Toolbox to compute statistics. More...

Namespaces
namespace	array_type
	Container type.

namespace	kernel
	Collect kernels.

Classes
class	ClusterLabeller
	(Incrementally) Label clusters (0 as background, 1..n as labels). More...

class	Ensemble
	Compute ensemble averaged statistics, by repetitively calling the member-function of a certain statistical measure with different data. More...

Enumerations
enum class	path_mode { Bresenham , actual , full }
	Different methods to compute a pixel-path. More...

Functions
array_type::tensor< int, 2 >	path (const array_type::tensor< int, 1 > &x0, const array_type::tensor< int, 1 > &x1, path_mode mode=path_mode::Bresenham)
	Compute a path between two pixels.

array_type::array< int >	dummy_circles (const std::vector< size_t > &shape, const array_type::tensor< int, 1 > &row, const array_type::tensor< int, 1 > &col, const array_type::tensor< int, 1 > &r, bool periodic=true)
	Dummy image with circles.

array_type::array< int >	dummy_circles (const std::vector< size_t > &shape, bool periodic=true, uint64_t seed=0)
	Dummy image with circles.

template<class T , class S , std::enable_if_t< std::is_integral< typename T::value_type >::value &&std::is_integral< typename S::value_type >::value, int > = 0>
T	dilate (const T &f, const S &kernel, const array_type::tensor< size_t, 1 > &iterations, bool periodic=true)
	Dilate image.

template<class T , std::enable_if_t< std::is_integral< typename T::value_type >::value, int > = 0>
T	dilate (const T &f, const array_type::tensor< size_t, 1 > &iterations, bool periodic=true)
	Dilate image.

template<class T , class S , std::enable_if_t< std::is_integral< typename T::value_type >::value &&std::is_integral< typename S::value_type >::value, int > = 0>
T	dilate (const T &f, const S &kernel, size_t iterations=1, bool periodic=true)
	Dilate image.

template<class T , std::enable_if_t< std::is_integral< typename T::value_type >::value, int > = 0>
T	dilate (const T &f, size_t iterations=1, bool periodic=true)
	Dilate image.

template<class T >
array_type::tensor< typename T::value_type, 2 >	labels_map (const T &a, const T &b)
	Get a map to relabel from `a` to `b`.

template<class L , class A >
L	labels_rename (const L &labels, const A &rename)
	Rename labels.

template<class T >
T	labels_prune (const T &labels)
	Prune labels: renumber labels to lowest possible label starting from 1.

template<class L , class A >
L	labels_reorder (const L &labels, const A &order)
	Reorder labels.

template<class T >
array_type::tensor< typename T::value_type, 2 >	labels_sizes (const T &labels)
	Size per label.

template<class T , class N >
array_type::tensor< typename T::value_type, 1 >	labels_sizes (const T &labels, const N &names)
	Size per label.

template<class T >
array_type::array< int >	clusters (const T &f, bool periodic=true)
	Compute clusters.

array_type::tensor< double, 1 >	center (const array_type::tensor< double, 1 > &shape, const array_type::tensor< double, 2 > &positions, bool periodic=true)
	Return the geometric center of a list of positions.

array_type::tensor< double, 1 >	center_of_mass (const array_type::tensor< double, 1 > &shape, const array_type::tensor< double, 2 > &positions, const array_type::tensor< double, 1 > &weights, bool periodic=true)
	Return the geometric center of a list of positions.

template<class T , class N >
array_type::tensor< double, 2 >	labels_centers (const T &labels, const N &names, bool periodic=true)
	Get the position of the center of each label.

template<class T , class W , class N >
array_type::tensor< double, 2 >	labels_centers_of_mass (const T &labels, const W &weights, const N &names, bool periodic=true)
	Get the position of the center of each label.

auto	distance (const std::vector< size_t > &roi)
	Get the relative distance of each pixel in the 'region-of-interest' to its center.

auto	distance (const std::vector< size_t > &roi, size_t axis)
	Get the relative distance of each pixel in the 'region-of-interest' to its center.

auto	distance (const std::vector< size_t > &roi, const std::vector< double > &h)
	Get the relative distance of each pixel in the 'region-of-interest' to its center.

