# dlib C++ Library - edge_detector.h

    // Copyright (C) 2008  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_EDGE_DETECTOr_
    #define DLIB_EDGE_DETECTOr_

    #include "edge_detector_abstract.h"
    #include "../pixel.h"
    #include "../array2d.h"
    #include "../geometry.h"
    #include <vector>
    #include "../image_keypoint/build_separable_poly_filters.h"

    namespace dlib
    {

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

        template <
            typename T
            >
        inline char edge_orientation (
            const T& x_,
            const T& y_
        )
        {

            // if this is a perfectly horizontal gradient then return right away
            if (x_ == 0)
            {
                return '|';
            }
            else if (y_ == 0) // if this is a perfectly vertical gradient then return right away
            {
                return '-';
            }

            // Promote x so that when we multiply by 128 later we know overflow won't happen.
            typedef typename promote<T>::type type;
            type x = x_;
            type y = y_;

            if (x < 0)
            {
                x = -x;
                if (y < 0)
                {
                    y = -y;
                    x *= 128;
                    const type temp = x/y;
                    if (temp > 309)
                        return '-';
                    else if (temp > 53)
                        return '/';
                    else
                        return '|';
                }
                else
                {
                    x *= 128;
                    const type temp = x/y;
                    if (temp > 309)
                        return '-';
                    else if (temp > 53)
                        return '\\';
                    else
                        return '|';
                }
            }
            else
            {
                if (y < 0)
                {
                    y = -y;
                    x *= 128;

                    const type temp = x/y;
                    if (temp > 309)
                        return '-';
                    else if (temp > 53)
                        return '\\';
                    else
                        return '|';
                }
                else
                {
                    x *= 128;

                    const type temp = x/y;
                    if (temp > 309)
                        return '-';
                    else if (temp > 53)
                        return '/';
                    else
                        return '|';
                }
            }

        }

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

        template <
            typename in_image_type,
            typename out_image_type
            >
        void sobel_edge_detector (
            const in_image_type& in_img_,
            out_image_type& horz_,
            out_image_type& vert_
        )
        {
            typedef typename image_traits<out_image_type>::pixel_type pixel_type;
            COMPILE_TIME_ASSERT(pixel_traits<pixel_type>::is_unsigned == false);
            DLIB_ASSERT( !is_same_object(in_img_,horz_) && !is_same_object(in_img_,vert_) &&
                         !is_same_object(horz_,vert_),
                "\tvoid sobel_edge_detector(in_img_, horz_, vert_)"
                << "\n\t You can't give the same image as more than one argument"
                << "\n\t is_same_object(in_img_,horz_): " << is_same_object(in_img_,horz_)
                << "\n\t is_same_object(in_img_,vert_): " << is_same_object(in_img_,vert_)
                << "\n\t is_same_object(horz_,vert_):    " << is_same_object(horz_,vert_)
                );

            const int vert_filter[3][3] = {{-1,-2,-1},
            {0,0,0},
            {1,2,1}};
            const int horz_filter[3][3] = { {-1,0,1},
            {-2,0,2},
            {-1,0,1}};

            const long M = 3;
            const long N = 3;

            const_image_view<in_image_type> in_img(in_img_);
            image_view<out_image_type> horz(horz_);
            image_view<out_image_type> vert(vert_);

            horz.set_size(in_img.nr(),in_img.nc());
            vert.set_size(in_img.nr(),in_img.nc());

            assign_border_pixels(horz,1,1,0);
            assign_border_pixels(vert,1,1,0);

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

            // 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 pixel_traits<typename image_traits<in_image_type>::pixel_type>::basic_pixel_type bp_type;

                    typename promote<bp_type>::type p, horz_temp, vert_temp;
                    horz_temp = 0;
                    vert_temp = 0;
                    for (long m = 0; m < M; ++m)
                    {
                        for (long n = 0; n < N; ++n)
                        {
                            // pull out the current pixel and put it into p
                            p = get_pixel_intensity(in_img[r-M/2+m][c-N/2+n]);

                            horz_temp += p*horz_filter[m][n];
                            vert_temp += p*vert_filter[m][n];
                        }
                    }

                    assign_pixel(horz[r][c] , horz_temp);
                    assign_pixel(vert[r][c] , vert_temp);

