BoxCountingDimension

MLModule

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

Purpose

The module BoxCountingDimension 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 the fractal lying on an evenly spaced grid, and count how many boxes are required to cover the set. The box-counting dimension is determined by observing how this number changes as the grid becomes 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

When 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.