Add higher order kernel support for Sobel operator

include/boost/gil/detail/math.hpp

@@ -1,5 +1,6 @@
 //
 // Copyright 2019 Olzhas Zhumabek <[email protected]>
+// Copyright 2021 Prathamesh Tagore <[email protected]>
 //
 // Use, modification and distribution are subject to the Boost Software License,
 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
@@ -8,17 +9,36 @@
 #ifndef BOOST_GIL_IMAGE_PROCESSING_DETAIL_MATH_HPP
 #define BOOST_GIL_IMAGE_PROCESSING_DETAIL_MATH_HPP
 
-#include <array>
 #include <boost/gil/extension/numeric/kernel.hpp>
+#include <array>
+#include <cmath>
+#include <vector>
 
 namespace boost { namespace gil { namespace detail {
 
+enum class kernel_type
+{
+    sobel_dx,
+    sobel_dy,
+};
+
 static constexpr double pi = 3.14159265358979323846;
 
 static constexpr std::array<float, 9> dx_sobel = {{-1, 0, 1, -2, 0, 2, -1, 0, 1}};
+static constexpr std::array<float, 25> dx_sobel2 = {{
+    -1,-2,0,2,1,-4,-8,0,8,4,-6,-12,0,12,6,-4,-8,0,8,4,-1,-2,0,2,1
+}}; 
+// In variable name "dx_sobel2", "2" indicates that the order of Sobel derivative in x-direction 
+// is 2.
 static constexpr std::array<float, 9> dx_scharr = {{-1, 0, 1, -1, 0, 1, -1, 0, 1}};
 static constexpr std::array<float, 9> dy_sobel = {{1, 2, 1, 0, 0, 0, -1, -2, -1}};
+static constexpr std::array<float, 25> dy_sobel2 = {{
+    -1,-4,-6,-4,-1,-2,-8,-12,-8,-2,0,0,0,0,0,2,8,12,8,2,1,4,6,4,1
+}};
+// In variable name "dy_sobel2", "2" indicates that the order of Sobel derivative in y-direction 
+// is 2.
 static constexpr std::array<float, 9> dy_scharr = {{1, 1, 1, 0, 0, 0, -1, -1, -1}};
+static const std::vector<std::vector<float>> smoothing_kernel {{1,2,1},{2,4,2},{1,2,1}};
 
 template <typename T, typename Allocator>
 inline detail::kernel_2d<T, Allocator> get_identity_kernel()
@@ -28,6 +48,158 @@ inline detail::kernel_2d<T, Allocator> get_identity_kernel()
     return kernel;
 }
 
