LieAnalysis Package

Orientation Scores from 2D images

CakeWaveletStack — Creates a Cake Wavelets stack for 2D images

GaborWaveletStack — Creates a Gabor Wavelet stack for 2D images

MultiScaleCakeWaveletStack — Creates a Multi-scale Cake Wavelet stack

OrientationScoreTransform — Computes Orientation Scores from a 2D image

LeftInvariantDerivatives — Computes Left Invariant Derivatives from orientation score

OrientationScoreTensor — Computes the derivative tensor from Orientation Score

InverseOrientationScoreTransform — Applies reconstruction to the Orientation Score

OrientationScoreGaugeFrames — Computes the data-adaptive frame from an Orientation Score

Orientation Scores from 3D images

CakeWaveletStack3D — Creates a Cake Wavelet stack for 3D images

OrientationScoreTransform3D — Computes Orientation Scores from a 3D image

LeftInvariantDerivatives3D — Computes Left-Invariant Derivatives from orientation scores

OrientationScoreTensor — Computes the derivative tensor from Orientation Score

InverseOrientationScoreTransform3D — Applies reconstruction to the Orientation Score

OrientationScoreGaugeFrames3D — Computes the data-adaptive frame from an Orientation Score

GlyphPlot — Glyph visualization for position orientation data

Other

FastMarching — Computes the shortest path between two points

OrientationScoreData — Provides example data used to test / examine the Lie Package

$LieAnalysisVersion — Symbol that stores the current version of the package

Tutorials

Working With Objects  ▪  Internal Functions  ▪  Fast Marching  ▪  Enhancing Diffusion's on 2D Images  ▪  Enhancing Diffusion's on 3D Images  ▪  Step by Step Gauge Frames SE(2)  ▪  Processing on 2D Images  ▪  Processing on 3D Images

Lie Analysis Objects

Many functions within the Lie Analysis package output an Lie Analysis objects.

Object — Mother of all objects

ObjWavelet — Mother of wavelet object

ObjOrientationWavelet — Mother of all oriented wavelet objects

ObjCakeWavelet — Container for cake wavelets for 2D images

ObjGaborWavelet — Container for Gabor wavelets for 2D images

ObjScaleCakeWavelet — Container for scale cake wavelets for 2D images

ObjPositionOrientationData — Container for 2D position orientation data

ObjScaleOrientationScores2D — Container for scale 2D position orientation data

ObjTensor — General tensor container

ObjFastMarchingResult — Container for the result of fast marching

ObjOrientationWavelet3D — Mother wavelet of orientated wavelets for 3D image processing

ObjCakeWavelet3D — Container for cake wavelets for 3D images

Obj3DPositionOrientationData — Container for 3D position orientation data

ObjSphereSampling — Container for sampling on the sphere

ObjWaveletTransform — Container for keeping wavelet transform results

Classes Implementation

Affix — returns a copy of an instance with an element affixed

AffixTo — affixes an element to the object

ClassQ — returns whenever a symbol is a class or not

ClassSet — sets the class property of an instance

ClassSetDelayed — sets the class property of an instance using delayed evaluation

DeclareClass — declare a symbol as a class

DeclareDefaults — declare elements and their default values

DeclareInvariant — declares the invariant for the class

Retrieve — retrieves the value of an instance of a class

ValidQ — returns a Boolean indicating if the symbol is a valid class

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