                }
            }
        }

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

        namespace impl
        {
            template <typename T>
            typename promote<T>::type square (const T& a)
            {
                return static_cast<T>(a)*static_cast<T>(a);
            }
        }

        template <
            typename in_image_type,
            typename out_image_type
            >
        void suppress_non_maximum_edges (
            const in_image_type& horz_,
            const in_image_type& vert_,
            out_image_type& out_img_
        )
        {
            const_image_view<in_image_type> horz(horz_);
            const_image_view<in_image_type> vert(vert_);
            image_view<out_image_type> out_img(out_img_);

            COMPILE_TIME_ASSERT(is_signed_type<typename image_traits<in_image_type>::pixel_type>::value);
            DLIB_ASSERT( horz.nr() == vert.nr() && horz.nc() == vert.nc(),
                "\tvoid suppress_non_maximum_edges(horz, vert, out_img)"
                << "\n\tYou have to give horz and vert gradient images that are the same size"
                << "\n\thorz.nr():   " << horz.nr()
                << "\n\thorz.nc():   " << horz.nc()
                << "\n\tvert.nr():   " << vert.nr()
                << "\n\tvert.nc():   " << vert.nc()
                );
            DLIB_ASSERT( !is_same_object(out_img_,horz_) && !is_same_object(out_img_,vert_),
                "\tvoid suppress_non_maximum_edges(horz_, vert_, out_img_)"
                << "\n\t out_img can't be the same as one of the input images."
                << "\n\t is_same_object(out_img_,horz_):    " << is_same_object(out_img_,horz_)
                << "\n\t is_same_object(out_img_,vert_):    " << is_same_object(out_img_,vert_)
                );

            using std::min;
            using std::abs;

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

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

            zero_border_pixels(out_img,1,1);

            // now do non maximum suppression while we copy the
            const long M = 3;
            const long N = 3;

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

            // 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 promote<typename image_traits<in_image_type>::pixel_type>::type T;
                    const T y = horz[r][c];
                    const T x = vert[r][c];

                    using impl::square;

                    const T val = square(horz[r][c]) + square(vert[r][c]);

                    const char ori = edge_orientation(x,y);
                    const unsigned char zero = 0;
                    switch (ori)
                    {
                        case '-':
                            if (square(horz[r-1][c])+square(vert[r-1][c]) > val || square(horz[r+1][c]) + square(vert[r+1][c]) > val)
                                assign_pixel(out_img[r][c] , zero);
                            else
                                assign_pixel(out_img[r][c] , std::sqrt((double)val));
                            break;

                        case '|':
                            if (square(horz[r][c-1]) + square(vert[r][c-1]) > val || square(horz[r][c+1]) + square(vert[r][c+1]) > val)
                                assign_pixel(out_img[r][c] , zero);
                            else
                                assign_pixel(out_img[r][c] , std::sqrt((double)val));
                            break;

                        case '/':
                            if (square(horz[r-1][c-1]) + square(vert[r-1][c-1]) > val || square(horz[r+1][c+1]) + square(vert[r+1][c+1]) > val)
                                assign_pixel(out_img[r][c] , zero);
                            else
                                assign_pixel(out_img[r][c] , std::sqrt((double)val));
                            break;

                        case '\\':
                            if (square(horz[r+1][c-1]) + square(vert[r+1][c-1]) > val || square(horz[r-1][c+1]) + square(vert[r-1][c+1]) > val)
                                assign_pixel(out_img[r][c] , zero);
                            else
                                assign_pixel(out_img[r][c] , std::sqrt((double)val));
                            break;

                    }
                }
            }
        }

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

        template <
            typename image_type
            >
        void normalize_image_gradients (
            image_type& img1_,
            image_type& img2_
        )
        {
            image_view<image_type> img1(img1_);
            image_view<image_type> img2(img2_);

            using pixel_type = typename image_traits<image_type>::pixel_type;
            static_assert(std::is_same<pixel_type,float>::value ||
                std::is_same<pixel_type,double>::value ||
                std::is_same<pixel_type,long double>::value,
                "normalize_image_gradients() requires the input images to use floating point pixel types.");

            DLIB_CASSERT(img1.nr() == img2.nr());
            DLIB_CASSERT(img1.nc() == img2.nc());