auto	distance (const std::vector< size_t > &roi, const std::vector< double > &h, size_t axis)
	Get the relative distance of each pixel in the 'region-of-interest' to its center.

template<class T >
auto	S2 (const std::vector< size_t > &roi, const T &f, const T &g, bool periodic=true)
	2-point correlation: P(f(i) * g(i + di)).

template<class T , class M >
auto	S2 (const std::vector< size_t > &roi, const T &f, const T &g, const M &fmask, const M &gmask, bool periodic=true)
	2-point correlation: P(f(i) * g(i + di)).

template<class T >
auto	C2 (const std::vector< size_t > &roi, const T &f, const T &g, bool periodic=true)
	2-point cluster function: P(f(i) == g(i + di)).

template<class T , class M >
auto	C2 (const std::vector< size_t > &roi, const T &f, const T &g, const M &fmask, const M &gmask, bool periodic=true)
	2-point cluster function: P(f(i) == g(i + di)).

template<class T >
auto	W2 (const std::vector< size_t > &roi, const T &w, const T &f, bool periodic=true)
	Weighted 2-point correlation.

template<class T , class M >
auto	W2 (const std::vector< size_t > &roi, const T &w, const T &f, const M &fmask, bool periodic=true)
	Weighted 2-point correlation.

template<class C , class T >
auto	W2c (const std::vector< size_t > &roi, const C &clusters, const C &centers, const T &f, path_mode mode=path_mode::Bresenham, bool periodic=true)
	Collapsed weighted 2-point correlation.

template<class C , class T , class M >
auto	W2c (const std::vector< size_t > &roi, const C &clusters, const C &centers, const T &f, const M &fmask, path_mode mode=path_mode::Bresenham, bool periodic=true)
	Collapsed weighted 2-point correlation.

template<class T >
auto	heightheight (const std::vector< size_t > &roi, const T &f, bool periodic=true)
	Height-height correlation.

template<class T , class M >
auto	heightheight (const std::vector< size_t > &roi, const T &f, const M &fmask, bool periodic=true)
	Height-height correlation.

template<class T >
auto	L (const std::vector< size_t > &roi, const T &f, bool periodic=true, path_mode mode=path_mode::Bresenham)
	Lineal-path function.

std::string	version ()
	Return version string, e.g.

Detailed Description

Toolbox to compute statistics.

Enumeration Type Documentation

◆ path_mode

enum class GooseEYE::path_mode

strong

Different methods to compute a pixel-path.

Enumerator
Bresenham	Bresenham algorithm.
actual	The actual path.
full	Similar to actual selecting every voxel that is crossed.

Definition at line 93 of file GooseEYE.h.

Function Documentation

◆ C2() [1/2]

template<class T >

auto GooseEYE::C2	(	const std::vector< size_t > &	roi,
		const T &	f,
		const T &	g,
		bool	periodic = true )

inline

2-point cluster function: P(f(i) == g(i + di)).

Parameters

roi	Region-of-interest.
f	The image.
g	The comparison image.
periodic	Switch to assume image periodic.

Definition at line 75 of file GooseEYE.hpp.

◆ C2() [2/2]

template<class T , class M >

auto GooseEYE::C2	(	const std::vector< size_t > &	roi,
		const T &	f,
		const T &	g,
		const M &	fmask,
		const M &	gmask,
		bool	periodic = true )

inline

2-point cluster function: P(f(i) == g(i + di)).

Parameters

roi	Region-of-interest.
f	The image.
g	The comparison image.
fmask	Mask certain pixels of f (binary, 1: masked, 0: not masked).
gmask	Mask certain pixels of g (binary, 1: masked, 0: not masked).
periodic	Switch to assume image periodic.

Definition at line 84 of file GooseEYE.hpp.

◆ center()

array_type::tensor< double, 1 > GooseEYE::center	(	const array_type::tensor< double, 1 > &	shape,
		const array_type::tensor< double, 2 > &	positions,
		bool	periodic = true )

inline

Return the geometric center of a list of positions.

