module #include "diplib/generation.h"
Test image generation Generating images with test objects or functions
Classes

struct dip::
TestObjectParams  Describes the parameters for a test object, used by
dip::TestObject
.
Functions

void dip::
GaussianEdgeClip (dip::Image const& in, dip::Image& out, Image::Pixel const& value = {1}, dip::dfloat sigma = 1.0, dip::dfloat truncation = 3.0)  Maps input values through an error function, can be used to generate arbitrary bandlimited objects.

void dip::
GaussianLineClip (dip::Image const& in, dip::Image& out, Image::Pixel const& value = {1}, dip::dfloat sigma = 1.0, dip::dfloat truncation = 3.0)  Maps input values through a Gaussian function, can be used to generate arbitrary bandlimited lines.

void dip::
FillDelta (dip::Image& out, dip::String const& origin = "")  Fills an image with a delta function.

void dip::
CreateDelta (dip::Image& out, dip::UnsignedArray const& sizes, dip::String const& origin = "")  Creates a delta function image.

auto dip::
CreateDelta (dip::UnsignedArray const& sizes, dip::String const& origin = "") > dip::Image  Overload for the function above, which takes image sizes instead of an image.

void dip::
CreateGauss (dip::Image& out, dip::FloatArray const& sigmas, dip::UnsignedArray derivativeOrder = {0}, dip::dfloat truncation = 3.0, dip::UnsignedArray exponents = {0})  Creates a Gaussian kernel.

void dip::
CreateGabor (dip::Image& out, dip::FloatArray const& sigmas, dip::FloatArray const& frequencies, dip::dfloat truncation = 3.0)  Creates a Gabor kernel.

void dip::
FTEllipsoid (dip::Image& out, dip::FloatArray radius = {1}, dip::dfloat amplitude = 1)  Generates the Fourier transform of an ellipsoid.

auto dip::
FTEllipsoid (dip::UnsignedArray const& sizes, dip::FloatArray const& radius = {1}, dip::dfloat amplitude = 1) > dip::Image  Overload for the function above, which takes image sizes instead of an image.

void dip::
FTBox (dip::Image& out, dip::FloatArray length = {1}, dip::dfloat amplitude = 1)  Generates the Fourier transform of a box.

auto dip::
FTBox (dip::UnsignedArray const& sizes, dip::FloatArray const& length = {1}, dip::dfloat amplitude = 1) > dip::Image  Overload for the function above, which takes image sizes instead of an image.

void dip::
FTCross (dip::Image& out, dip::FloatArray length = {1}, dip::dfloat amplitude = 1)  Generates the Fourier transform of a cross.

auto dip::
FTCross (dip::UnsignedArray const& sizes, dip::FloatArray const& length = {1}, dip::dfloat amplitude = 1) > dip::Image  Overload for the function above, which takes image sizes instead of an image.

void dip::
FTGaussian (dip::Image& out, dip::FloatArray sigma, dip::dfloat amplitude = 1, dip::dfloat truncation = 3)  Generates the Fourier transform of a Gaussian.

auto dip::
FTGaussian (dip::UnsignedArray const& sizes, dip::FloatArray const& sigma, dip::dfloat amplitude = 1, dip::dfloat truncation = 3) > dip::Image  Overload for the function above, which takes image sizes instead of an image.

void dip::
TestObject (dip::Image& out, dip::TestObjectParams const& params, dip::Random& random)  Generates a test object according to
params
. 
auto dip::
TestObject (dip::UnsignedArray const& sizes, dip::TestObjectParams const& params, dip::Random& random) > dip::Image  Overload for the function above, which takes image sizes instead of an image.

void dip::
TestObject (dip::Image& out, dip::TestObjectParams const& params = {})  Calls the main
dip::TestObject
function with a defaultinitializeddip::Random
object. 
auto dip::
TestObject (dip::UnsignedArray const& sizes = {256,256}, dip::TestObjectParams const& params = {}) > dip::Image  Overload for the function above, which takes image sizes instead of an image.

void dip::
FillPoissonPointProcess (dip::Image& out, dip::Random& random, dip::dfloat density = 0.01)  Fills the binary image
out
with a Poisson point process ofdensity
. 
void dip::
CreatePoissonPointProcess (dip::Image& out, dip::UnsignedArray const& sizes, dip::Random& random, dip::dfloat density = 0.01)  Creates a binary image with a Poisson point process of
density
. 
void dip::
FillRandomGrid (dip::Image& out, dip::Random& random, dip::dfloat density = 0.01, dip::String const& type = S::RECTANGULAR, dip::String const& mode = S::TRANSLATION)  Fills the binary image
out
with a grid that is randomly placed over the image. 
void dip::
CreateRandomGrid (dip::Image& out, dip::UnsignedArray const& sizes, dip::Random& random, dip::dfloat density = 0.01, dip::String const& type = S::RECTANGULAR, dip::String const& mode = S::TRANSLATION)  Creates a binary image with a random grid.
Class documentation
struct dip::TestObjectParams
Describes the parameters for a test object, used by dip::TestObject
.
Variables  

dip::String objectShape 
Can be "ellipsoid" , "ellipsoid shell" , "box" , "box shell" , or "custom" .