            // normalize all the gradients
            for (long r = 0; r < img1.nr(); ++r)
            {
                for (long c = 0; c < img1.nc(); ++c)
                {
                    if (img1[r][c] != 0 || img2[r][c] != 0)
                    {
                        double len = std::sqrt(img1[r][c]*img1[r][c] + img2[r][c]*img2[r][c]);
                        img1[r][c] /= len;
                        img2[r][c] /= len;
                    }
                }
            }
        }

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

        template <
            typename image_type
            >
        std::vector<point> remove_incoherent_edge_pixels (
            const std::vector<point>& line,
            const image_type& horz_gradient_,
            const image_type& vert_gradient_,
            double angle_threshold
        )
        {
            const_image_view<image_type> horz_gradient(horz_gradient_);
            const_image_view<image_type> vert_gradient(vert_gradient_);

            DLIB_CASSERT(horz_gradient.nr() == vert_gradient.nr());
            DLIB_CASSERT(horz_gradient.nc() == vert_gradient.nc());
            DLIB_CASSERT(angle_threshold >= 0);
    #ifdef ENABLE_ASSERTS
            for (auto& p : line)
                DLIB_ASSERT(get_rect(horz_gradient).contains(p), "All line points must be inside the given images.");
    #endif

            // We make sure that each vector is within this threshold of the mean vector.  So
            // to make sure they are pairwise within the user supplied angel threshold we need
            // to divide by 2 before we proceed.
            angle_threshold /= 2;

            const double dotthresh = std::cos(angle_threshold*pi/180);
            // find the average gradient on this line
            dpoint avg;
            for (auto p : line)
                avg += dpoint(horz_gradient[p.y()][p.x()], vert_gradient[p.y()][p.x()]);
            dpoint ref = avg.normalize();

            // now iterate a few times and find the most common average gradient.
            for (int i = 0; i < 10; ++i)
            {
                avg = dpoint();
                for (auto p : line)
                {
                    const dpoint v(horz_gradient[p.y()][p.x()], vert_gradient[p.y()][p.x()]);
                    const double dp = ref.dot(v);
                    if (dp > dotthresh)
                        avg += v;
                    else if (-dp > dotthresh)
                        avg -= v;
                }
                ref = avg.normalize();
            }

            // now remove all the points that deviate from the average gradient too much.
            std::vector<point> newpixels;
            for (auto p : line)
            {
                dpoint v(horz_gradient[p.y()][p.x()], vert_gradient[p.y()][p.x()]);
                if (std::abs(ref.dot(v)) > dotthresh)
                    newpixels.push_back(p);
            }
            return newpixels;
        }

        template <
            typename image_type
            >
        std::vector<std::vector<point>> remove_incoherent_edge_pixels (
            const std::vector<std::vector<point>>& line_pixels,
            const image_type& horz_gradient_,
            const image_type& vert_gradient_,
            const double angle_threshold
        )
        {
            std::vector<std::vector<point>> temp;
            temp.reserve(line_pixels.size());
            for (auto& line : line_pixels)
                temp.emplace_back(remove_incoherent_edge_pixels(line, horz_gradient_, vert_gradient_, angle_threshold));
            return temp;
        }

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

        class image_gradients
        {

        public:

            image_gradients (
            ) : image_gradients(1) {}

            image_gradients (
                long scale
            ) : the_scale(scale)
            {
                DLIB_CASSERT(scale >= 1);

                scale = 2*scale+1;

                auto dfilters = build_separable_poly_filters(2,scale);
                DLIB_CASSERT(dfilters[1].size() == 1);
                DLIB_CASSERT(dfilters[2].size() == 1);
                DLIB_CASSERT(dfilters[3].size() == 1);
                DLIB_CASSERT(dfilters[4].size() == 1);
                DLIB_CASSERT(dfilters[5].size() == 1);

                filter_x.first = matrix_cast<float>(dfilters[1][0].first);
                filter_x.second = matrix_cast<float>(dfilters[1][0].second);

                filter_y.first = matrix_cast<float>(dfilters[2][0].first);
                filter_y.second = matrix_cast<float>(dfilters[2][0].second);

                // We multiply by 2 so that the filter gives the gradient rather than the x^2
                // polynomial coefficient.
                filter_xx.first = 2*matrix_cast<float>(dfilters[3][0].first);
                filter_xx.second = matrix_cast<float>(dfilters[3][0].second);

                filter_xy.first = matrix_cast<float>(dfilters[4][0].first);
                filter_xy.second = matrix_cast<float>(dfilters[4][0].second);

