ImageProcessingMath

Math operations for IP algorithms. More...

Functions
double	lanczos (double x, std::ptrdiff_t a)
	Lanczos response at point x. More...
template<typename T = float, typename Allocator = std::allocator<T>>
auto	generate_normalized_mean (std::size_t side_length) -> detail::kernel_2d< T, Allocator >
	Generate mean kernel. More...
template<typename T = float, typename Allocator = std::allocator<T>>
auto	generate_unnormalized_mean (std::size_t side_length) -> detail::kernel_2d< T, Allocator >
	Generate kernel with all 1s. More...
template<typename T = float, typename Allocator = std::allocator<T>>
auto	generate_gaussian_kernel (std::size_t side_length, double sigma) -> detail::kernel_2d< T, Allocator >
	Generate Gaussian kernel. More...
template<typename T = float, typename Allocator = std::allocator<T>>
auto	generate_dx_sobel (unsigned int degree=1) -> detail::kernel_2d< T, Allocator >
	Generates Sobel operator in horizontal direction. More...
template<typename T = float, typename Allocator = std::allocator<T>>
auto	generate_dx_scharr (unsigned int degree=1) -> detail::kernel_2d< T, Allocator >
	Generate Scharr operator in horizontal direction. More...
template<typename T = float, typename Allocator = std::allocator<T>>
auto	generate_dy_sobel (unsigned int degree=1) -> detail::kernel_2d< T, Allocator >
	Generates Sobel operator in vertical direction. More...
template<typename T = float, typename Allocator = std::allocator<T>>
auto	generate_dy_scharr (unsigned int degree=1) -> detail::kernel_2d< T, Allocator >
	Generate Scharr operator in vertical direction. More...
template<typename GradientView , typename OutputView >
void	compute_hessian_entries (GradientView dx, GradientView dy, OutputView ddxx, OutputView dxdy, OutputView ddyy)
	Compute xy gradient, and second order x and y gradients. More...

Detailed Description

Math operations for IP algorithms.

This is mostly handful of mathemtical operations that are required by other image processing algorithms

Normalized cardinal sine

normalized_sinc(x) = sin(pi * x) / (pi * x)

Function Documentation

compute_hessian_entries()

void boost::gil::compute_hessian_entries ( GradientView  dx, GradientView  dy, OutputView  ddxx, OutputView  dxdy, OutputView  ddyy  )

inline

Compute xy gradient, and second order x and y gradients.

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

generate_dx_scharr()

auto boost::gil::generate_dx_scharr ( unsigned int  degree = 1 ) -> detail::kernel_2d<T, Allocator>

inline

Generate Scharr operator in horizontal direction.

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

generate_dx_sobel()

auto boost::gil::generate_dx_sobel ( unsigned int  degree = 1 ) -> detail::kernel_2d<T, Allocator>

inline

Generates Sobel operator in horizontal direction.

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

generate_dy_scharr()

auto boost::gil::generate_dy_scharr ( unsigned int  degree = 1 ) -> detail::kernel_2d<T, Allocator>

inline

Generate Scharr operator in vertical direction.

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

generate_dy_sobel()

auto boost::gil::generate_dy_sobel ( unsigned int  degree = 1 ) -> detail::kernel_2d<T, Allocator>

inline

Generates Sobel operator in vertical direction.

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

generate_gaussian_kernel()

auto boost::gil::generate_gaussian_kernel ( std::size_t  side_length, double  sigma  ) -> detail::kernel_2d<T, Allocator>

inline

Generate Gaussian kernel.

Fills supplied view with values taken from Gaussian distribution. See https://en.wikipedia.org/wiki/Gaussian_blur

generate_normalized_mean()

auto boost::gil::generate_normalized_mean ( std::size_t  side_length ) -> detail::kernel_2d<T, Allocator>

inline

Generate mean kernel.

Fills supplied view with normalized mean in which all entries will be equal to

1 / (dst.size()) 

generate_unnormalized_mean()

auto boost::gil::generate_unnormalized_mean ( std::size_t  side_length ) -> detail::kernel_2d<T, Allocator>

inline

Generate kernel with all 1s.

Fills supplied view with 1s (ones)

lanczos()

double boost::gil::lanczos ( double  x, std::ptrdiff_t  a  )

inline

Lanczos response at point x.

Lanczos response is defined as: x == 0: 1 -a < x && x < a: 0 otherwise: normalized_sinc(x) / normalized_sinc(x / a)