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// // Copyright 2019 Olzhas Zhumabek // Copyright 2021 Pranam Lashkari // // 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_NUMERIC_HPP #define BOOST_GIL_IMAGE_PROCESSING_NUMERIC_HPP #include #include #include #include #include // fixes ambiguous call to std::abs, https://stackoverflow.com/a/30084734/4593721 #include #include namespace boost { namespace gil { /// \defgroup ImageProcessingMath /// \brief Math operations for IP algorithms /// /// This is mostly handful of mathemtical operations that are required by other /// image processing algorithms /// /// \brief Normalized cardinal sine /// \ingroup ImageProcessingMath /// /// normalized_sinc(x) = sin(pi * x) / (pi * x) /// inline double normalized_sinc(double x) { return std::sin(x * boost::gil::detail::pi) / (x * boost::gil::detail::pi); } /// \brief Lanczos response at point x /// \ingroup ImageProcessingMath /// /// Lanczos response is defined as: /// x == 0: 1 /// -a < x && x < a: 0 /// otherwise: normalized_sinc(x) / normalized_sinc(x / a) inline double lanczos(double x, std::ptrdiff_t a) { // means == but <= avoids compiler warning if (0 <= x && x <= 0) return 1; if (static_cast(-a) < x && x < static_cast(a)) return normalized_sinc(x) / normalized_sinc(x / static_cast(a)); return 0; } #if BOOST_WORKAROUND(BOOST_MSVC, >= 1400) #pragma warning(push) #pragma warning(disable:4244) // 'argument': conversion from 'const Channel' to 'BaseChannelValue', possible loss of data #endif inline void compute_tensor_entries( boost::gil::gray16s_view_t dx, boost::gil::gray16s_view_t dy, boost::gil::gray32f_view_t m11, boost::gil::gray32f_view_t m12_21, boost::gil::gray32f_view_t m22) { for (std::ptrdiff_t y = 0; y < dx.height(); ++y) { for (std::ptrdiff_t x = 0; x < dx.width(); ++x) { auto dx_value = dx(x, y); auto dy_value = dy(x, y); m11(x, y) = dx_value * dx_value; m12_21(x, y) = dx_value * dy_value; m22(x, y) = dy_value * dy_value; } } } #if BOOST_WORKAROUND(BOOST_MSVC, >= 1400) #pragma warning(pop) #endif /// \brief Generate mean kernel /// \ingroup ImageProcessingMath /// /// Fills supplied view with normalized mean /// in which all entries will be equal to /// \code 1 / (dst.size()) \endcode template > inline auto generate_normalized_mean(std::size_t side_length) -> detail::kernel_2d { if (side_length % 2 != 1) throw std::invalid_argument("kernel dimensions should be odd and equal"); const float entry = 1.0f / static_cast(side_length * side_length); detail::kernel_2d result(side_length, side_length / 2, side_length / 2); for (auto& cell: result) { cell = entry; } return result; } /// \brief Generate kernel with all 1s /// \ingroup ImageProcessingMath /// /// Fills supplied view with 1s (ones) template > inline auto generate_unnormalized_mean(std::size_t side_length) -> detail::kernel_2d { if (side_length % 2 != 1) throw std::invalid_argument("kernel dimensions should be odd and equal"); detail::kernel_2d result(side_length, side_length / 2, side_length / 2); for (auto& cell: result) { cell = 1.0f; } return result; } /// \brief Generate Gaussian kernel /// \ingroup ImageProcessingMath /// /// Fills supplied view with values taken from Gaussian distribution. See /// https://en.wikipedia.org/wiki/Gaussian_blur template > inline auto generate_gaussian_kernel(std::size_t side_length, double sigma) -> detail::kernel_2d { if (side_length % 2 != 1) throw std::invalid_argument("kernel dimensions should be odd and equal"); const double denominator = 2 * boost::gil::detail::pi * sigma * sigma; auto const middle = side_length / 2; std::vector values(side_length * side_length); T sum{0}; for (std::size_t y = 0; y < side_length; ++y) { for (std::size_t x = 0; x < side_length; ++x) { const auto delta_x = x - middle; const auto delta_y = y - middle; const auto power = static_cast(delta_x * delta_x + delta_y * delta_y) / (2 * sigma * sigma); const double nominator = std::exp(-power); const auto value = static_cast(nominator / denominator); values[y * side_length + x] = value; sum += value; } } // normalize so that Gaussian kernel sums up to 1. std::transform(values.begin(), values.end(), values.begin(), [&sum](const auto & v) { return v/sum; }); return