diffusion.hpp

//
// Copyright 2020 Olzhas Zhumabek <anonymous.from.applecity@gmail.com>
// Copyright 2021 Pranam Lashkari <plashkari628@gmail.com>
//
// Use, modification and distribution are subject to the Boost Software License,
// Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//
 
#ifndef BOOST_GIL_IMAGE_PROCESSING_DIFFUSION_HPP
#define BOOST_GIL_IMAGE_PROCESSING_DIFFUSION_HPP
 
#include "boost/gil/detail/math.hpp"
#include <boost/gil/algorithm.hpp>
#include <boost/gil/color_base_algorithm.hpp>
#include <boost/gil/image.hpp>
#include <boost/gil/image_view.hpp>
#include <boost/gil/image_view_factory.hpp>
#include <boost/gil/pixel.hpp>
#include <boost/gil/point.hpp>
#include <boost/gil/typedefs.hpp>
#include <functional>
#include <numeric>
#include <vector>
 
namespace boost { namespace gil {
namespace conductivity {
struct perona_malik_conductivity
{
    double kappa;
    template <typename Pixel>
    Pixel operator()(Pixel input)
    {
        using channel_type = typename channel_type<Pixel>::type;
        // C++11 doesn't seem to capture members
        static_transform(input, input, [this](channel_type value) {
            value /= kappa;
            return std::exp(-std::abs(value));
        });
 
        return input;
    }
};
 
struct gaussian_conductivity
{
    double kappa;
    template <typename Pixel>
    Pixel operator()(Pixel input)
    {
        using channel_type = typename channel_type<Pixel>::type;
        // C++11 doesn't seem to capture members
        static_transform(input, input, [this](channel_type value) {
            value /= kappa;
            return std::exp(-value * value);
        });
 
        return input;
    }
};
 
struct wide_regions_conductivity
{
    double kappa;
    template <typename Pixel>
    Pixel operator()(Pixel input)
    {
        using channel_type = typename channel_type<Pixel>::type;
        // C++11 doesn't seem to capture members
        static_transform(input, input, [this](channel_type value) {
            value /= kappa;
            return 1.0 / (1.0 + value * value);
        });
 
        return input;
    }
};
 
struct more_wide_regions_conductivity
{
    double kappa;
    template <typename Pixel>
    Pixel operator()(Pixel input)
    {
        using channel_type = typename channel_type<Pixel>::type;
        // C++11 doesn't seem to capture members
        static_transform(input, input, [this](channel_type value) {
            value /= kappa;
            return 1.0 / std::sqrt((1.0 + value * value));
        });
 
        return input;
    }
};
} // namespace diffusion
 
namespace laplace_function {
// The functions assume clockwise enumeration of stencil points, as such
// NW   North NE          0 1 2      (-1, -1) (0, -1) (+1, -1)
// West       East   ===> 7   3 ===> (-1, 0)          (+1, 0)
// SW   South SE          6 5 4      (-1, +1) (0, +1) (+1, +1)
 
inline std::array<gil::point_t, 8> get_directed_offsets()
{
    return {point_t{-1, -1}, point_t{0, -1}, point_t{+1, -1}, point_t{+1, 0},
            point_t{+1, +1}, point_t{0, +1}, point_t{-1, +1}, point_t{-1, 0}};
}
 
template <typename PixelType>
using stencil_type = std::array<PixelType, 8>;
 
struct stencil_5points
{
    double delta_t = 0.25;
 
    template <typename SubImageView>
    stencil_type<typename SubImageView::value_type> compute_laplace(SubImageView view,
                                                                    point_t origin)
    {
        auto current = view(origin);
        stencil_type<typename SubImageView::value_type> stencil;
        using channel_type = typename channel_type<typename SubImageView::value_type>::type;
        std::array<gil::point_t, 8> offsets(get_directed_offsets());
        typename SubImageView::value_type zero_pixel;
        static_fill(zero_pixel, 0);
        for (std::size_t index = 0; index < offsets.size(); ++index)
        {
            if (index % 2 != 0)
            {
                static_transform(view(origin.x + offsets[index].x, origin.y + offsets[index].y),
                                 current, stencil[index], std::minus<channel_type>{});
            }
            else
            {
                stencil[index] = zero_pixel;
            }
        }
        return stencil;
    }
 