                // We multiply by 2 so that the filter gives the gradient rather than the y^2
                // polynomial coefficient.
                filter_yy.first = 2*matrix_cast<float>(dfilters[5][0].first);
                filter_yy.second = matrix_cast<float>(dfilters[5][0].second);
            }

            long get_scale() const { return the_scale; }

            template <
                typename in_image_type,
                typename out_image_type
                >
            rectangle gradient_x(
                const in_image_type& img,
                out_image_type& out
            ) const
            {
                return spatially_filter_image_separable(img, out, filter_x.second, filter_x.first);
            }

            template <
                typename in_image_type,
                typename out_image_type
                >
            rectangle gradient_y(
                const in_image_type& img,
                out_image_type& out
            ) const
            {
                return spatially_filter_image_separable(img, out, filter_y.second, filter_y.first);
            }

            template <
                typename in_image_type,
                typename out_image_type
                >
            rectangle gradient_xx(
                const in_image_type& img,
                out_image_type& out
            )  const
            {
                return spatially_filter_image_separable(img, out, filter_xx.second, filter_xx.first);
            }

            template <
                typename in_image_type,
                typename out_image_type
                >
            rectangle gradient_xy(
                const in_image_type& img,
                out_image_type& out
            ) const
            {
                return spatially_filter_image_separable(img, out, filter_xy.second, filter_xy.first);
            }

            template <
                typename in_image_type,
                typename out_image_type
                >
            rectangle gradient_yy(
                const in_image_type& img,
                out_image_type& out
            ) const
            {
                return spatially_filter_image_separable(img, out, filter_yy.second, filter_yy.first);
            }

            matrix<float> get_x_filter()  const { return filter_x.first*trans(filter_x.second); }
            matrix<float> get_y_filter()  const { return filter_y.first*trans(filter_y.second); }
            matrix<float> get_xx_filter() const { return filter_xx.first*trans(filter_xx.second); }
            matrix<float> get_xy_filter() const { return filter_xy.first*trans(filter_xy.second); }
            matrix<float> get_yy_filter() const { return filter_yy.first*trans(filter_yy.second); }

        private:
            std::pair<matrix<float,0,1>,matrix<float,0,1>> filter_x;
            std::pair<matrix<float,0,1>,matrix<float,0,1>> filter_y;
            std::pair<matrix<float,0,1>,matrix<float,0,1>> filter_xx;
            std::pair<matrix<float,0,1>,matrix<float,0,1>> filter_xy;
            std::pair<matrix<float,0,1>,matrix<float,0,1>> filter_yy;

            long the_scale;
        };

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

        namespace impl
        {
            template <
                typename in_image_type,
                typename out_image_type
                >
            void find_lines(
                const in_image_type& xx_,
                const in_image_type& xy_,
                const in_image_type& yy_,
                out_image_type& horz_,
                out_image_type& vert_,
                double positive_if_should_find_dark_lines
            )
            {
                typedef typename image_traits<out_image_type>::pixel_type out_pixel_type;
                static_assert(std::is_same<float,out_pixel_type>::value || std::is_same<double,out_pixel_type>::value,
                    "Output images must contain either float or double valued pixels");

                const_image_view<in_image_type> xx(xx_);
                const_image_view<in_image_type> xy(xy_);
                const_image_view<in_image_type> yy(yy_);

                DLIB_CASSERT(xx.nr() == xy.nr());
                DLIB_CASSERT(xx.nr() == yy.nr());
                DLIB_CASSERT(xx.nc() == xy.nc());
                DLIB_CASSERT(xx.nc() == yy.nc());

                image_view<out_image_type> x(horz_);
                image_view<out_image_type> y(vert_);

                x.set_size(xx.nr(), xx.nc());
                y.set_size(xx.nr(), xx.nc());

                // store the max eigenvalue into xy and then the associated eigen vector into [xx,yy]
                for (long r = 0; r < xx.nr(); ++r)
                {
                    for (long c = 0; c < xx.nc(); ++c)
                    {
                        // negate to that lambda will be the *minimum* eigenvalue
                        double w1 = positive_if_should_find_dark_lines*xx[r][c]/2.0;
                        double w2 = positive_if_should_find_dark_lines*yy[r][c]/2.0;
                        double w3 = positive_if_should_find_dark_lines*xy[r][c];

