(norm[y+1][x+2],
                                        norm[y][x+2],
                                        norm[y+1][x+1],
                                        norm[y][x+1]);

                        const simd4f z3(norm[y+2][x+1],
                                        norm[y+1][x+1],
                                        norm[y+2][x],
                                        norm[y+1][x]);

                        const simd4f z4(norm[y+2][x+2],
                                        norm[y+1][x+2],
                                        norm[y+2][x+1],
                                        norm[y+1][x+1]);

                        const simd4f nn = 0.2*sqrt(z1+z2+z3+z4+eps);
                        const simd4f n = 0.1/nn;

                        simd4f t = 0;

                        const int xx = x+padding_cols_offset;

                        // contrast-sensitive features
                        for (int o = 0; o < 18; o+=3)
                        {
                            simd4f temp0(hist[y+1+1][x+1+1](o));
                            simd4f temp1(hist[y+1+1][x+1+1](o+1));
                            simd4f temp2(hist[y+1+1][x+1+1](o+2));
                            simd4f h0 = min(temp0,nn)*n;
                            simd4f h1 = min(temp1,nn)*n;
                            simd4f h2 = min(temp2,nn)*n;
                            set_hog(hog,o,xx,yy,   sum(h0));
                            set_hog(hog,o+1,xx,yy, sum(h1));
                            set_hog(hog,o+2,xx,yy, sum(h2));
                            t += h0+h1+h2;
                        }

                        t *= 2*0.2357;

                        // contrast-insensitive features
                        for (int o = 0; o < 9; o+=3)
                        {
                            simd4f temp0 = hist[y+1+1][x+1+1](o)   + hist[y+1+1][x+1+1](o+9);
                            simd4f temp1 = hist[y+1+1][x+1+1](o+1) + hist[y+1+1][x+1+1](o+9+1);
                            simd4f temp2 = hist[y+1+1][x+1+1](o+2) + hist[y+1+1][x+1+1](o+9+2);
                            simd4f h0 = min(temp0,nn)*n;
                            simd4f h1 = min(temp1,nn)*n;
                            simd4f h2 = min(temp2,nn)*n;
                            set_hog(hog,o+18,xx,yy, sum(h0));
                            set_hog(hog,o+18+1,xx,yy, sum(h1));
                            set_hog(hog,o+18+2,xx,yy, sum(h2));
                        }

                        float temp[4];
                        t.store(temp);

                        // texture features
                        set_hog(hog,27,xx,yy, temp[0]);
                        set_hog(hog,28,xx,yy, temp[1]);
                        set_hog(hog,29,xx,yy, temp[2]);
                        set_hog(hog,30,xx,yy, temp[3]);
                    }
                }
            }

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

            inline void create_fhog_bar_images (
                dlib::array<matrix<float> >& mbars,
                const long w
            )
            {
                const long bdims = 9;
                // Make the oriented lines we use to draw on each HOG cell.
                mbars.resize(bdims);
                dlib::array<array2d<unsigned char> > bars(bdims);
                array2d<unsigned char> temp(w,w);
                for (unsigned long i = 0; i < bars.size(); ++i)
                {
                    assign_all_pixels(temp, 0);
                    draw_line(temp, point(w/2,0), point(w/2,w-1), 255);
                    rotate_image(temp, bars[i], i*-pi/bars.size());

                    mbars[i] = subm(matrix_cast<float>(mat(bars[i])), centered_rect(get_rect(bars[i]),w,w) );
                }
            }

        } // end namespace impl_fhog

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

        template <
            typename image_type,
            typename T,
            typename mm1,
            typename mm2
            >
        void extract_fhog_features(
            const image_type& img,
            dlib::array<array2d<T,mm1>,mm2>& hog,
            int cell_size = 8,
            int filter_rows_padding = 1,
            int filter_cols_padding = 1
        )
        {
            impl_fhog::impl_extract_fhog_features(img, hog, cell_size, filter_rows_padding, filter_cols_padding);
            // If the image is too small then the above function outputs an empty feature map.
            // But to make things very uniform in usage we require the output to still have the
            // 31 planes (but they are just empty).
            if (hog.size() == 0)
                hog.resize(31);
        }

        template <
            typename image_type,
            typename T,
            typename mm
            >
        void extract_fhog_features(
            const image_type& img,
            array2d<matrix<T,31,1>,mm>& hog,
            int cell_size = 8,
            int filter_rows_padding = 1,
            int filter_cols_padding = 1
        )
        {
            impl_fhog::impl_extract_fhog_features(img, hog, cell_size, filter_rows_padding, filter_cols_padding);
        }

