Module: Fractal Dimension ()

Description:

For an introduction, see:

• section Analysis
• section Porosity

This module computes the fractal dimension of a binary 2D or 3D image. It should be used only if the feature is known as being potentially a fractal one. This is the case of complex and irregular curves which cannot be easily described with traditional geometric tools, and/or for curves which are very similar to a part of themselves at different scales.

2D definition:
The 2D fractal dimension is a number greater than 1 and strictly lower than 2. The result is 1 in case of standard geometric features (straight lines, broken lines, circles, ...). Applied to 2D images the fractal dimension is quite an effective indicator to measure and compare the irregularity and the fragmentation at different magnifications. It is also a good indicator to evaluate how the curve fills the space. The less smooth the curve is, the bigger the fractal dimension.
Caution:
Do not use this module on surfaces but on contours, according to the fractal definition. To be able to compare results, the outlines thickness should be very similar between the studied images and as small as possible so as to keep as much information as possible.

3D definition:
The 3D fractal dimension is a number greater than 2 and strictly lower than 3. The result is 2 in case of standard geometric surfaces (cubes, planes, ellipsoids, ...). Applied to 3D images the fractal dimension is quite an effective indicator to measure and compare the roughness of a surface. It is also a good indicator to evaluate how the curve fills the space. The less smooth the surface is, the bigger the fractal dimension. It can also be interpreted as a quantification of how complex the surface is and how it fills the space.
Caution:
Do not use this module on volumes but on surfaces, according to the fractal definition. To be able to compare results, the surface thickness should be very similar between the studied images and as small as possible so as to keep as much information as possible.

See also: Eccentricity, Anisotropy Degree, Structure Model Index, ASBMR Porosity

Connections:

Input Binary Image [required]
The image to be analyzed. Supported types include: binary images (Uniform Label Field with 2 labels).

Ports:

Interpretation

This port specifies whether the input will be interpreted as a 3D volume or a stack of 2D images for processing.

• "3D": the module configuration is set to 3D. The image will be processed as a whole in 3D.
• "XY planes": the module configuration is set to 2D. The image will be processed slice per slice.

Use Only Borders

This port indicates if only the objects borders are used to compute the measure.