                        auto lambda = w1 + w2 + std::sqrt((w1-w2)*(w1-w2) + w3*w3);
                        if (lambda < 0)
                            lambda = 0;

                        if (2*w1!=lambda)
                        {
                            x[r][c] = -w3/(2*w1-lambda);
                            y[r][c] = 1;

                            double norm = std::sqrt(x[r][c]*x[r][c] + y[r][c]*y[r][c]);
                            x[r][c] *= lambda/norm;
                            y[r][c] *= lambda/norm;
                        }
                        else
                        {
                            x[r][c] = lambda;
                            y[r][c] = 0;
                        }
                    }
                }
            }
        }

        template <
            typename in_image_type,
            typename out_image_type
            >
        void find_bright_lines(
            const in_image_type& xx,
            const in_image_type& xy,
            const in_image_type& yy,
            out_image_type& horz,
            out_image_type& vert
        )
        {
            impl::find_lines(xx,xy,yy,horz,vert,-1);
        }

        template <
            typename in_image_type,
            typename out_image_type
            >
        void find_dark_lines(
            const in_image_type& xx,
            const in_image_type& xy,
            const in_image_type& yy,
            out_image_type& horz,
            out_image_type& vert
        )
        {
            impl::find_lines(xx,xy,yy,horz,vert,+1);
        }

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

        template <
            typename in_image_type,
            typename out_image_type
            >
        void find_bright_keypoints(
            const in_image_type& xx_,
            const in_image_type& xy_,
            const in_image_type& yy_,
            out_image_type& saliency_
        )
        {
            typedef typename image_traits<out_image_type>::pixel_type out_pixel_type;
            static_assert(std::is_same<float,out_pixel_type>::value || std::is_same<double,out_pixel_type>::value,
                "Output images must contain either float or double valued pixels");

            const_image_view<in_image_type> xx(xx_);
            const_image_view<in_image_type> xy(xy_);
            const_image_view<in_image_type> yy(yy_);

            DLIB_CASSERT(xx.nr() == xy.nr());
            DLIB_CASSERT(xx.nr() == yy.nr());
            DLIB_CASSERT(xx.nc() == xy.nc());
            DLIB_CASSERT(xx.nc() == yy.nc());

            image_view<out_image_type> saliency(saliency_);
            saliency.set_size(xx.nr(), xx.nc());

            for (long r = 0; r < xx.nr(); ++r)
            {
                for (long c = 0; c < xx.nc(); ++c)
                {
                    matrix<double,2,2> tmp;
                    tmp = xx[r][c], xy[r][c],
                          xy[r][c], yy[r][c];

                    matrix<double,2,1> e = real_eigenvalues(tmp);
                    saliency[r][c] = prod(upperbound(e,0));
                }
            }
        }

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

        template <
            typename in_image_type,
            typename out_image_type
            >
        void find_dark_keypoints(
            const in_image_type& xx_,
            const in_image_type& xy_,
            const in_image_type& yy_,
            out_image_type& saliency_
        )
        {
            typedef typename image_traits<out_image_type>::pixel_type out_pixel_type;
            static_assert(std::is_same<float,out_pixel_type>::value || std::is_same<double,out_pixel_type>::value,
                "Output images must contain either float or double valued pixels");

            const_image_view<in_image_type> xx(xx_);
            const_image_view<in_image_type> xy(xy_);
            const_image_view<in_image_type> yy(yy_);

            DLIB_CASSERT(xx.nr() == xy.nr());
            DLIB_CASSERT(xx.nr() == yy.nr());
            DLIB_CASSERT(xx.nc() == xy.nc());
            DLIB_CASSERT(xx.nc() == yy.nc());

            image_view<out_image_type> saliency(saliency_);
            saliency.set_size(xx.nr(), xx.nc());

            for (long r = 0; r < xx.nr(); ++r)
            {
                for (long c = 0; c < xx.nc(); ++c)
                {
                    matrix<double,2,2> tmp;
                    tmp = xx[r][c], xy[r][c],
                          xy[r][c], yy[r][c];

                    matrix<double,2,1> e = real_eigenvalues(tmp);
                    saliency[r][c] = prod(lowerbound(e,0));
                }
            }
        }

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

    }

    #endif // DLIB_EDGE_DETECTOr_