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

        template <
            typename image_type,
            typename T
            >
        void extract_fhog_features(
            const image_type& img,
            matrix<T,0,1>& feats,
            int cell_size = 8,
            int filter_rows_padding = 1,
            int filter_cols_padding = 1
        )
        {
            dlib::array<array2d<T> > hog;
            extract_fhog_features(img, hog, cell_size, filter_rows_padding, filter_cols_padding);
            feats.set_size(hog.size()*hog[0].size());
            for (unsigned long i = 0; i < hog.size(); ++i)
            {
                const long size = hog[i].size();
                set_rowm(feats, range(i*size, (i+1)*size-1)) = reshape_to_column_vector(mat(hog[i]));
            }
        }

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

        template <
            typename image_type
            >
        matrix<double,0,1> extract_fhog_features(
            const image_type& img,
            int cell_size = 8,
            int filter_rows_padding = 1,
            int filter_cols_padding = 1
        )
        {
            matrix<double,0,1> feats;
            extract_fhog_features(img, feats, cell_size, filter_rows_padding, filter_cols_padding);
            return feats;
        }

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

        inline point image_to_fhog (
            point p,
            int cell_size = 8,
            int filter_rows_padding = 1,
            int filter_cols_padding = 1
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( cell_size > 0 &&
                filter_rows_padding > 0 &&
                filter_cols_padding > 0 ,
                "\t point image_to_fhog()"
                << "\n\t Invalid inputs were given to this function. "
                << "\n\t cell_size: " << cell_size
                << "\n\t filter_rows_padding: " << filter_rows_padding
                << "\n\t filter_cols_padding: " << filter_cols_padding
            );

            // There is a one pixel border around the image.
            p -= point(1,1);
            // There is also a 1 "cell" border around the HOG image formation.
            return p/cell_size - point(1,1) + point((filter_cols_padding-1)/2,(filter_rows_padding-1)/2);
        }

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

        inline rectangle image_to_fhog (
            const rectangle& rect,
            int cell_size = 8,
            int filter_rows_padding = 1,
            int filter_cols_padding = 1
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( cell_size > 0 &&
                filter_rows_padding > 0 &&
                filter_cols_padding > 0 ,
                "\t rectangle image_to_fhog()"
                << "\n\t Invalid inputs were given to this function. "
                << "\n\t cell_size: " << cell_size
                << "\n\t filter_rows_padding: " << filter_rows_padding
                << "\n\t filter_cols_padding: " << filter_cols_padding
            );

            return rectangle(image_to_fhog(rect.tl_corner(),cell_size,filter_rows_padding,filter_cols_padding),
                             image_to_fhog(rect.br_corner(),cell_size,filter_rows_padding,filter_cols_padding));
        }

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

        inline point fhog_to_image (
            point p,
            int cell_size = 8,
            int filter_rows_padding = 1,
            int filter_cols_padding = 1
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( cell_size > 0 &&
                filter_rows_padding > 0 &&
                filter_cols_padding > 0 ,
                "\t point fhog_to_image()"
                << "\n\t Invalid inputs were given to this function. "
                << "\n\t cell_size: " << cell_size
                << "\n\t filter_rows_padding: " << filter_rows_padding
                << "\n\t filter_cols_padding: " << filter_cols_padding
            );

            // Convert to image space and then set to the center of the cell.
            point offset;

            p = (p+point(1,1)-point((filter_cols_padding-1)/2,(filter_rows_padding-1)/2))*cell_size + point(1,1);
            if (p.x() >= 0 && p.y() >= 0) offset = point(cell_size/2,cell_size/2);
            if (p.x() <  0 && p.y() >= 0) offset = point(-cell_size/2,cell_size/2);
            if (p.x() >= 0 && p.y() <  0) offset = point(cell_size/2,-cell_size/2);
            if (p.x() <  0 && p.y() <  0) offset = point(-cell_size/2,-cell_size/2);
            return p + offset;
        }

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

        inline rectangle fhog_to_image (
            const rectangle& rect,
            int cell_size = 8,
            int filter_rows_padding = 1,
            int filter_cols_padding = 1
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( cell_size > 0 &&
                filter_rows_padding > 0 &&
                filter_cols_padding > 0 ,
                "\t rectangle fhog_to_image()"
                << "\n\t Invalid inputs were given to this function. "
                << "\n\t cell_size: " << cell_size
                << "\n\t filter_rows_padding: " << filter_rows_padding
                << "\n\t filter_cols_padding: " << filter_cols_padding
            );

            return rectangle(fhog_to_image(rect.tl_corner(),cell_size,filter_rows_padding,filter_cols_padding),
                             fhog_to_image(rect.br_corner(),cell_size,filter_rows_padding,filter_cols_padding));
        }

