Hessian corner detector

example/hessian.cpp

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+#include <boost/gil/image.hpp>
+#include <boost/gil/image_view.hpp>
+#include <boost/gil/image_processing/numeric.hpp>
+#include <boost/gil/image_processing/hessian.hpp>
+#include <boost/gil/extension/io/png.hpp>
+#include <vector>
+#include <functional>
+#include <set>
+#include <iostream>
+#include <fstream>
+
+namespace gil = boost::gil;
+
+// some images might produce artifacts
+// when converted to grayscale,
+// which was previously observed on
+// canny edge detector for test input
+// used for this example.
+// the algorithm here follows sRGB gamma definition
+// taken from here (luminance calculation):
+// https://en.wikipedia.org/wiki/Grayscale
+gil::gray8_image_t to_grayscale(gil::rgb8_view_t original)
+{
+    gil::gray8_image_t output_image(original.dimensions());
+    auto output = gil::view(output_image);
+    constexpr double max_channel_intensity = (std::numeric_limits<std::uint8_t>::max)();
+    for (long int y = 0; y < original.height(); ++y)
+    {
+        for (long int x = 0; x < original.width(); ++x)
+        {
+            // scale the values into range [0, 1] and calculate linear intensity
+            auto& p = original(x, y);
+            double red_intensity = p.at(std::integral_constant<int, 0>{})
+                / max_channel_intensity;
+            double green_intensity = p.at(std::integral_constant<int, 1>{})
+                / max_channel_intensity;
+            double blue_intensity = p.at(std::integral_constant<int, 2>{})
+                / max_channel_intensity;
+            auto linear_luminosity = 0.2126 * red_intensity
+                                    + 0.7152 * green_intensity
+                                    + 0.0722 * blue_intensity;
+
+            // perform gamma adjustment
+            double gamma_compressed_luminosity = 0;
+            if (linear_luminosity < 0.0031308)
+            {
+                gamma_compressed_luminosity = linear_luminosity * 12.92;
+            } else
+            {
+                gamma_compressed_luminosity = 1.055 * std::pow(linear_luminosity, 1 / 2.4) - 0.055;
+            }
+
+            // since now it is scaled, descale it back
+            output(x, y) = gamma_compressed_luminosity * max_channel_intensity;
+        }
+    }
+
+    return output_image;
+}
+
+void apply_gaussian_blur(gil::gray8_view_t input_view, gil::gray8_view_t output_view)
+{
+    constexpr static auto filter_height = 5ull;
+    constexpr static auto filter_width = 5ull;
+    constexpr static double filter[filter_height][filter_width] =
+    {
+        2,  4,  6,  4,  2,
+        4, 9, 12, 9,  4,
+        5, 12, 15, 12,  5,
+        4, 9, 12, 9,  4,
+        2,  4,  5,  4,  2,
+    };
+    constexpr double factor = 1.0 / 159;
+    constexpr double bias = 0.0;
+
+    const auto height = input_view.height();
+    const auto width = input_view.width();
+    for (std::ptrdiff_t x = 0; x < width; ++x)
+    {
+        for (std::ptrdiff_t y = 0; y < height; ++y)
+        {
+            double intensity = 0.0;
+            for (std::ptrdiff_t filter_y = 0; filter_y < filter_height; ++filter_y)
+            {
+                for (std::ptrdiff_t filter_x = 0; filter_x < filter_width; ++filter_x)
+                {
+                    int image_x = x - filter_width / 2 + filter_x;
+                    int image_y = y - filter_height / 2 + filter_y;
+                    if (image_x >= input_view.width() || image_x < 0 ||
+                        image_y >= input_view.height() || image_y < 0)
+                    {
+                        continue;
+                    }
+                    const auto& pixel = input_view(image_x, image_y);
+                    intensity += pixel.at(std::integral_constant<int, 0>{})
+                        * filter[filter_y][filter_x];
+                }
+            }
+            auto& pixel = output_view(gil::point_t(x, y));
+            pixel = (std::min)((std::max)(int(factor * intensity + bias), 0), 255);
+        }
+
+    }
+}
+
+void calculate_gradients(gil::gray8_view_t input,
+    gil::gray16_view_t x_gradient,
+    gil::gray16_view_t y_gradient)
+{
+    using x_coord_t = gil::gray16_view_t::x_coord_t;
+    using y_coord_t = gil::gray16_view_t::y_coord_t;
+    using pixel_t = std::remove_reference<decltype(x_gradient(0, 0))>::type;
+    using channel_t = typename std::remove_reference<