+// Please refer https://stackoverflow.com/a/10032882/14958679 for getting an overview of the
+// concept applied for obtaining higher order Sobel kernels.
+
+/// \defgroup KernelGeneration
+/// \brief Contains documentation for functions used in kernel generation.
+///
+/// Separate functions are used for generating only those kernels whose dimensions are greater than
+/// 5x5. Smaller kernels are fed directly to the algorithm.
+///
+
+/// \addtogroup KernelGeneration
+/// @{
+
+/// \brief Produces higher order kernel vector by performing discrete convolution between lower
+/// order kernel vector and a smoothing kernel vector(kernel used for suppressing noise).
+/// \param kernel1 - First argument for kernel vector convolution.
+/// \param kernel2 - Second argument for kernel vector convolution.
+/// \tparam T1 - Type of first argument for kernel vector convolution.
+/// \tparam T2 - Type of second argument for kernel vector convolution.
+template<typename T1, typename T2>
+static auto kernel_convolve_impl(T1 kernel1, T2 kernel2) -> std::vector<std::vector<float>>
+{
+    size_t convolved_kernel_size = kernel1.size() + kernel2.size() - 1;
+    std::vector<std::vector<float>> convolved_kernel(convolved_kernel_size,
+        std::vector<float>(convolved_kernel_size)),dummy_kernel(convolved_kernel_size,
+        std::vector<float>(convolved_kernel_size));
+
+    // 'dummy_kernel' will be made by padding 'kernel1' with appropriate no. of rows and columns 
+    // containing zeros to match the size specified by 'convolved_kernel_size'.
+
+    // 'convolved kernel' will store the result obtained after applying convolution between 
+    // 'dummy_kernel' and 'kernel2'.
+
+    // 'padding_origin' will be used for determining indices of blocks from where padding begins 
+    // inside 'dummy_kernel'. It will be used for applying appropriate padding with zeros around 
+    // 'kernel1' to create 'dummy_kernel'.
+
+    std::ptrdiff_t padding_origin = (kernel2.size() - 1) / 2;
+    for(std::ptrdiff_t row = padding_origin;row < dummy_kernel.size() - padding_origin; ++row)
+    {
+        for(std::ptrdiff_t col = padding_origin;col < dummy_kernel.size() - padding_origin; ++col)
+        {
+            dummy_kernel[row][col] = kernel1[row - padding_origin][col - padding_origin];
+        }
+    }
+
+    std::ptrdiff_t flip_kernel_row, flip_kernel_col, row_boundary, col_boundary;
+    float aux_total;
+    for(std::ptrdiff_t dummy_row = 0;dummy_row < convolved_kernel_size; ++dummy_row)
+    {
+        for(std::ptrdiff_t dummy_col = 0;dummy_col < convolved_kernel_size; ++dummy_col)
+        {
+            aux_total = 0.0f;
+            for(std::ptrdiff_t kernel2_row = 0;kernel2_row < kernel2.size(); ++kernel2_row)
+            {
+                flip_kernel_row = kernel2.size() - 1 - kernel2_row;
+                for(std::ptrdiff_t kernel2_col = 0;kernel2_col < kernel2.size(); ++kernel2_col)
+                {
+                    flip_kernel_col = kernel2.size() - 1 - kernel2_col;
+                    row_boundary = dummy_row + kernel2.size()/2 - flip_kernel_row;
+                    col_boundary = dummy_col + kernel2.size()/2 - flip_kernel_col;
+
+                    // ignore input samples which are out of bound
+                    if (row_boundary >= 0 && row_boundary < convolved_kernel_size &&
+                        col_boundary >= 0 && col_boundary < convolved_kernel_size)
+                    {
+                        aux_total +=
+                            kernel2[flip_kernel_row][flip_kernel_col] *
+                            dummy_kernel[row_boundary][col_boundary];
+                    }
+                }
+            }
+            convolved_kernel[dummy_row][dummy_col] = aux_total;
+        }
+    }
+    return convolved_kernel;
+}
+
+/// \brief Fills kernel vector given as argument with a second order kernel in horizontal or
+/// vertical direction. The type of the kernel which is to be used for filling will be indicated 
+/// by the variable 'type'.
+/// \param kernel - Kernel vector which will be filled.
+/// \param type - Indicates the type of second order derivative kernel which is to be filled inside
+/// first argument.
+static void kernel_vector_fill(std::vector<std::vector<float>>& kernel, kernel_type type)
+{
+    if(type == kernel_type::sobel_dx)
+    {
+        for(std::ptrdiff_t row = 0;row < 5; ++row)
+        {
+            for(std::ptrdiff_t col = 0;col < 5; ++col)
+            {
+                kernel[row][col] = dx_sobel2[5 * row + col];
+            }
+        }
+    }
+    else if(type == kernel_type::sobel_dy)
+    {
+        for(std::ptrdiff_t row =0;row < 5; ++row)
+        {
+            for(std::ptrdiff_t col = 0;col < 5; ++col)
+            {
+                kernel[row][col] = dy_sobel2[5 * row + col];
+            }
+        }
+    }
+}
+
+/// \brief Passes parameters to 'kernel_convolve_impl()' repeatedly until kernel vector of desired
+/// order is obtained.
+/// \param order - Indicates order of derivative whose kernel vector is to be returned.
+/// \param type - Indicates the type of kernel vector which is to be returned.
+static auto kernel_convolve(unsigned int order, kernel_type type) -> std::vector<float>
+{
+    std::vector<float> convolved_kernel_flatten;
+    std::vector<std::vector<float>> convolved_kernel(5, std::vector<float>(5));
+
+    kernel_vector_fill(convolved_kernel, type);
+
+    std::vector<std::vector<float>>smoothing_dummy = smoothing_kernel;
+
+    // Variable 'smooth_repetition' will store the number of times we need to convolve 
+    // 'smoothing_dummy' with itself. This number when used as a power of 2 in its exponentiation,
+    // will result in a number which is the largest power of 2 smaller than 'order - 2'.
+    unsigned int smooth_repetition = (unsigned int)log2(order - 2);
+
+    for(unsigned int i = 0;i < smooth_repetition; ++i)
+    {
+        smoothing_dummy = kernel_convolve_impl(smoothing_dummy, smoothing_dummy);
+    }
+
+    convolved_kernel = kernel_convolve_impl(convolved_kernel, smoothing_dummy);
+
+    // Variable 'order_decrease' will store the amount of decrease in order obtained due to the above 
+    // optimization. It stores the largest power of 2 smaller than 'order - 2'.
+    unsigned int order_decrease = pow(2, smooth_repetition);
+    for(unsigned int i = 0;i < order - 2 - order_decrease; ++i)
+    {
+        convolved_kernel = kernel_convolve_impl(convolved_kernel, smoothing_kernel);
+    }
+
+    for(std::ptrdiff_t row = 0;row < convolved_kernel.size(); ++row)
+    {
+        for(std::ptrdiff_t col = 0;col < convolved_kernel.size(); ++col)
+        {
+            convolved_kernel_flatten.push_back(convolved_kernel[row][col]);
+        }
+    }
+
+    return convolved_kernel_flatten;
+}
+/// @}
 }}} // namespace boost::gil::detail
 
