Diffusion Diffusion Filters Filters S. Derin Babacan S. Derin Babacan Department of Electrical and Computer Department of Electrical and Computer Engineering Engineering Northwestern University Northwestern University March March 7 7 , 200 , 200 6 6 ECE 463 Term Project
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Diffusion Filters S. Derin Babacan Department of Electrical and Computer Engineering Northwestern University March 7, 2006 ECE 463 Term Project.
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Diffusion FiltersDiffusion Filters
S Derin BabacanS Derin BabacanDepartment of Electrical and Computer Department of Electrical and Computer
EngineeringEngineeringNorthwestern UniversityNorthwestern University
MarchMarch 77 200 20066
ECE 463 Term Project
IntroductionIntroduction
Filters for enhancement restoration Filters for enhancement restoration smoothing and feature extractionsmoothing and feature extraction
Varying for each data entry based on Varying for each data entry based on local featureslocal features u u = [u(0)u(1)u(n-1)u(n)]= [u(0)u(1)u(n-1)u(n)] ww = [ = [ww0 0 w w1 1 w wn-1 n-1 w wn n ]]
Fickrsquos LawFickrsquos Law Continuity Continuity
Diffusion EquationDiffusion Equation
Gradient (uGradient (uxx u uyy) )
Divergence div Divergence div ΨΨ = = ΨΨ xx + + ΨΨ yy
Concentration replaced by data valuesConcentration replaced by data values
FluxDiffusion Tensor
Gradient
Concentration
Diffusion FiltersDiffusion Filters
D a scalar (flux and gradient are parallel)D a scalar (flux and gradient are parallel) Isotropic diffusion Isotropic diffusion D spatially invariant (fixed) Homogeneous D spatially invariant (fixed) Homogeneous
linear linear D = g(D = g() Inhomogeneous (linearnonlinear)) Inhomogeneous (linearnonlinear)
D a matrix (rotation andor scaling) flux D a matrix (rotation andor scaling) flux and gradient are generally not paralleland gradient are generally not parallel Anisotropic diffusionAnisotropic diffusion Eigenvectors of D determine the diffusion Eigenvectors of D determine the diffusion
Incorporate adaptation based on the current Incorporate adaptation based on the current filtered image instead of the initial imagefiltered image instead of the initial image Spatial and temporal adaptationSpatial and temporal adaptation
D = g(D = g()) g a function of ug a function of u
High contrast region low diffusionHigh contrast region low diffusion Low contrast region high diffusionLow contrast region high diffusion
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Thank youThank you
Questions Questions
IntroductionIntroduction
Filters for enhancement restoration Filters for enhancement restoration smoothing and feature extractionsmoothing and feature extraction
Varying for each data entry based on Varying for each data entry based on local featureslocal features u u = [u(0)u(1)u(n-1)u(n)]= [u(0)u(1)u(n-1)u(n)] ww = [ = [ww0 0 w w1 1 w wn-1 n-1 w wn n ]]
Fickrsquos LawFickrsquos Law Continuity Continuity
Diffusion EquationDiffusion Equation
Gradient (uGradient (uxx u uyy) )
Divergence div Divergence div ΨΨ = = ΨΨ xx + + ΨΨ yy
Concentration replaced by data valuesConcentration replaced by data values
FluxDiffusion Tensor
Gradient
Concentration
Diffusion FiltersDiffusion Filters
D a scalar (flux and gradient are parallel)D a scalar (flux and gradient are parallel) Isotropic diffusion Isotropic diffusion D spatially invariant (fixed) Homogeneous D spatially invariant (fixed) Homogeneous
linear linear D = g(D = g() Inhomogeneous (linearnonlinear)) Inhomogeneous (linearnonlinear)
D a matrix (rotation andor scaling) flux D a matrix (rotation andor scaling) flux and gradient are generally not paralleland gradient are generally not parallel Anisotropic diffusionAnisotropic diffusion Eigenvectors of D determine the diffusion Eigenvectors of D determine the diffusion
Incorporate adaptation based on the current Incorporate adaptation based on the current filtered image instead of the initial imagefiltered image instead of the initial image Spatial and temporal adaptationSpatial and temporal adaptation
D = g(D = g()) g a function of ug a function of u
High contrast region low diffusionHigh contrast region low diffusion Low contrast region high diffusionLow contrast region high diffusion
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Thank youThank you
Questions Questions
Physics of DiffusionPhysics of Diffusion
Fickrsquos LawFickrsquos Law Continuity Continuity
Diffusion EquationDiffusion Equation
Gradient (uGradient (uxx u uyy) )
Divergence div Divergence div ΨΨ = = ΨΨ xx + + ΨΨ yy
Concentration replaced by data valuesConcentration replaced by data values
FluxDiffusion Tensor
Gradient
Concentration
Diffusion FiltersDiffusion Filters
D a scalar (flux and gradient are parallel)D a scalar (flux and gradient are parallel) Isotropic diffusion Isotropic diffusion D spatially invariant (fixed) Homogeneous D spatially invariant (fixed) Homogeneous
linear linear D = g(D = g() Inhomogeneous (linearnonlinear)) Inhomogeneous (linearnonlinear)
D a matrix (rotation andor scaling) flux D a matrix (rotation andor scaling) flux and gradient are generally not paralleland gradient are generally not parallel Anisotropic diffusionAnisotropic diffusion Eigenvectors of D determine the diffusion Eigenvectors of D determine the diffusion
Incorporate adaptation based on the current Incorporate adaptation based on the current filtered image instead of the initial imagefiltered image instead of the initial image Spatial and temporal adaptationSpatial and temporal adaptation
D = g(D = g()) g a function of ug a function of u
High contrast region low diffusionHigh contrast region low diffusion Low contrast region high diffusionLow contrast region high diffusion
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Thank youThank you
Questions Questions