+                        decltype(
+                            std::declval<gil::gray16_pixel_t>().at(
+                                std::integral_constant<int, 0>{}
+                            )
+                        )
+                       >::type;
+
+    constexpr double x_kernel[3][3] =
+    {
+        {1, 0, -1},
+        {2, 0, -2},
+        {1, 0, -1}
+    };
+    constexpr double y_kernel[3][3] =
+    {
+        {1, 2, 1},
+        {0, 0, 0},
+        {-1, -2, -1}
+    };
+    constexpr auto chosen_channel = std::integral_constant<int, 0>{};
+    for (y_coord_t y = 1; y < input.height() - 1; ++y)
+    {
+        for (x_coord_t x = 1; x < input.width() - 1; ++x)
+        {
+            gil::gray16_pixel_t x_result;
+            boost::gil::static_transform(x_result, x_result,
+                [](channel_t) { return static_cast<channel_t>(0); });
+            gil::gray16_pixel_t y_result;
+            boost::gil::static_transform(y_result, y_result,
+                [](channel_t) { return static_cast<channel_t>(0); });
+            for (y_coord_t y_filter = 0; y_filter < 2; ++y_filter)
+            {
+                for (x_coord_t x_filter = 0; x_filter < 2; ++x_filter)
+                {
+                    auto adjusted_y = y + y_filter - 1;
+                    auto adjusted_x = x + x_filter - 1;
+                    x_result.at(std::integral_constant<int, 0>{}) +=
+                        input(adjusted_x, adjusted_y).at(chosen_channel)
+                        * x_kernel[y_filter][x_filter];
+                    y_result.at(std::integral_constant<int, 0>{}) +=
+                        input(adjusted_x, adjusted_y).at(chosen_channel)
+                        * y_kernel[y_filter][x_filter];
+                }
+            }
+            x_gradient(x, y) = static_cast<std::uint8_t>(x_result.at(chosen_channel));
+            y_gradient(x, y) = static_cast<std::uint8_t>(y_result.at(chosen_channel));
+        }
+    }
+}
+
+std::vector<gil::point_t> suppress(
+    gil::gray32f_view_t harris_response,
+    double harris_response_threshold)
+{
+    std::vector<gil::point_t> corner_points;
+    for (gil::gray32f_view_t::coord_t y = 1; y < harris_response.height() - 1; ++y)
+    {
+        for (gil::gray32f_view_t::coord_t x = 1; x < harris_response.width() - 1; ++x)
+        {
+            auto value = [](gil::gray32f_pixel_t pixel) {
+                return pixel.at(std::integral_constant<int, 0>{});
+            };
+            double values[9] = {
+                value(harris_response(x - 1, y - 1)),
+                value(harris_response(x, y - 1)),
+                value(harris_response(x + 1, y - 1)),
+                value(harris_response(x - 1, y)),
+                value(harris_response(x, y)),
+                value(harris_response(x + 1, y)),
+                value(harris_response(x - 1, y + 1)),
+                value(harris_response(x, y + 1)),
+                value(harris_response(x + 1, y + 1))
+            };
+
+            auto maxima = *std::max_element(
+                values,
+                values + 9,
+                [](double lhs, double rhs)
+                {
+                    return lhs < rhs;
+                }
+            );
+
+            if (maxima == value(harris_response(x, y))
+                && std::count(values, values + 9, maxima) == 1
+                && maxima >= harris_response_threshold)
+            {
+                corner_points.emplace_back(x, y);
+            }
+        }
+    }
+
+    return corner_points;
+}
+
+int main(int argc, char* argv[]) {
+    if (argc != 5)
+    {
+        std::cout << "usage: " << argv[0] << " <input.png> <odd-window-size>"
+            " <hessian-response-threshold> <output.png>\n";
+        return -1;
+    }
+
+    long int window_size = std::stoi(argv[2]);
+    long hessian_determinant_threshold = std::stol(argv[3]);
+
+    gil::rgb8_image_t input_image;
+
+    gil::read_image(argv[1], input_image, gil::png_tag{});
+
+    auto input_view = gil::view(input_image);
+    auto grayscaled = to_grayscale(input_view);
+    gil::gray8_image_t smoothed_image(grayscaled.dimensions());
+    auto smoothed = gil::view(smoothed_image);
+    apply_gaussian_blur(gil::view(grayscaled), smoothed);
+    gil::gray16_image_t x_gradient_image(grayscaled.dimensions());
+    gil::gray16_image_t y_gradient_image(grayscaled.dimensions());
+
+    auto x_gradient = gil::view(x_gradient_image);
+    auto y_gradient = gil::view(y_gradient_image);
