BoxCountingDim¶

MLModule¶

genre	`Statistics`
status	`stable`
author	`Regina Ochotzki`
package	`MeVisLab/Standard`
dll	`MLFilter2`
definition	mlFilter2.def
keywords	`Box`, `Counting`, `Dimension`, `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:

../../../Modules/ML/MLFilter2/mhelp/Images/boxCountingDimensionFormula.png

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¶

../../../Modules/ML/MLFilter2/mhelp/Images/Screenshots/BoxCountingDim._default.png

Input Fields¶

input0¶

name: input0, type: Image¶: Input scalar image.

Output Fields¶

outCurveList¶

name: outCurveList, type: 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.

Parameter Fields¶

Field Index¶

Box Counting Dimension: Float

Info: String

Lower Threshold: Float

Update: Trigger

Update Mode: Enum

Upper Threshold: Float

Visible Fields¶

Box Counting Dimension¶

name: boxCountingDimension, type: Float, default: 0¶: Shows the calculated box-counting dimension.

Info¶

name: info, type: String¶: Shows information about the calculation.

Upper Threshold¶

name: objectMax, type: Float, default: 0, deprecated name: upperThreshold¶: Sets the upper threshold for defining object voxels.

Lower Threshold¶

name: objectMin, type: Float, 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.

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