dip::FloatArray objectSizes  Sizes of the object along each dimension. 
dip::dfloat objectAmplitude  Brightness of object pixels. 
bool randomShift  If true, add a random subpixel shift in the range [0.5,0.5]. 
dip::String generationMethod 
Can be "gaussian" (spatial domain method) or "fourier" (frequency domain method).

dip::dfloat modulationDepth  Strength of modulation, if 0 no modulation is applied. 
dip::FloatArray modulationFrequency  Frequency of a sine modulation added to the object, units are periods/pixel. 
dip::String pointSpreadFunction 
PSF, can be "gaussian" , "incoherent" , or "none" .

dip::dfloat oversampling  Determines size of PSF (Gaussian PSF has sigma = 0.9*oversampling). 
dip::dfloat backgroundValue  Background intensity, must be nonnegative. 
dip::dfloat signalNoiseRatio  SNR = average object energy divided by average noise power. If SNR > 0, adds a mixture of Gaussian and Poisson noise. 
dip::dfloat gaussianNoise  Relative amount of Gaussian noise. 
dip::dfloat poissonNoise  Relative amount of Poisson noise. 
Function documentation
void
dip::GaussianEdgeClip (dip::Image const& in,
dip::Image& out,
Image::Pixel const& value = {1},
dip::dfloat sigma = 1.0,
dip::dfloat truncation = 3.0)
Maps input values through an error function, can be used to generate arbitrary bandlimited objects.
in
is a scalar, realvalued function whose zero level set represents the edges of an object. The function
indicates the Euclidean distance to these edges, with positive values inside the object. out
will have a
value of value
inside the object, zero outside the object, and a Gaussian profile in the transition. If
sigma
is larger or equal to about 0.8, and the input image is well formed, the output will be approximately
bandlimited.
The error function mapping is computed in band around the zero crossings where the input image has values
smaller than sigma * truncation
.
If value
has more than one element, the output will be a tensor image with the same number of elements.
The following example draws a bandlimited cross, where the horizontal and vertical bars both have 20.5 pixels width, and different subpixel shifts. The foreground has a value of 255, and the background of 0.
dip::UnsignedArray outSize{ 256, 256 }; dip::Image xx = 20.5  dip::Abs( dip::CreateXCoordinate( outSize ) + 21.3 ); dip::Image yy = 20.5  dip::Abs( dip::CreateYCoordinate( outSize )  7.8 ); dip::Image cross = dip::GaussianEdgeClip( dip::Supremum( xx, yy ), { 255 } );
void
dip::GaussianLineClip (dip::Image const& in,
dip::Image& out,
Image::Pixel const& value = {1},
dip::dfloat sigma = 1.0,
dip::dfloat truncation = 3.0)
Maps input values through a Gaussian function, can be used to generate arbitrary bandlimited lines.
in
is a scalar, realvalued function whose zero level set represents the lines to be drawn. The function
indicates the Euclidean distance to these edges. out
will have lines with a Gaussian profile and a weight
of value
(the integral perpendicular to the line is value
), and a value of zero away from the lines. If
sigma
is larger or equal to about 0.8, and the input image is well formed, the output will be approximately
bandlimited.
The Gaussian function mapping is computed in band around the zero crossings where the input image has values
smaller than sigma * truncation
.
If value
has more than one element, the output will be a tensor image with the same number of elements.
The following example draws a bandlimited cross outline, where the horizontal and vertical bars both have 20.5 pixels width, and different subpixel shifts. The lines have a weight of 1500, and the background has a value of 0.
dip::UnsignedArray outSize{ 256, 256 }; dip::Image xx = 20.5  dip::Abs( dip::CreateXCoordinate( outSize ) + 21.3 ); dip::Image yy = 20.5  dip::Abs( dip::CreateYCoordinate( outSize )  7.8 ); dip::Image cross = dip::GaussianLineClip( dip::Supremum( xx, yy ), { 1500 } );
void
dip::FillDelta (dip::Image& out,
dip::String const& origin = "")
Fills an image with a delta function.
All pixels will be zero except at the origin, where it will be 1.
out
must be forged, and scalar.
origin
specifies where the origin lies:
"right"
: The origin is on the pixel right of the center (at integer division result ofsize/2
). This is the default."left"
: The origin is on the pixel left of the center (at integer division result of(size1)/2
)."corner"
: The origin is on the first pixel. This is the default if no other option is given.
void
dip::CreateDelta (dip::Image& out,
dip::UnsignedArray const& sizes,
dip::String const& origin = "")
Creates a delta function image.
All pixels will be zero except at the origin, where it will be 1.
