R' DOSIL, X' M' PARDO, A' MOSQUERA, D' CABELLO

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Curvature dependent diffusion forfeature
detection in 3D medical images

• R. DOSIL, X. M. PARDO, A. MOSQUERA, D. CABELLO
  

Grupo de Visión ArtificialDepartamento de
Electrónica e ComputaciónUniversidade de
Santiago de Compostela
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Feature detection in medical images

• Objectives
• Calculus of gradient and curvature
• Detection of boundaries and corners
• Applications
• Energy minimization techniques definition of
  image potentials
• Matching techniques detection of characteristic
  features

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Feature detection in medical images

• Problems Noise, textures, ...
• Erroneous calculus of gradient and curvature
• Failure in boundary and corner detection
• Typical solution gaussian smoothing
• Alteration of gradient and curvature values
• Dislocation of boundaries and rounding of corners
• Proposal use of adaptive filtering based on
  diffusion processes

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Outline

• Introduction
• Feature enhancement with diffusion
• Tangential diffusion
• Construction of the diffusion tensor
• Threshold parameter
• Corner preserving diffusion
• Previous works
• Curvature dependent diffusivity
• Results

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Introduction

• Diffusion equation

with
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Introduction

• Linear
• C is a scalar constant
• It blurs boundaries as gaussian filtering does
• Nonlinear (Perona Malik, 1990)
• C depends on local image properties
• If C is a decreasing function of ?u
• Boundaries are not blurred
• Noise is preserved at surfaces
• Nonlinear anisotropic (Weickert, 1994)
• C is a tensor ? Flux vector is not parallel to
  gradient
• Different diffusivity values ?i for different
  directions e i

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Feature enhancement with diffusion

• Tangential diffusion
• Diffusivity is reduced in the normal dir. at each
  point
• Boundaries are not blurred
• Diffusion is maintained in the tangent plane
• Reduces noise by flattening surfaces
• It rounds corners

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Feature enhancement with diffusion

• Construction of C
• e i are the eigenvectors of the hessian matrix
• ?i are their correspondent desired eigenvalues

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Feature enhancement with diffusion

• Threshold parameter ?
• Represents the gradient threshold at which flux
  stops growing
• Automatic estimation of ? using robust statistics
  (Black, 1998)

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Corner preserving diffusion

• Previous work by Krissian, 1996
• Diffusion in the max. curvature dir. is removed

• It avoids corner rounding
• Noise reduction is lower

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Corner preserving diffusion

• Curvature dependent diffusivity
• Diffusion in the max. curvature direction depends
  on a corner measure

• Diffusion in the max. curvature dir. is reduced
  on corners
• Remainder surface regions are flattened in the
  tangent plane

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ResultsComparison of different schemes

• Construction of a synthetic image with gaussian
  noise of variance ? 50

• Filtering with four different diffusion schemes

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ResultsAnisotropic filter Vs Gaussian filter

• Test with synthetic image with gaussian noise of
  variance ? 50

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ResultsAnisotropic filter Vs Gaussian filter

• Surface points location

Error in location of corners
Error in sphere radius estimation
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ResultsAnisotropic filter Vs Gaussian filter

• Curvature estimation

Error in curvature estimation using gaussian
filter
Error in curvature estimation using anisotropic
filter
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ResultsMedical image example

• MRI image of aorta

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Results Medical image example

• MRI image of aorta

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Conclusions

• Contributions
• Use of diffusion techniques to improve gradient
  and curvature measures in 3D medical imaging
• definition of image potentials
• feature detection
• Design of corner preserving diffusion filter
• Automatic estimation of filter parameters
• Future work
• Introduction of adaptive estimation of threshold
  parameters

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End