Operations on Images#

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

Basic arithmetic operations#

Operation	Description
Sum	\(z_{M} = \sum_{k=0}^{M-1}{z_{k}}\)
Average	\(z_{M} = \dfrac{1}{M}\sum_{k=0}^{M-1}{z_{k}}\)
Difference	\(z_{2} = z_{1} - z_{0}\)
Quadratic difference	\(z_{2} = \dfrac{z_{1} - z_{0}}{\sqrt{2}}\)
Product	\(z_{M} = \prod_{k=0}^{M-1}{z_{k}}\)
Division	\(z_{2} = \dfrac{z_{1}}{z_{0}}\)

Operations with a constant#

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

Operation	Equation
Addition	\(z_{k} = z_{k-1} + conv(c)\)
Subtraction	\(z_{k} = z_{k-1} - conv(c)\)
Multiplication	\(z_{k} = conv(z_{k-1} \times c)\)
Division	\(z_{k} = conv(\dfrac{z_{k-1}}{c})\)

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).

Real and imaginary parts#

Operation	Description
Absolute value	\(z_{k} = \|z_{k-1}\|\)
Real part	\(z_{k} = \Re(z_{k-1})\)
Imaginary part	\(z_{k} = \Im(z_{k-1})\)

Data type conversion#

The “Convert data type” convert_dtype 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 cdl.algorithms.datatypes.clip_astype() function which relies on numpy.ndarray.astype() function with the default parameters (casting=’unsafe’).

Basic mathematical functions#

Function	Description
Exponential	\(z_{k} = \exp(z_{k-1})\)
Logarithm (base 10)	\(z_{k} = \log_{10}(z_{k-1})\)
Log10(z+n)	\(z_{k} = \log_{10}(z_{k-1}+n)\) (avoid Log10(0) on image background)

Other operations#

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.

Rotation#

Create a new image which is the result of rotating (90°, 270° or arbitrary angle) or flipping (horizontally or vertically) data.

Intensity profiles#

Line profile

Extract an horizontal or vertical profile from each selected image, and create new signals from these profiles.

../../_images/i_profile.png — Line profile dialog. Parameters may also be set manually (“Edit profile parameters” button).#

Segment profile

Extract a segment profile from each selected image, and create new signals from these profiles.

Average profile

Extract an horizontal or vertical profile averaged over a rectangular area, from each selected image, and create new signals from these profiles.

../../_images/i_profile_average.png — Average profile dialog: the area is defined by a rectangle shape. Parameters may also be set manually (“Edit profile parameters” button).#

Radial profile extraction

Extract a radial profile from each selected image, and create new signals from these profiles.

The following parameters are available:

Parameter	Description
Center	Center around which the radial profile is computed: centroid, image center, or user-defined
X	X coordinate of the center (if user-defined), in pixels
Y	Y coordinate of the center (if user-defined), in pixels

Distribute images along a grid#

Feature	Description
Distribute on a grid	Distribute selected images on a regular grid
Reset image positions	Reset the positions of the selected images to first image (x0, y0) coordinates