# alg - Image Processing Algorithms¶

## Applying algorithms¶

While image properties are usually manipulated using method of the ImageHandle class, their data content is manipulated using image algorithms. Image algorithms are objects. Each of them is a class, and its methods are used to handle the algorithm parameters. Applying an algorithm to an image is then conceptually a two-step process. First, an instance of an algorithm class is created, yielding an algorithm object. In a second step, the algorithm object is applied to an image. An algorithm can be applied in-place (using the ApplyIP() method), modifying the image, or out-of-place, (using Apply() ), leaving the original image untouched, and returning the result as a new image.

Here is an example. All the algorithms used in the following are described in the Selected Algorithms section.

# creates an algorithm object
rand_alg = img.alg.Randomize()
# applies algorithm object in place, overwriting the image
im.ApplyIP( rand_alg )


Sometimes, there is no need to create a permanent instance of an algorithm object. A temporary object enough:

# applies temporary algorithm object in-place
im.ApplyIP( img.alg.GaussianFilter(4.0) )


When used this way, the algorithm class will cease to exist as soon as the algorithm is applied. However, some algorithm are stateful and store information. One good example is the Stat algorithm, which does not modify the image when applied, but change its internal state to store information extracted from the image, which can be recovered later. For example:

# creates and applies an algorithm object
stat=img.alg.Stat()
im.ApplyIP(stat)
# extracts information from the algorithm
mean=stat.GetMean()


It is important to remember that when the algorithms ceases to exist, all information it stores is lost.

## Fourier Transforming Images¶

An image can be Fourier-transformed using either the FFT algorithm or the DFT algorithm. The difference between the two is that the DFT algorithm honors the The spatial origin of the image, and applies the corresponding phase shift in Fourier space. The FFT does not follow this behavior.

# create an instance of the Dft algorithm object
dft=img.alg.DFT()
# do the actual Fourier transformation
im_ft=im.Apply(dft)
# back-transform
im2 = im_ft.Apply(dft)


The FFT and DFT algorithms do not require a direction to be given (forward or back transform). This is implicitly determined by the current The data domain of the image being transformed. The following rules apply.

• SPATIAL -> HALF_FREQUENCY

• HALF_FREQUENCY -> SPATIAL

• FREQUENCY -> COMPLEX_SPATIAL

• COMPLEX_SPATIAL -> FREQUENCY

## Filters¶

OpenStructure makes several image filters available. Most of them are Fourier space filters, others are real space ones. However, since the ImagerHandle class is aware of its own The data domain, the user does not need to convert the image to Fourier space or to real space. Irrespective of which domain the filter applies to, OpenStructure will internally convert the image to the appropriate domain, apply the filter, and then return the image to its original conditions.

The following filters are available (their are described in the Selected Algorithms section below)

Fourier space filters:

Real space filters:

## Selected Algorithms¶

Many algorithms are available for image manipulation. What follows is a description of the most important ones.

class DFT

This algorithm performs a Fourier Transform of the image, honoring its The spatial origin, thus applying the corresponding phase shift in Fourier space.

class DiscreteShrink(block_size)

The algorithm performs a scaling of the original image by merging adjacent blocks of pixels. The block size is passed in the constructor in the form of a Size but can be changed later using the relevant method. The Size and the Extent of the image are changed when the algorithm is applied. The Pixel sampling of the image is also adjusted according to the scaling, so that the size of the image in the absolute reference system used by OpenStructure stays constant.

Parameters:

block_size (Size) – Size of the blocks to be merged

GetBlocksize()

Returns the current size of the blocks to be merged

Return type:

Size

SetBlocksize(block size)

Sets the size of the blocks to be shrunk to the specified value

Parameters:

block_size (Size) –

class FFT

This algorithm performs a Fourier Transform of the image, without honoring its The spatial origin (See DFT)

class LowPassFilter(cutoff=1.0)

This algorithm applies a Fourier low pass filter to the image. The filter cutoff frequency needs to be provided in sampling units (for example 8 Angstrom). Please notice that this filter features a sharp dropoff.