+    calculate_gradients(smoothed, x_gradient, y_gradient);
+
+    gil::gray32f_image_t m11(x_gradient.dimensions());
+    gil::gray32f_image_t m12_21(x_gradient.dimensions());
+    gil::gray32f_image_t m22(x_gradient.dimensions());
+    gil::compute_hessian_entries(
+        x_gradient,
+        y_gradient,
+        gil::view(m11),
+        gil::view(m12_21),
+        gil::view(m22)
+    );
+
+    gil::gray32f_image_t hessian_response(x_gradient.dimensions());
+    gil::gray32f_image_t gaussian_kernel(gil::point_t(5, 5));
+    gil::generate_gaussian_kernel(gil::view(gaussian_kernel), 0.84089642);
+    gil::compute_hessian_responses(
+        gil::view(m11),
+        gil::view(m12_21),
+        gil::view(m22),
+        gil::view(gaussian_kernel),
+        gil::view(hessian_response)
+    );
+
+    auto corner_points = suppress(gil::view(hessian_response), hessian_determinant_threshold);
+    for (auto point: corner_points) {
+        input_view(point) = gil::rgb8_pixel_t(0, 0, 0);
+        input_view(point).at(std::integral_constant<int, 1>{}) = 255;
+    }
+    gil::write_view(argv[4], input_view, gil::png_tag{});
+}

include/boost/gil/image_processing/hessian.hpp

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+#ifndef BOOST_GIL_IMAGE_PROCESSING_HESSIAN_HPP
+#define BOOST_GIL_IMAGE_PROCESSING_HESSIAN_HPP
+
+#include <boost/gil/image_view.hpp>
+#include <boost/gil/typedefs.hpp>
+#include <stdexcept>
+
+namespace boost { namespace gil {
+
+/// \brief Computes Hessian response
+///
+/// Computes Hessian response based on computed entries of Hessian matrix, e.g. second order
+/// derivates in x and y, and derivatives in both x, y.
+/// d stands for derivative, and x or y stand for derivative direction. For example,
+/// ddxx means taking two derivatives (gradients) in horizontal direction.
+/// Weights change perception of surroinding pixels.
+/// Additional filtering is strongly advised.
+template <typename GradientView, typename Weights, typename OutputView>
+inline void compute_hessian_responses(
+    GradientView ddxx,
+    GradientView dxdy,
+    GradientView ddyy,
+    Weights weights,
+    OutputView dst)
+{
+    if (ddxx.dimensions() != ddyy.dimensions()
+        || ddyy.dimensions() != dxdy.dimensions()
+        || dxdy.dimensions() != dst.dimensions()
+        || weights.width() != weights.height()
+        || weights.width() % 2 != 1)
+    {
+        throw std::invalid_argument("dimensions of views are not the same"
+            " or weights don't have equal width and height"
+            " or weights' dimensions are not odd");
+    }
+    // Use pixel type of output, as values will be written to output
+    using pixel_t = typename std::remove_reference<decltype(std::declval<OutputView>()(0, 0))>::type;
+
+    using channel_t = typename std::remove_reference
+        <
+            decltype(std::declval<pixel_t>().at(std::integral_constant<int, 0>{}))
+        >::type;
+
+    auto half_size = weights.width() / 2;
+    for (auto y = half_size; y < dst.height() - half_size; ++y)
+    {
+        for (auto x = half_size; x < dst.width() - half_size; ++x)
+        {
+            auto ddxx_i = channel_t();
+            auto ddyy_i = channel_t();
+            auto dxdy_i = channel_t();
+            constexpr std::integral_constant<int, 0> chosen_channel{};
+            for (typename OutputView::coord_t w_y = 0; w_y < weights.height(); ++w_y)
+            {
+                for (typename OutputView::coord_t w_x = 0; w_x < weights.width(); ++w_x)
+                {
+                    ddxx_i += ddxx(x + w_x - half_size, y + w_y - half_size)
+                        .at(std::integral_constant<int, 0>{})
+                         * weights(w_x, w_y).at(std::integral_constant<int, 0>{});
+                    ddyy_i += ddyy(x + w_x - half_size, y + w_y - half_size)
+                        .at(std::integral_constant<int, 0>{})
+                         * weights(w_x, w_y).at(std::integral_constant<int, 0>{});
+                    dxdy_i += dxdy(x + w_x - half_size, y + w_y - half_size)
+                        .at(std::integral_constant<int, 0>{})
+                         * weights(w_x, w_y).at(std::integral_constant<int, 0>{});
+                }
+            }
+            auto determinant = ddxx_i * ddyy_i - dxdy_i * dxdy_i;
+            dst(x, y).at(std::integral_constant<int, 0>{}) = determinant;
+        }
+    }
+}
+
+}} // namespace boost::gil
+
+#endif