BoxCountingDimension

MLModule

genre	Statistics
author	MeVis Medical Solutions AG
package	MeVisLab/Standard
dll	MLFilter2
definition	mlFilter2.def
keywords	fractal, minkowski

Purpose

The module BoxCountingDim calculates the Minkowski-Bouligand dimension of an object that is constituted by voxels with values in a specified range.

Details

The Minkowski-Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a set S in a Euclidean space R_n, or more generally in a metric space (X, d).

To calculate this dimension for a fractal S, imagine this fractal lying on an evenly-spaced grid, and count how many boxes are required to cover the set. The box-counting dimension is calculated by seeing how this number changes as we make the grid finer.

Suppose that N(ε) is the number of boxes of side length (ε required to cover the set. Then the box-counting dimension is defined as:

Tips

Because the algorithm is starting at the original resolution and then recursively bisects the image, the original image extent must be x = y = z = 2ⁿ.

Windows

Default Panel

Input Fields

input0

name: input0, type: Image

Input scalar image.

Output Fields

outCurveList

name: outCurveList, type: CurveList(MLBase)

A curve that shows the log_n (1 / BoxExtension) on the x-axis and log_n (numberOfBoxes) on the y-axis.

Also, a line fitted to those points is shown.

For accessing this object via scripting see the Scripting Reference: MLCurveListWrapper.

Parameter Fields

Field Index

Box Counting Dimension: Float

Info: String

Lower Threshold: Double

Update: Trigger

Update Mode: Enum

Upper Threshold: Double

Visible Fields

Box Counting Dimension

name: boxCountingDimension, type: Float, persistent: no

Shows the calculated box-counting dimension.

Info

name: info, type: String, persistent: no

Shows information about the calculation.

Upper Threshold

name: objectMax, type: Double, default: 0, deprecated name: upperThreshold

Sets the upper threshold for defining object voxels.

Lower Threshold

name: objectMin, type: Double, default: 0, deprecated name: lowerThreshold

Sets the lower threshold for defining object voxels.

Update

name: update, type: Trigger, deprecated name: calculate

If pressed, the module computes anew.

Update Mode

name: updateMode, type: Enum, default: Off

Defines the update mode.

Values:

Title	Name	Description
Auto Update	AutoUpdate	The module computes anew on any field change.
Off	Off	The module does nothing on a field change.