    template <typename Pixel>
    Pixel reduce(const stencil_type<Pixel>& stencil)
    {
        auto first = stencil.begin();
        auto last = stencil.end();
        using channel_type = typename channel_type<Pixel>::type;
        auto result = []() {
            Pixel zero_pixel;
            static_fill(zero_pixel, channel_type(0));
            return zero_pixel;
        }();
 
        for (std::size_t index : {1u, 3u, 5u, 7u})
        {
            static_transform(result, stencil[index], result, std::plus<channel_type>{});
        }
        Pixel delta_t_pixel;
        static_fill(delta_t_pixel, delta_t);
        static_transform(result, delta_t_pixel, result, std::multiplies<channel_type>{});
 
        return result;
    }
};
 
struct stencil_9points_standard
{
    double delta_t = 0.125;
 
    template <typename SubImageView>
    stencil_type<typename SubImageView::value_type> compute_laplace(SubImageView view,
                                                                    point_t origin)
    {
        stencil_type<typename SubImageView::value_type> stencil;
        auto out = stencil.begin();
        auto current = view(origin);
        using channel_type = typename channel_type<typename SubImageView::value_type>::type;
        std::array<gil::point_t, 8> offsets(get_directed_offsets());
        for (auto offset : offsets)
        {
            static_transform(view(origin.x + offset.x, origin.y + offset.y), current, *out++,
                             std::minus<channel_type>{});
        }
 
        return stencil;
    }
 
    template <typename Pixel>
    Pixel reduce(const stencil_type<Pixel>& stencil)
    {
        using channel_type = typename channel_type<Pixel>::type;
        auto result = []() {
            Pixel zero_pixel;
            static_fill(zero_pixel, channel_type(0));
            return zero_pixel;
        }();
        for (std::size_t index : {1u, 3u, 5u, 7u})
        {
            static_transform(result, stencil[index], result, std::plus<channel_type>{});
        }
 
        for (std::size_t index : {0u, 2u, 4u, 6u})
        {
            Pixel half_pixel;
            static_fill(half_pixel, channel_type(1 / 2.0));
            static_transform(stencil[index], half_pixel, half_pixel,
                             std::multiplies<channel_type>{});
            static_transform(result, half_pixel, result, std::plus<channel_type>{});
        }
 
        Pixel delta_t_pixel;
        static_fill(delta_t_pixel, delta_t);
        static_transform(result, delta_t_pixel, result, std::multiplies<channel_type>{});
 
        return result;
    }
};
} // namespace laplace_function
 
namespace brightness_function {
using laplace_function::stencil_type;
struct identity
{
    template <typename Pixel>
    stencil_type<Pixel> operator()(const stencil_type<Pixel>& stencil)
    {
        return stencil;
    }
};
 
// TODO: Figure out how to implement color gradient brightness, as it
// seems to need dx and dy using sobel or scharr kernels
 
struct rgb_luminance
{
    using pixel_type = rgb32f_pixel_t;
    stencil_type<pixel_type> operator()(const stencil_type<pixel_type>& stencil)
    {
        stencil_type<pixel_type> output;
        std::transform(stencil.begin(), stencil.end(), output.begin(), [](const pixel_type& pixel) {
            float32_t luminance = 0.2126f * pixel[0] + 0.7152f * pixel[1] + 0.0722f * pixel[2];
            pixel_type result_pixel;
            static_fill(result_pixel, luminance);
            return result_pixel;
        });
        return output;
    }
};
 
} // namespace brightness_function
 
enum class matlab_connectivity
{
    minimal,
    maximal
};
 
enum class matlab_conduction_method
{
    exponential,
    quadratic
};
 
template <typename InputView, typename OutputView>
void classic_anisotropic_diffusion(const InputView& input, const OutputView& output,
                                   unsigned int num_iter, double kappa)
{
    anisotropic_diffusion(input, output, num_iter, laplace_function::stencil_5points{},
                          brightness_function::identity{},
                          conductivity::perona_malik_conductivity{kappa});
}
 
