Operations on Images#

This section describes the operations that can be performed on images.

Operations with a constant#

Create a new image which is the result of a constant operation on each selected image:

Operation	Equation
Add	\(z_{k} = z_{k-1} + conv(c)\)
Subtract	\(z_{k} = z_{k-1} - conv(c)\)
Multiply	\(z_{k} = conv(z_{k-1} \times c)\)
Divide	\(z_{k} = conv(\dfrac{z_{k-1}}{c})\)

where \(c\) is the constant value and \(conv\) is the conversion function which handles data type conversion (keeping the same data type as the input image).

Basic arithmetic operations#

Arithmetic operations are performed pixel by pixel between the selected images.

Operation	Description
Sum	\(z_{M} = \sum_{k=0}^{M-1}{z_{k}}\)
Difference	\(z_{2} = z_{1} - z_{0}\)
Product	\(z_{M} = \prod_{k=0}^{M-1}{z_{k}}\)
Division	\(z_{2} = \dfrac{z_{1}}{z_{0}}\)
Inverse	\(z_{2} = \dfrac{1}{z_{1}}\)
Exponential	\(z_{2} = \exp(z_{1})\)
Logarithm (base 10)	\(z_{2} = \log_{10}(z_{1})\)

Basic mathematical functions#

Function	Description
Exponential	\(z_{k} = \exp(z_{k})\)
Logarithm (base 10)	\(z_{k} = \log_{10}(z_{k})\)
Log10(z+10)	\(z_{k} = \log_{10}(z_{k}+n)\) (useful if image background is zero)

Convolution and Deconvolution#

Operation	Implementation
Convolution	Based on scipy.signal.convolve
Deconvolution	Frequency domain deconvolution

Absolute value and complex image operations#

Operation	Description
Absolute value	\(z_{k} = \|z_{k-1}\|\)
Phase (argument)	`sigima.proc.image.phase()`
Combine with phase	Consider current image as the module and allow to select a image representing the phase to merge them in a complex image `sigima.proc.image.complex_from_magnitude_phase()`
Real part	\(z_{k} = \Re(z_{k-1})\)
Imaginary part	\(z_{k} = \Im(z_{k-1})\)
Combine with imaginary part	Consider current image as the real part and allow to select a image representing the imaginary part to merge them in a complex image `sigima.proc.image.complex_from_real_imag()`

Data type conversion#

The “Convert data type” action allows you to convert the data type of the selected images. For integer data types, the conversion is done by clipping the values to the new data type range before effectively converting the data type. For floating point data types, the conversion is straightforward.

Note

Data type conversion uses the sigima.tools.datatypes.clip_astype() function which relies on numpy.ndarray.astype() function with the default parameters (casting=’unsafe’).

Statistics between images#

Create a new image which is the result of a statistical operation on each pixel of the selected images:

Operation	Description
Average	\(z_{M} = \dfrac{1}{M}\sum_{k=0}^{M-1}{z_{k}}\)
Standard Deviation	\(z_{M} = \sqrt{\dfrac{1}{M}\sum_{k=0}^{M-1}{(y_{k} - \bar{y})^{2}}}\)
Quadratic difference	\(z_{2} = \dfrac{z_{1} - z_{0}}{\sqrt{2}}\)

Flat-field correction#

Create a new image which is flat-field correction of the two selected images:

\[\begin{split}z_{1} = \begin{cases} \dfrac{z_{0}}{z_{f}}.\overline{z_{f}} & \text{if } z_{0} > z_{threshold} \\ z_{0} & \text{otherwise} \end{cases}`\end{split}\]

where \(z_{0}\) is the raw image, \(z_{f}\) is the flat field image, \(z_{threshold}\) is an adjustable threshold and \(\overline{z_{f}}\) is the flat field image average value:

\[\overline{z_{f}}= \dfrac{1}{N_{row}.N_{col}}.\sum_{i=0}^{N_{row}}\sum_{j=0}^{N_{col}}{z_{f}(i,j)}\]

Note

Raw image and flat field image are supposedly already corrected by performing a dark frame subtraction.