out
will be of size sizes
, scalar, and of type dip::DT_SFLOAT
.
See dip::FillDelta
for the meaning of origin
.
void
dip::CreateGauss (dip::Image& out,
dip::FloatArray const& sigmas,
dip::UnsignedArray derivativeOrder = {0},
dip::dfloat truncation = 3.0,
dip::UnsignedArray exponents = {0})
Creates a Gaussian kernel.
out
is reforged to the required size to hold the kernel. These sizes are always odd. sigmas
determines
the number of dimensions. order
and exponents
will be adjusted if necessary to match.
derivativeOrder
is the derivative order, and can be a value between 0 and 3 for each dimension.
If derivativeOrder
is 0, the size of the kernel is given by 2 * std::ceil( truncation * sigma ) + 1
.
The default value for truncation
is 3, which assures a good approximation of the Gaussian kernel without
unnecessary expense. For derivatives, the value of truncation
is increased by 0.5 * derivativeOrder
.
Truncation is limited to avoid unusefully small values.
By setting exponents
to a positive value for each dimension, the created kernel will be multiplied by
the coordinates to the power of exponents
.
void
dip::CreateGabor (dip::Image& out,
dip::FloatArray const& sigmas,
dip::FloatArray const& frequencies,
dip::dfloat truncation = 3.0)
Creates a Gabor kernel.
out
is reforged to the required size to hold the kernel. These sizes are always odd. sigmas
determines
the number of dimensions. frequencies
must have the same number of elements as sigmas
.
Frequencies are in the range [0, 0.5), with 0.5 being the frequency corresponding to a period of the size of the image.
The size of the kernel is given by 2 * std::ceil( truncation * sigma ) + 1
.
The default value for truncation
is 3, which assures a good approximation of the kernel without
unnecessary expense. Truncation is limited to avoid unusefully small values.
void
dip::FTEllipsoid (dip::Image& out,
dip::FloatArray radius = {1},
dip::dfloat amplitude = 1)
Generates the Fourier transform of an ellipsoid.
The length of the axes of the ellipsoid are specified through radius
, which indicates the halflength
of the axes along each dimension. amplitude
specifies the brightness of the ellipsoid.
The function is defined for images between 1 and 3 dimensions. out
must be forged, scalar, and of a
floatingpoint type.
void
dip::FTBox (dip::Image& out,
dip::FloatArray length = {1},
dip::dfloat amplitude = 1)
Generates the Fourier transform of a box.
The length of the sides of the box are specified through length
, which indicates the halflength
of the sides along each dimension. amplitude
specifies the brightness of the box.
out
must be forged, scalar, and of a floatingpoint type.
void
dip::FTCross (dip::Image& out,
dip::FloatArray length = {1},
dip::dfloat amplitude = 1)
Generates the Fourier transform of a cross.
The length of the sides of the cross are specified through length
, which indicates the halflength
of the sides along each dimension. amplitude
specifies the brightness of the cross.
out
must be forged, scalar, and of a floatingpoint type.
void
dip::FTGaussian (dip::Image& out,
dip::FloatArray sigma,
dip::dfloat amplitude = 1,
dip::dfloat truncation = 3)
Generates the Fourier transform of a Gaussian.
The size of the Gaussian is specified with sigma
(note that the Fourier transform of a Gaussian is also a
Gaussian). volume
is the integral of the Gaussian in the spatial domain.
out
must be forged, scalar, and of a floatingpoint type.
void
dip::TestObject (dip::Image& out,
dip::TestObjectParams const& params,
dip::Random& random)
Generates a test object according to params
.
Generates a test object in the center of out
, which must be forged, scalar and of a floatingpoint type.
The test object can optionally be modulated using a sine function, blurred, and have noise added.
params
describes how the object is generated:
params.generationMethod
can be one of:"gaussian"
: creates the shape directly in the spatial domain, the shape will have Gaussian edges with a sigma of 0.9."fourier"
: creates the shape in the frequency domain, the shape will be truly bandlimited.
params.objectShape
can be one of:"ellipsoid"
or"ellipsoid shell"
: the shape is drawn withdip::DrawBandlimitedBall
ordip::FTEllipsoid
, depending on the generation method. In the case of"gaussian"
(spatialdomain generation), the shape must be isotropic (have same sizes in all dimensions). In the case of"fourier"
, the image cannot have more than three dimensions."box"
or"box shell"
: the shape is drawn withdip::DrawBandlimitedBox
ordip::FTBox
, depending on the generation method."custom"
:out
already contains a shape, which is used asis. In the case thatparams.generationMethod