Diffusion FiltersDiffusion Filters
D a scalar (flux and gradient are parallel)D a scalar (flux and gradient are parallel) Isotropic diffusion Isotropic diffusion D spatially invariant (fixed) Homogeneous D spatially invariant (fixed) Homogeneous
linear linear D = g(D = g() Inhomogeneous (linearnonlinear)) Inhomogeneous (linearnonlinear)
D a matrix (rotation andor scaling) flux D a matrix (rotation andor scaling) flux and gradient are generally not paralleland gradient are generally not parallel Anisotropic diffusionAnisotropic diffusion Eigenvectors of D determine the diffusion Eigenvectors of D determine the diffusion
Incorporate adaptation based on the current Incorporate adaptation based on the current filtered image instead of the initial imagefiltered image instead of the initial image Spatial and temporal adaptationSpatial and temporal adaptation
D = g(D = g()) g a function of ug a function of u
High contrast region low diffusionHigh contrast region low diffusion Low contrast region high diffusionLow contrast region high diffusion
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Incorporate adaptation based on the current Incorporate adaptation based on the current filtered image instead of the initial imagefiltered image instead of the initial image Spatial and temporal adaptationSpatial and temporal adaptation
D = g(D = g()) g a function of ug a function of u
High contrast region low diffusionHigh contrast region low diffusion Low contrast region high diffusionLow contrast region high diffusion
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Thank youThank you
Questions Questions
Linear Diffusion FiltersLinear Diffusion Filters
rarr
HL
IHL
Linear Diffusion FiltersLinear Diffusion Filters
Inhomogeneous case Inhomogeneous case Decrease blurring of the important Decrease blurring of the important
Incorporate adaptation based on the current Incorporate adaptation based on the current filtered image instead of the initial imagefiltered image instead of the initial image Spatial and temporal adaptationSpatial and temporal adaptation
D = g(D = g()) g a function of ug a function of u
High contrast region low diffusionHigh contrast region low diffusion Low contrast region high diffusionLow contrast region high diffusion
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Thank youThank you
Questions Questions
Linear Diffusion FiltersLinear Diffusion Filters
Inhomogeneous case Inhomogeneous case Decrease blurring of the important Decrease blurring of the important
Incorporate adaptation based on the current Incorporate adaptation based on the current filtered image instead of the initial imagefiltered image instead of the initial image Spatial and temporal adaptationSpatial and temporal adaptation
D = g(D = g()) g a function of ug a function of u
High contrast region low diffusionHigh contrast region low diffusion Low contrast region high diffusionLow contrast region high diffusion
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Incorporate adaptation based on the current Incorporate adaptation based on the current filtered image instead of the initial imagefiltered image instead of the initial image Spatial and temporal adaptationSpatial and temporal adaptation
D = g(D = g()) g a function of ug a function of u
High contrast region low diffusionHigh contrast region low diffusion Low contrast region high diffusionLow contrast region high diffusion
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
So far adaptation is only done spatially So far adaptation is only done spatially andor temporally but diffusion direction is andor temporally but diffusion direction is fixedfixed
Adaptation of the diffusion orientationAdaptation of the diffusion orientation D is chosen as a matrix (scaling andor rotation)D is chosen as a matrix (scaling andor rotation)
Varying the diffusion direction over the Varying the diffusion direction over the image can preserveenhance localsemilocal image can preserveenhance localsemilocal featuresfeatures
Intraregion smoothing instead of Intraregion smoothing instead of interregion smoothinginterregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Thank youThank you
Questions Questions
Edge Enhancing FilterEdge Enhancing Filter
Change the orientation and the Change the orientation and the strength of the diffusion at an edgestrength of the diffusion at an edge
Smooth along the edge boundarySmooth along the edge boundary Diffusion along the edgesDiffusion along the edges
ReduceStop diffusion across the ReduceStop diffusion across the edge (eg Orthogonal to the edge)edge (eg Orthogonal to the edge)
Intraregion smoothingIntraregion smoothing
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Thank youThank you
Questions Questions
Edge Enhancing FilterEdge Enhancing Filter
Create a positive semidefinite diffusion Create a positive semidefinite diffusion tensor Dtensor D
Orthonormal eigenvectors of D Orthonormal eigenvectors of D υυ1 1 υυ2 2
Eigenvalues control the diffusion strengthEigenvalues control the diffusion strength 1)1)
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Create diffusion tensor as a function Create diffusion tensor as a function of structure tensor instead of the of structure tensor instead of the gradientgradient
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance
Thank youThank you
Questions Questions
ConclusionsConclusions
Fast and stable filtersFast and stable filters Highly flexible Highly flexible
Varying the parameters of the diffusion Varying the parameters of the diffusion tensor (orientation rotation strength)tensor (orientation rotation strength)
Incorporation of new features (texture Incorporation of new features (texture color etc)color etc)
Separate filters for each data entrySeparate filters for each data entry High performanceHigh performance