Parameters:

cutoff (float) – Frequency cutoff in sampling units

GetLimit()

Returns the current value of the filter cutoff frequency (in sampling units).

Return type:

float

SetLimit(cutoff)

Sets the value of the filter cutoff frequency to the specified value (in sampling units).

Parameters:

cutoff (float) – Frequency cutoff in sampling units

class HighPassFilter(cutoff=1.0)

This algorithm applies a Fourier high pass filter to the image. The filter cutoff frequency needs to be provided in sampling units (for example 8 Angstrom). Please notice that this filter features a sharp dropoff.

Parameters:

cutoff (float) – Frequency cutoff in sampling units

GetLimit()

Returns the current value of the filter cutoff frequency (in sampling units).

Return type:

float

SetLimit(cutoff)

Sets the value of the filter cutoff frequency to the specified value (in sampling units).

Parameters:

cutoff (float) – Frequency cutoff in sampling units

class GaussianLowPassFilter(cutoff=1.0)

This algorithm applies a Fourier Gaussian low pass filter to the image. The filter cutoff frequency needs to be provided in sampling units (for example 8 Angstrom).

Parameters:

cutoff (float) – Frequency cutoff in sampling units

GetLimit()

Returns the current value of the filter cutoff frequency (in sampling units).

Return type:

float

SetLimit(cutoff)

Sets the value of the filter cutoff frequency to the specified value (in sampling units).

Parameters:

cutoff (float) – Frequency cutoff in sampling units

class GaussianHighPassFilter(cutoff=1.0)

This algorithm applies a Fourier Gaussian High pass filter to the image. The filter cutoff frequency needs to be provided in sampling units (for example 8 Angstrom).

Parameters:

cutoff (float) – Frequency cutoff in sampling units

GetLimit()

Returns the current value of the filter cutoff frequency (in sampling units).

Return type:

float

SetLimit(cutoff)

Sets the value of the filter cutoff frequency to the specified value (in sampling units).

Parameters:

cutoff (float) – Frequency cutoff in sampling units

class FermiLowPassFilter(cutoff=1.0, t=1.0)

This algorithm applies a Fourier Fermi low pass filter to the image. The filter cutoff frequency and the temperature parameter T need to be provided in sampling units (for example 8 Angstrom).

Parameters:
• cutoff (float) – Frequency cutoff in sampling units

• t (float) – Temperature factor in sampling units

GetLimit()

Returns the current value of the filter cutoff frequency in sampling units.

Return type:

float

SetLimit(cutoff)

Sets the value of the filter cutoff frequency to the specified value (in sampling units).

Parameters:

cutoff (float) – Frequency cutoff in sampling units

GetT()

Returns the current value of the filter’s T factor (in sampling units).

Return type:

float

SetT(t_factor)

Sets the value of the filter’s T factor to the specified value (in sampling units).

Parameters:

t_factor (float) – Frequency cutoff in sampling units

class FermiHighPassFilter(cutoff=1.0, t=1.0)

This algorithm applies a Fourier Fermi high pass filter to the image. The filter cutoff frequency and the temperature parameter T need to be provided in sampling units (for example 8 Angstrom).

Parameters:
• cutoff (float) – Frequency cutoff in sampling units

• t (float) – Temperature factor in sampling units

GetLimit()

Returns the current value of the filter cutoff frequency in sampling units.

Return type:

float

SetLimit(cutoff)

Sets the value of the filter cutoff frequency to the specified value (in sampling units).

Parameters:

cutoff (float) – Frequency cutoff in sampling units

GetT()

Returns the current value of the filter’s T factor (in sampling units).

Return type:

float

SetT(t_factor)

Sets the value of the filter’s T factor to the specified value (in sampling units).

Parameters:

t_factor (float) – Frequency cutoff in sampling units

class ButterworthLowPassFilter(passband=1.0, stopband=1.0)

This algorithm applies a Fourier Butterworth low pass filter to the image. The filter passband and stopband frequencies need to be provided in sampling units (for example 8 Angstrom). The default values of the Epsilon and Maximum Passband Gain parameters are set to 0.882 and 10.624 respectively.