is"gaussian"
,out
is taken to be in the spatial domain, and in the case of"fourier"
, in the frequency domain.
params.objectSizes
determines the extent of the object along each dimension. Must have either one element or as many elements as image dimensions inout
.params.objectAmplitude
determines the brightness of the object.params.randomShift
, iftrue
, shifts the object with a random subpixel shift in the range [0.5,0.5]. This subpixel shift can be used to avoid bias due to digitization error over a sequence of generated objects.
params
also describes what effects are applied to the image:
Modulation is an additive sine wave along each dimension, and is controlled by:
params.modulationDepth
controls the strength of the modulation. If this value is zero, no modulation is applied.params.modulationFrequency
controls the frequency along each image axis. The units are number of periods per pixel, and hence values below 0.5 should be given to prevent aliasing.
Blurring is controlled by:
params.pointSpreadFunction
determines the point spread function (PSF) used. It can be"gaussian"
for Gaussian blurring,"incoherent"
for a 2D, infocus, diffraction limited incoherent PSF (applied through Fourier domain filtering), or"none"
for no blurring.params.oversampling
determines the size of the PSF. In the case of"gaussian"
, the sigma used for blurring is0.9 * params.oversampling
. In the case of"incoherent"
, this is theoversampling
parameter passed todip::IncoherentOTF
.
Noise is controlled by:
params.backgroundValue
determines the background intensity added to the image. This is relevant for the Poisson noise.params.signalNoiseRatio
determines the signal to noise ratio (SNR), which we define as the average object energy divided by average noise power (i.e. not in dB). If the SNR is larger than 0, a mixture of Gaussian and Poisson noise is added to the whole image.params.gaussianNoise
determines the relative amount of Gaussian noise used.params.poissonNoise
determines the relative amount of Poisson noise used. The magnitude of these two quantities is not relevant, only their relative values are. If they are equal, the requested SNR is divided equally between the Gaussian and the Poisson noise.
random
is the random number generator used for both the subpixel shift and the noise added to the image.
void
dip::FillPoissonPointProcess (dip::Image& out,
dip::Random& random,
dip::dfloat density = 0.01)
Fills the binary image out
with a Poisson point process of density
.
out
must be forged, binary and scalar. On average, one of every 1/density
pixels will be set.
void
dip::CreatePoissonPointProcess (dip::Image& out,
dip::UnsignedArray const& sizes,
dip::Random& random,
dip::dfloat density = 0.01)
Creates a binary image with a Poisson point process of density
.
out
will be of size sizes
, binary and scalar.
void
dip::FillRandomGrid (dip::Image& out,
dip::Random& random,
dip::dfloat density = 0.01,
dip::String const& type = S::RECTANGULAR,
dip::String const& mode = S::TRANSLATION)
Fills the binary image out
with a grid that is randomly placed over the image.
This grid can be useful for random systematic sampling.
type
determines the grid type. It can be "rectangular"
in any number of dimensions, this is the default grid.
For 2D images it can be "hexagonal"
. In 3D it can be "fcc"
or "bcc"
for facecentered cubic and bodycentered
cubic, respectively.
density
determines the grid density. On average, one of every 1/density
pixels will be set. The grid is
sampled equally densely along all dimensions. If the density doesn’t lead to an integer grid spacing, the grid
locations will be rounded, leading to an uneven spacing. density
must be such that the grid spacing is at
least 2. Therefore, density
must be smaller than , with the image dimensionality,
in the rectangular case. In the hexagonal case, this is .
mode
determines how the random grid location is determined. It can be either "translation"
or "rotation"
.
In the first case, only a random translation is applied to the grid, it will be aligned with the image axes.
In the second case, the grid will also be randomly rotated. This option is used only for 2D and 3D grids.
out
must be forged, binary and scalar.
void
dip::CreateRandomGrid (dip::Image& out,
dip::UnsignedArray const& sizes,
dip::Random& random,
dip::dfloat density = 0.01,
dip::String const& type = S::RECTANGULAR,
dip::String const& mode = S::TRANSLATION)
Creates a binary image with a random grid.
out
will be of size sizes
, binary and scalar.
See dip::FillRandomGrid
for the meaning of the remainder of the parameters, which define the grid.