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

        template <
            typename T,
            typename mm1,
            typename mm2
            >
        matrix<unsigned char> draw_fhog(
            const dlib::array<array2d<T,mm1>,mm2>& hog,
            const long cell_draw_size = 15
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( cell_draw_size > 0 && hog.size()==31,
                "\t matrix<unsigned char> draw_fhog()"
                << "\n\t Invalid inputs were given to this function. "
                << "\n\t cell_draw_size: " << cell_draw_size
                << "\n\t hog.size(): " << hog.size()
            );

            dlib::array<matrix<float> > mbars;
            impl_fhog::create_fhog_bar_images(mbars,cell_draw_size);

            // now draw the bars onto the HOG cells
            matrix<float> himg(hog[0].nr()*cell_draw_size, hog[0].nc()*cell_draw_size);
            himg = 0;
            for (unsigned long d = 0; d < mbars.size(); ++d)
            {
                for (long r = 0; r < himg.nr(); r+=cell_draw_size)
                {
                    for (long c = 0; c < himg.nc(); c+=cell_draw_size)
                    {
                        const float val = hog[d][r/cell_draw_size][c/cell_draw_size] +
                            hog[d+mbars.size()][r/cell_draw_size][c/cell_draw_size] +
                            hog[d+mbars.size()*2][r/cell_draw_size][c/cell_draw_size];
                        if (val > 0)
                        {
                            set_subm(himg, r, c, cell_draw_size, cell_draw_size) += val*mbars[d%mbars.size()];
                        }
                    }
                }
            }

            const double thresh = mean(himg) + 4*stddev(himg);
            if (thresh != 0)
                return matrix_cast<unsigned char>(upperbound(round(himg*255/thresh),255));
            else
                return matrix_cast<unsigned char>(himg);
        }

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

        template <
            typename T
            >
        matrix<unsigned char> draw_fhog (
            const std::vector<matrix<T> >& hog,
            const long cell_draw_size = 15
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( cell_draw_size > 0 && hog.size()==31,
                "\t matrix<unsigned char> draw_fhog()"
                << "\n\t Invalid inputs were given to this function. "
                << "\n\t cell_draw_size: " << cell_draw_size
                << "\n\t hog.size(): " << hog.size()
            );

            // Just convert the input into the right object and then call the above draw_fhog()
            // function on it.
            dlib::array<array2d<T> > temp(hog.size());
            for (unsigned long i = 0; i < temp.size(); ++i)
            {
                temp[i].set_size(hog[i].nr(), hog[i].nc());
                for (long r = 0; r < hog[i].nr(); ++r)
                {
                    for (long c = 0; c < hog[i].nc(); ++c)
                    {
                        temp[i][r][c] = hog[i](r,c);
                    }
                }
            }
            return draw_fhog(temp,cell_draw_size);
        }

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

        template <
            typename T,
            typename mm
            >
        matrix<unsigned char> draw_fhog(
            const array2d<matrix<T,31,1>,mm>& hog,
            const long cell_draw_size = 15
        )
        {
            // make sure requires clause is not broken
            DLIB_ASSERT( cell_draw_size > 0,
                "\t matrix<unsigned char> draw_fhog()"
                << "\n\t Invalid inputs were given to this function. "
                << "\n\t cell_draw_size: " << cell_draw_size
            );

            dlib::array<matrix<float> > mbars;
            impl_fhog::create_fhog_bar_images(mbars,cell_draw_size);

            // now draw the bars onto the HOG cells
            matrix<float> himg(hog.nr()*cell_draw_size, hog.nc()*cell_draw_size);
            himg = 0;
            for (unsigned long d = 0; d < mbars.size(); ++d)
            {
                for (long r = 0; r < himg.nr(); r+=cell_draw_size)
                {
                    for (long c = 0; c < himg.nc(); c+=cell_draw_size)
                    {
                        const float val = hog[r/cell_draw_size][c/cell_draw_size](d) +
                            hog[r/cell_draw_size][c/cell_draw_size](d+mbars.size()) +
                            hog[r/cell_draw_size][c/cell_draw_size](d+mbars.size()*2);
                        if (val > 0)
                        {
                            set_subm(himg, r, c, cell_draw_size, cell_draw_size) += val*mbars[d%mbars.size()];
                        }
                    }
                }
            }

            const double thresh = mean(himg) + 4*stddev(himg);
            if (thresh != 0)
                return matrix_cast<unsigned char>(upperbound(round(himg*255/thresh),255));
            else
                return matrix_cast<unsigned char>(himg);
        }

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

    }

    #endif // DLIB_fHOG_Hh_