LIE ANALYSIS SYMBOL

# LeftInvariantDerivatives3D LeftInvariantDerivatives3D[ObjPositionOrientationData, {σSpatial, σOrientation}, derivativeIndex]
Computes the AderivativeIndex derivative(s) from ObjPositionOrientationData using Gaussian derivatives with the specified σSpatial and σOrientation.

LeftInvariantDerivatives3D[ObjOrientationScores3D, derivativeIndex, options]
Computes AderivativeIndex derivative(s) using a finite differences method which can be specified using options.

## DetailsDetails

• Computes the left-invariant derivatives from an orientation score using either Gaussian derivatives or Finite Differences depending.
• If the input orientation score is an complex orientation score, than both the real and imaginary part of the orientation scores are processed.
• The output of the function is again (just as the input) an Orientation Score
• The input argument derivativeIndex can either be a integer or list of integers.
• The finite difference implementation is also available in the common context.
• Using Normal on the output of LeftInvariantDerivatives3D results in an Association.
• Options that are supplied when using the Gaussian derivatives implementation are ignored as they are only valid in case of the Finite Difference method.

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

Computing the first order derivative A3U using Gaussian derivatives

 In:= Out= Computing multiple left invariant derivatives at once using Gaussian derivatives.

 In:= Out= Computing the first order derivative A3U using Finite Differences

 In:= Out= ### Properties & Relations  (4)Properties & Relations  (4)

OrientationScoreTransform3D OrientationScoreDerivatives CakeWaveletStack3D OrientationScoreTensor3D