LIE ANALYSIS TUTORIAL

Enhancing Diffusion's on 2D Images

LeftInvariantDerivatives[os, derivativeIndex]computes the left-invariant derivatives from os (ObjPositionOrientationData)using a finite differences method.
LeftInvariantDerivatives[os,{σs,σo},derivativeIndex]computes the left-invariant derivatives from os using the Gaussian scales σs and σo
OrientationScoreTensor[os,derivativeIndex]construct tensor derivativeIndex from os using the defined Gaussian σs and σo
OrientationScoreTensor[os,{σs,σo},derivativeIndex]construct tensor derivativeIndex from os using a finite differences method
OrientationScoreGaugeFrames[os,{σs,σo}]construct Gauge frames from os usins the Gaussian scales σs and σo
OrientationScoreTransform[data]constructs an orientation score from data

Functions used for enhancing diffusion's.

Load the package
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Set example data
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Generate some noise
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Left Invariant Hypo-elliptic Diffusion

Initialization

Construct orientation scores
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The effective parameters (based on the grid size)
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The diffusion constants relative to the ξ-normalized geometry
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The corresponding diffusion time (to reach the desired standard deviations)
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Perform Diffusion in the Left-Invariant Frame

Function to compute left-invariant finite differences gradient
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Perform diffusion with update step (u=u+dt*div(Mξ-1.D.Mξ-1.∇u)), note that the M_xi are due to the intrinsic geometry
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Show result
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Gauge Frames CEDOS

Initialization

Settings
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Compute Gauge Frames

Compute left-invariant Hessian
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Compute Gauge frames
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Perform ξ conversion to match
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Function for converting the tensor (in left-invariant frame)
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Compute the tensor in the gauge frame and compute the orientation confidence (Laplacian in plane perpendicular to the main direction)
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Adaptive diffusion constants

Perform Diffusion along the Gauge Frames

Eq. (72) Franken Duits IJCV
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Helper function for computing the divergence of an orientation score object
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Perform diffusion with Tschumperlé–Deriche trace based update step (update via the Hessian)
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Left Invariant CEDOS

Left Invariant CEDOS
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Show results
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