Parameters:
• passband (float) – Passband frequency in sampling units

• stopband (float) – Stopband frequency in sampling units

GetLimit()

Returns the current value of the filter passband frequency in sampling units.

Return type:

float

SetLimit(passband)

Sets the value of the filter passband frequency to the specified value (in sampling units).

Parameters:

passband (float) – Frequency cutoff in sampling units

GetStop()

Returns the current value of the filter’s stopband frequency (in sampling units).

Return type:

float

SetStop(stopband)

Sets the value of the filter’s stopband frequency to the specified value (in sampling units).

Parameters:

stopband (float) – Frequency cutoff in sampling units

GetEps()

Returns the current value of the filter’s Epsilon parameter.

Return type:

float

SetEps(epsilon)

Sets the value of the filter’s epsilon parameter to the specified value.

Parameters:

eps (float) – Epsilon parameter

GetA()

Returns the current value of the filter’s Maximum Passband Gain parameter.

Return type:

float

SetA(gain)

Sets the value of the filter’s Maximum Passband Gain parameter to the specified value.

Parameters:

gain (float) – Maximum Passband Gain parameter

class ButterworthHighPassFilter(passband=1.0, stopband=1.0)

This algorithm applies a Fourier Butterworth high pass filter to the image. The filter passband and stopband frequencies need to be provided in sampling units (for example 8 Angstrom). The default values of the Epsilon and Maximum Passband Gain parameters are set to 0.882 and 10.624 respectively.

Parameters:
• passband (float) – Passband frequency in sampling units

• stopband (float) – Stopband frequency in sampling units

GetLimit()

Returns the current value of the filter passband frequency in sampling units.

Return type:

float

SetLimit(passband)

Sets the value of the filter passband frequency to the specified value (in sampling units).

Parameters:

passband (float) – Frequency cutoff in sampling units

GetStop()

Returns the current value of the filter’s stopband frequency (in sampling units).

Return type:

float

SetStop(stopband)

Sets the value of the filter’s stopband frequency to the specified value (in sampling units).

Parameters:

stopband (float) – Frequency cutoff in sampling units

GetEps()

Returns the current value of the filter’s Epsilon parameter.

Return type:

float

SetEps(epsilon)

Sets the value of the filter’s epsilon parameter to the specified value.

Parameters:

eps (float) – Epsilon parameter

GetA()

Returns the current value of the filter’s Maximum Passband Gain parameter.

Return type:

float

SetA(gain)

Sets the value of the filter’s Maximum Passband Gain parameter to the specified value.

Parameters:

gain (float) – Maximum Passband Gain parameter

class GaussianFilter(sigma=1.0)

This algorithm applies a real space Gaussian filter to the image, as defined in the following publication:

I.T.Young, L.J. van Vliet,”Recursive implementation of the Gaussian filter”,Signal Processing, 44(1995), 139-151

Parameters:

sigma (float) – Width of the Gaussian filter

GetSigma()

Returns the current value of the filter’s width.

Return type:

float

SetSigma(width)

Sets the value of the filter’s width to the specified value.

Parameters:

sigma (float) – Width of the Gaussian filter

SetQ(q_param)

Sets the value of the filter’s Q parameter (see publication) to the specified value.

Parameters:

q_param (float) – Filter’s Q parameter

class Histogram(bins, minimum, maximum)

This algorithm performs an histogram analysis of the image. The minimum and maximum pixel values of the histogram representation must be provided when the algorithm object is created, as well as the number of bins in the histogram. Bins are equally spaced and minimum and maximum values for each bin are automatically computed.

When the algorithm is applied to an image, the analysis is carried out. A python ‘list’ object containing in sequence the pixel counts for all the bins can the be recovered from the algorithm object.

Parameters:
• bins (int) – Number of bins in the histogram

• minimum (float) – Minimum value in the histogram

• maximum – Maximum value in the histogram

GetBins()

Returns the bins of the histogram representation

Return type:

list of ints

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