Note

The positions are organised as one column per dimension. For example, in 2d, the positions are organised as positions = np.hstack((rows.reshape(-1, 1), cols.reshape(-1, 1))). You can also use positions = np.argwhere(condition). This means that the following two calls are equivalent:

>>> centers(shape=labels.shape, positions=np.argwhere(labels == 1), periodic=True)
>>> labels_centers(labels=labels, names=[1], periodic=True)[0, :]

For periodic algorithm, see: https://en.wikipedia.org/wiki/Center_of_mass#Systems_with_periodic_boundary_conditions

Parameters

shape	Shape of the box to which the coordinates below (needed to apply periodicity).
positions	List of positions (in array coordinates, e.g. `[rows, columns]`).
periodic	Switch to assume array periodic.

Returns: Coordinates of the center (in array coordinates, e.g. [center_row, center_col]).

Definition at line 1246 of file GooseEYE.h.

◆ center_of_mass()

array_type::tensor< double, 1 > GooseEYE::center_of_mass	(	const array_type::tensor< double, 1 > &	shape,
		const array_type::tensor< double, 2 > &	positions,
		const array_type::tensor< double, 1 > &	weights,
		bool	periodic = true )

inline

Return the geometric center of a list of positions.

Note

The positions are organised as one column per dimension. For example, in 2d, the positions are organised as positions = np.hstack((rows.reshape(-1, 1), cols.reshape(-1, 1))). You can also use positions = np.argwhere(condition). This means that the following two calls are equivalent:

>>> centers(shape=labels.shape, positions=np.argwhere(labels == 1), periodic=True)
>>> labels_centers(labels=labels, names=[1], periodic=True)[0, :]

For periodic algorithm, see: https://en.wikipedia.org/wiki/Center_of_mass#Systems_with_periodic_boundary_conditions

Parameters

shape	Shape of the box to which the coordinates below (needed to apply periodicity).
positions	List of positions (in array coordinates, e.g. `[rows, columns]`).
periodic	Switch to assume array periodic.

Returns: Coordinates of the center (in array coordinates, e.g. [center_row, center_col]).

Parameters

weights Weight for each position.

Definition at line 1274 of file GooseEYE.h.

◆ clusters()

template<class T >

array_type::array< int > GooseEYE::clusters	(	const T &	f,
		bool	periodic = true )

inline

Compute clusters.

Parameters

f	Image.
periodic	Interpret image as periodic.

Returns: 'Image' with labels (1..n) for labels, 0 for background.

Definition at line 1198 of file GooseEYE.h.

◆ dilate() [1/4]

template<class T , std::enable_if_t< std::is_integral< typename T::value_type >::value, int > = 0>

T GooseEYE::dilate	(	const T &	f,
		const array_type::tensor< size_t, 1 > &	iterations,
		bool	periodic = true )

inline

Dilate image.

Select "kernel::nearest" as kernel. See above for parameters.

Definition at line 388 of file GooseEYE.h.

◆ dilate() [2/4]

template<class T , class S , std::enable_if_t< std::is_integral< typename T::value_type >::value &&std::is_integral< typename S::value_type >::value, int > = 0>

T GooseEYE::dilate	(	const T &	f,
		const S &	kernel,
		const array_type::tensor< size_t, 1 > &	iterations,
		bool	periodic = true )

inline

Dilate image.

The input image can be binary (1), or have integer labels (>=1). In each case the background are 0.

Parameters

f	The image (integer).
kernel	The kernel with which to dilate (binary).
iterations	Number of iterations per label.
periodic	Switch to assume image periodic.

Returns: The dilated image.

Definition at line 299 of file GooseEYE.h.

◆ dilate() [3/4]

template<class T , class S , std::enable_if_t< std::is_integral< typename T::value_type >::value &&std::is_integral< typename S::value_type >::value, int > = 0>

T GooseEYE::dilate	(	const T &	f,
		const S &	kernel,
		size_t	iterations = 1,
		bool	periodic = true )

inline

Dilate image.

Fixed number of iterations for all labels. See above for parameters.

Definition at line 404 of file GooseEYE.h.

◆ dilate() [4/4]

template<class T , std::enable_if_t< std::is_integral< typename T::value_type >::value, int > = 0>

T GooseEYE::dilate	(	const T &	f,
		size_t	iterations = 1,
		bool	periodic = true )

inline

Dilate image.