template <typename InputView, typename OutputView>
void matlab_anisotropic_diffusion(const InputView& input, const OutputView& output,
                                  unsigned int num_iter, double kappa,
                                  matlab_connectivity connectivity,
                                  matlab_conduction_method conduction_method)
{
    if (connectivity == matlab_connectivity::minimal)
    {
        if (conduction_method == matlab_conduction_method::exponential)
        {
            anisotropic_diffusion(input, output, num_iter, laplace_function::stencil_5points{},
                                  brightness_function::identity{},
                                  conductivity::gaussian_conductivity{kappa});
        }
        else if (conduction_method == matlab_conduction_method::quadratic)
        {
            anisotropic_diffusion(input, output, num_iter, laplace_function::stencil_5points{},
                                  brightness_function::identity{},
                                  conductivity::gaussian_conductivity{kappa});
        }
        else
        {
            throw std::logic_error("unhandled conduction method found");
        }
    }
    else if (connectivity == matlab_connectivity::maximal)
    {
        if (conduction_method == matlab_conduction_method::exponential)
        {
            anisotropic_diffusion(input, output, num_iter, laplace_function::stencil_5points{},
                                  brightness_function::identity{},
                                  conductivity::gaussian_conductivity{kappa});
        }
        else if (conduction_method == matlab_conduction_method::quadratic)
        {
            anisotropic_diffusion(input, output, num_iter, laplace_function::stencil_5points{},
                                  brightness_function::identity{},
                                  conductivity::gaussian_conductivity{kappa});
        }
        else
        {
            throw std::logic_error("unhandled conduction method found");
        }
    }
    else
    {
        throw std::logic_error("unhandled connectivity found");
    }
}
 
template <typename InputView, typename OutputView>
void default_anisotropic_diffusion(const InputView& input, const OutputView& output,
                                   unsigned int num_iter, double kappa)
{
    anisotropic_diffusion(input, output, num_iter, laplace_function::stencil_9points_standard{},
                          brightness_function::identity{}, conductivity::gaussian_conductivity{kappa});
}
 
template <typename InputView, typename OutputView,
          typename LaplaceStrategy = laplace_function::stencil_9points_standard,
          typename BrightnessFunction = brightness_function::identity,
          typename DiffusivityFunction = conductivity::gaussian_conductivity>
void anisotropic_diffusion(const InputView& input, const OutputView& output, unsigned int num_iter,
                           LaplaceStrategy laplace, BrightnessFunction brightness,
                           DiffusivityFunction diffusivity)
{
    using input_pixel_type = typename InputView::value_type;
    using pixel_type = typename OutputView::value_type;
    using channel_type = typename channel_type<pixel_type>::type;
    using computation_image = image<pixel_type>;
    const auto width = input.width();
    const auto height = input.height();
    const point_t dims(width, height);
    const auto zero_pixel = []() {
        pixel_type pixel;
        static_fill(pixel, static_cast<channel_type>(0));
 
        return pixel;
    }();
    computation_image result_image(width + 2, height + 2, zero_pixel);
    auto result = view(result_image);
    computation_image scratch_result_image(width + 2, height + 2, zero_pixel);
    auto scratch_result = view(scratch_result_image);
    transform_pixels(input, subimage_view(result, 1, 1, width, height),
                     [](const input_pixel_type& pixel) {
                         pixel_type converted;
                         for (std::size_t i = 0; i < num_channels<pixel_type>{}; ++i)
                         {
                             converted[i] = pixel[i];
                         }
                         return converted;
                     });
 
    for (unsigned int iteration = 0; iteration < num_iter; ++iteration)
    {
        for (std::ptrdiff_t relative_y = 0; relative_y < height; ++relative_y)
        {
            for (std::ptrdiff_t relative_x = 0; relative_x < width; ++relative_x)
            {
                auto x = relative_x + 1;
                auto y = relative_y + 1;
                auto stencil = laplace.compute_laplace(result, point_t(x, y));
                auto brightness_stencil = brightness(stencil);
                laplace_function::stencil_type<pixel_type> diffusivity_stencil;
                std::transform(brightness_stencil.begin(), brightness_stencil.end(),
                               diffusivity_stencil.begin(), diffusivity);
                laplace_function::stencil_type<pixel_type> product_stencil;
                std::transform(stencil.begin(), stencil.end(), diffusivity_stencil.begin(),
                               product_stencil.begin(), [](pixel_type lhs, pixel_type rhs) {
                                   static_transform(lhs, rhs, lhs, std::multiplies<channel_type>{});
                                   return lhs;
                               });
                static_transform(result(x, y), laplace.reduce(product_stencil),
                                 scratch_result(x, y), std::plus<channel_type>{});
            }
        }
        using std::swap;
        swap(result, scratch_result);
    }
 
    copy_pixels(subimage_view(result, 1, 1, width, height), output);
}
 
}} // namespace boost::gil
 
#endif