 #endif

include/boost/gil/image_processing/numeric.hpp

@@ -1,5 +1,6 @@
 //
 // Copyright 2019 Olzhas Zhumabek <[email protected]>
+// Copyright 2021 Prathamesh Tagore <[email protected]>
 //
 // Use, modification and distribution are subject to the Boost Software License,
 // Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
@@ -16,6 +17,7 @@
 // fixes ambigious call to std::abs, https://stackoverflow.com/a/30084734/4593721
 #include <cstdlib>
 #include <cmath>
+#include <vector>
 
 namespace boost { namespace gil {
 
@@ -161,24 +163,30 @@ inline detail::kernel_2d<T, Allocator> generate_gaussian_kernel(std::size_t side
 template <typename T = float, typename Allocator = std::allocator<T>>
 inline detail::kernel_2d<T, Allocator> generate_dx_sobel(unsigned int degree = 1)
 {
-    switch (degree)
+    if(degree == 0)
+        return detail::get_identity_kernel<T, Allocator>();
+    else if (degree == 1)
     {
-        case 0:
-        {
-            return detail::get_identity_kernel<T, Allocator>();
-        }
-        case 1:
-        {
-            detail::kernel_2d<T, Allocator> 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");
+        detail::kernel_2d<T, Allocator> result(3, 1, 1);
+        std::copy(detail::dx_sobel.begin(), detail::dx_sobel.end(), result.begin());
+        return result;
     }
-
-    //to not upset compiler
-    throw std::runtime_error("unreachable statement");
+    else if(degree == 2)
+    {
+        detail::kernel_2d<T, Allocator> result(5, 2, 2);
+        std::copy(detail::dx_sobel2.begin(), detail::dx_sobel2.end(), result.begin());
+        return result;
+    }
+    else if(degree <= 15)
+    {
+        detail::kernel_2d<T, Allocator> result(2 * degree + 1, degree, degree);
+        std::vector<float> dx_sobeln = detail::kernel_convolve(degree, detail::kernel_type::sobel_dx);
+        std::copy(dx_sobeln.begin(), dx_sobeln.end(), result.begin());
+        return result;
+    }
+    else 
+        throw std::length_error("Larger kernels than 31x31 may fail/delay other executions, hence "
+                                                                       "they are not yet provided");
 }
 
 /// \brief Generate Scharr operator in horizontal direction
@@ -221,24 +229,30 @@ inline detail::kernel_2d<T, Allocator> generate_dx_scharr(unsigned int degree =
 template <typename T = float, typename Allocator = std::allocator<T>>
 inline detail::kernel_2d<T, Allocator> generate_dy_sobel(unsigned int degree = 1)
 {
-    switch (degree)
+    if(degree == 0)
+        return detail::get_identity_kernel<T, Allocator>();
+    else if (degree == 1)
     {
-        case 0:
-        {
-            return detail::get_identity_kernel<T, Allocator>();
-        }
-        case 1:
-        {
-            detail::kernel_2d<T, Allocator> 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");
+        detail::kernel_2d<T, Allocator> result(3, 1, 1);
+        std::copy(detail::dy_sobel.begin(), detail::dy_sobel.end(), result.begin());
+        return result;
     }
-
-    //to not upset compiler
-    throw std::runtime_error("unreachable statement");
+    else if(degree == 2)
+    {
+        detail::kernel_2d<T, Allocator> result(5, 2, 2);
+        std::copy(detail::dy_sobel2.begin(), detail::dy_sobel2.end(), result.begin());
+        return result;
+    }
+    else if(degree <= 15)
+    {
+        detail::kernel_2d<T, Allocator> result(2 * degree + 1, degree, degree);
+        std::vector<float> dy_sobeln = detail::kernel_convolve(degree, detail::kernel_type::sobel_dy);
+        std::copy(dy_sobeln.begin(), dy_sobeln.end(), result.begin());
+        return result;
+    }
+    else
+        throw std::length_error("Larger kernels than 31x31 may fail/delay other executions, hence "
+                                                                       "they are not yet provided");
 }
 
 /// \brief Generate Scharr operator in vertical direction