Fixed number of iterations for all labels. Select "kernel::nearest" as kernel. See above for parameters.

Definition at line 415 of file GooseEYE.h.

◆ distance() [1/4]

auto GooseEYE::distance ( const std::vector< size_t > & roi )

inline

Get the relative distance of each pixel in the 'region-of-interest' to its center.

Parameters

roi	Region-of-interest.

Returns: The distances along the 'region-of-interest' set at construction.

Definition at line 28 of file GooseEYE.hpp.

◆ distance() [2/4]

auto GooseEYE::distance	(	const std::vector< size_t > &	roi,
		const std::vector< double > &	h )

inline

Get the relative distance of each pixel in the 'region-of-interest' to its center.

Parameters

roi	Region-of-interest.
h	The physical dimensions of one pixel (in each direction).

Returns: The distances along the 'region-of-interest' set at construction.

Definition at line 40 of file GooseEYE.hpp.

◆ distance() [3/4]

auto GooseEYE::distance	(	const std::vector< size_t > &	roi,
		const std::vector< double > &	h,
		size_t	axis )

inline

Get the relative distance of each pixel in the 'region-of-interest' to its center.

Parameters

roi	Region-of-interest.
h	The physical dimensions of one pixel (in each direction).
axis	Select axis.

Returns: The distances along the 'region-of-interest' set at construction.

Definition at line 46 of file GooseEYE.hpp.

◆ distance() [4/4]

auto GooseEYE::distance	(	const std::vector< size_t > &	roi,
		size_t	axis )

inline

Get the relative distance of each pixel in the 'region-of-interest' to its center.

Parameters

roi	Region-of-interest.
axis	Select axis.

Returns: The distances along the 'region-of-interest' set at construction.

Definition at line 34 of file GooseEYE.hpp.

◆ dummy_circles() [1/2]

array_type::array< int > GooseEYE::dummy_circles	(	const std::vector< size_t > &	shape,
		bool	periodic = true,
		uint64_t	seed = 0 )

inline

Dummy image with circles.

The positions and radii of the circles are randomly generated.

Parameters

shape	Shape of the output image.
periodic	Switch to assume image periodic.
seed	Seed for the random number generator.

Returns: The dummy image.

Definition at line 172 of file GooseEYE.h.

◆ dummy_circles() [2/2]

array_type::array< int > GooseEYE::dummy_circles	(	const std::vector< size_t > &	shape,
		const array_type::tensor< int, 1 > &	row,
		const array_type::tensor< int, 1 > &	col,
		const array_type::tensor< int, 1 > &	r,
		bool	periodic = true )

inline

Dummy image with circles.

Parameters

shape	Shape of the output image.
row	The x-position of each circle.
col	The y-position of each circle.
r	The radius of each circle.
periodic	Switch to assume image periodic.

Returns: The dummy image.

Definition at line 120 of file GooseEYE.h.

◆ heightheight() [1/2]

template<class T >

auto GooseEYE::heightheight	(	const std::vector< size_t > &	roi,
		const T &	f,
		bool	periodic = true )

inline

Height-height correlation.

Parameters

roi	Region-of-interest.
f	The image.
periodic	Switch to assume image periodic.

Definition at line 143 of file GooseEYE.hpp.

◆ heightheight() [2/2]

template<class T , class M >

auto GooseEYE::heightheight	(	const std::vector< size_t > &	roi,
		const T &	f,
		const M &	fmask,
		bool	periodic = true )

inline

Height-height correlation.

Parameters

roi	Region-of-interest.
f	The image.
fmask	Mask certain pixels of f (binary, 1: masked, 0: not masked).
periodic	Switch to assume image periodic.

Definition at line 151 of file GooseEYE.hpp.

◆ L()

template<class T >

auto GooseEYE::L	(	const std::vector< size_t > &	roi,
		const T &	f,
		bool	periodic = true,
		path_mode	mode = path_mode::Bresenham )

inline

Lineal-path function.

Parameters

roi	Region-of-interest.
f	The image.
periodic	Switch to assume image periodic.
mode	Method to use (see path_mode()).

Definition at line 159 of file GooseEYE.hpp.