detail::kernel_2d(values.begin(), values.size(), middle, middle); } /// \brief Generates Sobel operator in horizontal direction /// \ingroup ImageProcessingMath /// /// Generates a kernel which will represent Sobel operator in /// horizontal direction of specified degree (no need to convolve multiple times /// to obtain the desired degree). /// https://www.researchgate.net/publication/239398674_An_Isotropic_3_3_Image_Gradient_Operator template > inline auto generate_dx_sobel(unsigned int degree = 1) -> detail::kernel_2d { switch (degree) { case 0: { return detail::get_identity_kernel(); } case 1: { detail::kernel_2d result(3, 1, 1); std::copy(detail::dx_sobel.begin(), detail::dx_sobel.end(), result.begin()); return result; } default: throw std::logic_error("not supported yet"); } //to not upset compiler throw std::runtime_error("unreachable statement"); } /// \brief Generate Scharr operator in horizontal direction /// \ingroup ImageProcessingMath /// /// Generates a kernel which will represent Scharr operator in /// horizontal direction of specified degree (no need to convolve multiple times /// to obtain the desired degree). /// https://www.researchgate.net/profile/Hanno_Scharr/publication/220955743_Optimal_Filters_for_Extended_Optical_Flow/links/004635151972eda98f000000/Optimal-Filters-for-Extended-Optical-Flow.pdf template > inline auto generate_dx_scharr(unsigned int degree = 1) -> detail::kernel_2d { switch (degree) { case 0: { return detail::get_identity_kernel(); } case 1: { detail::kernel_2d result(3, 1, 1); std::copy(detail::dx_scharr.begin(), detail::dx_scharr.end(), result.begin()); return result; } default: throw std::logic_error("not supported yet"); } //to not upset compiler throw std::runtime_error("unreachable statement"); } /// \brief Generates Sobel operator in vertical direction /// \ingroup ImageProcessingMath /// /// Generates a kernel which will represent Sobel operator in /// vertical direction of specified degree (no need to convolve multiple times /// to obtain the desired degree). /// https://www.researchgate.net/publication/239398674_An_Isotropic_3_3_Image_Gradient_Operator template > inline auto generate_dy_sobel(unsigned int degree = 1) -> detail::kernel_2d { switch (degree) { case 0: { return detail::get_identity_kernel(); } case 1: { detail::kernel_2d result(3, 1, 1); std::copy(detail::dy_sobel.begin(), detail::dy_sobel.end(), result.begin()); return result; } default: throw std::logic_error("not supported yet"); } //to not upset compiler throw std::runtime_error("unreachable statement"); } /// \brief Generate Scharr operator in vertical direction /// \ingroup ImageProcessingMath /// /// Generates a kernel which will represent Scharr operator in /// vertical direction of specified degree (no need to convolve multiple times /// to obtain the desired degree). /// https://www.researchgate.net/profile/Hanno_Scharr/publication/220955743_Optimal_Filters_for_Extended_Optical_Flow/links/004635151972eda98f000000/Optimal-Filters-for-Extended-Optical-Flow.pdf template > inline auto generate_dy_scharr(unsigned int degree = 1) -> detail::kernel_2d { switch (degree) { case 0: { return detail::get_identity_kernel(); } case 1: { detail::kernel_2d result(3, 1, 1); std::copy(detail::dy_scharr.begin(), detail::dy_scharr.end(), result.begin()); return result; } default: throw std::logic_error("not supported yet"); } //to not upset compiler throw std::runtime_error("unreachable statement"); } /// \brief Compute xy gradient, and second order x and y gradients /// \ingroup ImageProcessingMath /// /// Hessian matrix is defined as a matrix of partial derivates /// for 2d case, it is [[ddxx, dxdy], [dxdy, ddyy]. /// d stands for derivative, and x or y stand for direction. /// For example, dx stands for derivative (gradient) in horizontal /// direction, and ddxx means second order derivative in horizon direction /// https://en.wikipedia.org/wiki/Hessian_matrix template inline void compute_hessian_entries( GradientView dx, GradientView dy, OutputView ddxx, OutputView dxdy, OutputView ddyy) { auto sobel_x = generate_dx_sobel(); auto sobel_y = generate_dy_sobel(); detail::convolve_2d(dx, sobel_x, ddxx); detail::convolve_2d(dx, sobel_y, dxdy); detail::convolve_2d(dy, sobel_y, ddyy); } }} // namespace boost::gil #endif