◆ labels_centers()

template<class T , class N >

array_type::tensor< double, 2 > GooseEYE::labels_centers	(	const T &	labels,
		const N &	names,
		bool	periodic = true )

inline

Get the position of the center of each label.

Note: To compute the center of a single label, you can also use GooseEYE::center().

Parameters

labels	An image with labels.
names	List of labels to compute the center for.
periodic	Switch to assume image periodic.

Returns: Coordinates of the center (in array coordinates), in order of the unique (sorted) labels.

Definition at line 1340 of file GooseEYE.h.

◆ labels_centers_of_mass()

template<class T , class W , class N >

array_type::tensor< double, 2 > GooseEYE::labels_centers_of_mass	(	const T &	labels,
		const W &	weights,
		const N &	names,
		bool	periodic = true )

inline

Get the position of the center of each label.

Note: To compute the center of a single label, you can also use GooseEYE::center().

Parameters

labels	An image with labels.
names	List of labels to compute the center for.
periodic	Switch to assume image periodic.

Returns: Coordinates of the center (in array coordinates), in order of the unique (sorted) labels.

Parameters

weights Weight for each pixel.

Definition at line 1368 of file GooseEYE.h.

◆ labels_map()

template<class T >

array_type::tensor< typename T::value_type, 2 > GooseEYE::labels_map	(	const T &	a,
		const T &	b )

inline

Get a map to relabel from a to b.

Parameters

a	Image with labels.
b	Image with labels.

Returns: Array with each row the pair (old_label, new_label).

Definition at line 428 of file GooseEYE.h.

◆ labels_prune()

template<class T >

T GooseEYE::labels_prune ( const T & labels )

inline

Prune labels: renumber labels to lowest possible label starting from 1.

Note that the background 0 is always kept 0.

Parameters

labels Image with labels.

Returns: Image with reordered labels.

Definition at line 490 of file GooseEYE.h.

◆ labels_rename()

template<class L , class A >

L GooseEYE::labels_rename	(	const L &	labels,
		const A &	rename )

inline

Rename labels.

Parameters

labels	Image with labels.
rename	Array with each row the pair (old_label, new_label).

Returns: Image with reordered labels.

Definition at line 457 of file GooseEYE.h.

◆ labels_reorder()

template<class L , class A >

L GooseEYE::labels_reorder	(	const L &	labels,
		const A &	order )

inline

Reorder labels.

Parameters

labels	Image with labels.
order	List of new order of labels (`unique(labels)` in desired order).

Returns: Image with reordered labels.

Definition at line 536 of file GooseEYE.h.

◆ labels_sizes() [1/2]

template<class T >

array_type::tensor< typename T::value_type, 2 > GooseEYE::labels_sizes ( const T & labels )

inline

Size per label.

Parameters

labels Image with labels.

Returns: List of size n + 1 with the size per label.

Definition at line 588 of file GooseEYE.h.

◆ labels_sizes() [2/2]

template<class T , class N >

array_type::tensor< typename T::value_type, 1 > GooseEYE::labels_sizes	(	const T &	labels,
		const N &	names )

inline

Size per label.

Parameters

labels	Image with labels.
names	List of 'names' to extract.

Returns: Size of each label in names.

Definition at line 612 of file GooseEYE.h.

◆ path()

array_type::tensor< int, 2 > GooseEYE::path	(	const array_type::tensor< int, 1 > &	x0,
		const array_type::tensor< int, 1 > &	x1,
		path_mode	mode = path_mode::Bresenham )

inline

Compute a path between two pixels.

Parameters

x0	Pixel coordinate (e.g. {0, 0}).
x1	Pixel coordinate (e.g. {10, 5}).
mode	Method to use (see "path_mode").

Returns: The path: the coordinate of one pixel per row.

Definition at line 15 of file GooseEYE.hpp.

◆ S2() [1/2]

template<class T >

auto GooseEYE::S2	(	const std::vector< size_t > &	roi,
		const T &	f,
		const T &	g,
		bool	periodic = true )

inline

2-point correlation: P(f(i) * g(i + di)).

Parameters

roi	Region-of-interest.
f	The image.
g	The comparison image.
periodic	Switch to assume image periodic.

Definition at line 53 of file GooseEYE.hpp.

◆ S2() [2/2]

template<class T , class M >

auto GooseEYE::S2	(	const std::vector< size_t > &	roi,
		const T &	f,
		const T &	g,
		const M &	fmask,
		const M &	gmask,
		bool	periodic = true )

inline

2-point correlation: P(f(i) * g(i + di)).

Parameters

roi	Region-of-interest.
f	The image.
g	The comparison image.
fmask	Mask certain pixels of f (binary, 1: masked, 0: not masked).
gmask	Mask certain pixels of g (binary, 1: masked, 0: not masked).
periodic	Switch to assume image periodic.

Definition at line 62 of file GooseEYE.hpp.

◆ version()

std::string GooseEYE::version ( )

inline

Return version string, e.g.

"0.8.0"

Returns: String.

Definition at line 25 of file version.hpp.

◆ W2() [1/2]

template<class T >

auto GooseEYE::W2	(	const std::vector< size_t > &	roi,
		const T &	w,
		const T &	f,
		bool	periodic = true )

inline

Weighted 2-point correlation.

Parameters

roi	Region-of-interest.
w	Weights.
f	The image.
periodic	Switch to assume image periodic.

Definition at line 97 of file GooseEYE.hpp.

◆ W2() [2/2]

template<class T , class M >

auto GooseEYE::W2	(	const std::vector< size_t > &	roi,
		const T &	w,
		const T &	f,
		const M &	fmask,
		bool	periodic = true )

inline

Weighted 2-point correlation.

Parameters

roi	Region-of-interest.
w	Weights.
f	The image.
fmask	Mask certain pixels of f (binary, 1: masked, 0: not masked).
periodic	Switch to assume image periodic.

Definition at line 106 of file GooseEYE.hpp.

◆ W2c() [1/2]

template<class C , class T , class M >

auto GooseEYE::W2c	(	const std::vector< size_t > &	roi,
		const C &	clusters,
		const C &	centers,
		const T &	f,
		const M &	fmask,
		path_mode	mode = path_mode::Bresenham,
		bool	periodic = true )

inline

Collapsed weighted 2-point correlation.

Parameters

roi	Region-of-interest.
clusters	The clusters.
centers	The cluster-centers: label only at the center.
f	The image.
fmask	Mask certain pixels of f (binary, 1: masked, 0: not masked).
mode	Method to use (see path_mode()).
periodic	Switch to assume image periodic.

Definition at line 129 of file GooseEYE.hpp.

◆ W2c() [2/2]

template<class C , class T >

auto GooseEYE::W2c	(	const std::vector< size_t > &	roi,
		const C &	clusters,
		const C &	centers,
		const T &	f,
		path_mode	mode = path_mode::Bresenham,
		bool	periodic = true )

inline

Collapsed weighted 2-point correlation.

Parameters

roi	Region-of-interest.
clusters	The clusters.
centers	The cluster-centers: label only at the center.
f	The image.
mode	Method to use (see path_mode()).
periodic	Switch to assume image periodic.

Definition at line 115 of file GooseEYE.hpp.

Namespaces

Classes

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ path_mode

Function Documentation

◆ C2() [1/2]

◆ C2() [2/2]

◆ center()

◆ center_of_mass()

◆ clusters()

◆ dilate() [1/4]

◆ dilate() [2/4]

◆ dilate() [3/4]

◆ dilate() [4/4]

◆ distance() [1/4]

◆ distance() [2/4]

◆ distance() [3/4]

◆ distance() [4/4]

◆ dummy_circles() [1/2]

◆ dummy_circles() [2/2]

◆ heightheight() [1/2]

◆ heightheight() [2/2]

◆ L()

◆ labels_centers()

◆ labels_centers_of_mass()

◆ labels_map()

◆ labels_prune()

◆ labels_rename()

◆ labels_reorder()

◆ labels_sizes() [1/2]

◆ labels_sizes() [2/2]

◆ path()

◆ S2() [1/2]

◆ S2() [2/2]

◆ version()

◆ W2() [1/2]

◆ W2() [2/2]

◆ W2c() [1/2]

◆ W2c() [2/2]