Scale space and edge detection using anisotropic diffusion
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Scale-Space and Edge Detection Using Anisotropic Diffusion. Presented By:Deepika Madupu Reference: Pietro Perona & Jitendra Malik. Introduction. Existing Scale-space technique Larger values of t,the scale space parameter, correspond to images at coarser resolutions.

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Scale-Space and Edge Detection Using Anisotropic Diffusion

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Scale space and edge detection using anisotropic diffusion

Scale-Space and Edge Detection Using Anisotropic Diffusion

Presented By:Deepika Madupu

Reference: Pietro Perona & Jitendra Malik


Introduction

Introduction

  • Existing Scale-space technique

  • Larger values of t,the scale space parameter, correspond to images at coarser resolutions.

  • Drawback: Difficult to obtain accurately the locations of the “semantically meaningful” edges at coarse scales.


Example of scale space technique

Example of scale-space technique

  • Example:

    Figure 1. Character N


Heat diffusion

Heat Diffusion

  • Scale-space can be viewed as the solution of the heat conduction, or diffusion as

    With the initial condition ,

    the original image.


Criteria

Criteria

  • Koenderink motivates the diffusion equation by stating these criteria

  • Causality

  • Homogeneity and Isotropy


Weakness of scale space paradigm

Weakness of scale-space paradigm

  • The true location of the edges that have been detected at a coarse scale is by tracking across the scale space to their position in the original image which proves complicated and expensive.

  • Gaussian blurring does not respect edges and boundaries


Example of scale space

Example of scale-space

  • Fig 3 shows that the region boundaries are generally quite diffuse instead of being sharp.


Improved criteria of anisotropic diffusion

Improved criteria of Anisotropic Diffusion

  • With this as motivation, any model for generating multiscale “semantically meaningful” description of images must satisfy:

  • Causality

  • Immediate Localization

  • Piecewise Smoothing


Edge detection at different scale levels

Edge Detection at different scale levels


Alternative scheme presented in paper

Alternative scheme presented in paper

  • An anisotropic diffusion process

  • Intraregion smoothing in preference to interregion smoothing

  • Objectives – Causality, Immediate Localization, Piecewise Smoothing


Approach

Approach

  • Establish that anisotropic satisfies the causality criterion

  • Modify the scale-space paradigm to achieve image objectives

  • Introduce a part of the edge detection step in the filtering itself


Anisotropic diffusion equation

Anisotropic Diffusion Equation

  • Perona & Malik proposed to replace the heat equation by a nonlinear equation

  • Coefficient c is not necessarily a constant as assumed by Koenderink, but 1 in the interior of each region and 0 at the boundaries


Anisotropic diffusion

Anisotropic Diffusion

Isotropic

(Heat equation)

Anisotropic


Experiments

Experiments

  • Numerical experiments

  • Utilize a square lattice

  • Each of 4-neighbors’ brightness contributing to the discretization of the Laplacian

  • Different values of c


Advantages of this scheme

Advantages of this Scheme

  • Locality: neighborhood where smoothing occurs are determined locally

  • Simplicity: simple, fewer steps, less expensive scheme

  • Parallelism: cheaper when run on parallel processors


Disadvantages

Disadvantages

  • computationally more expensive than convolution on sequential machines

  • Problems would be encountered in images where brightness gradient generated by noise is greater than those of the edges


Conclusions

Conclusions

  • Efficient and reliable scheme

  • Interesting benefits

  • Questions???


References

References

  • http://www.aso.ecei.tohoku.ac.jp/~machi/paper/pdf/icpr00-4-455.pdf

  • http://en.wikipedia.org/wiki/Scale_space

  • http://www.ipam.ucla.edu/publications/gbmcom/gbmcom_4201.ppt#403,85,Current

  • http://www-sop.inria.fr/epidaure/personnel/Pierre.Fillard/research/tensors/tensors.php

  • http://users.ntua.gr/karank/topo/PhD_notes/Anisotropic_Dif/main.htm

  • http://www.mia.uni-saarland.de/weickert/demos.html

  • Scale-Space and Edge Detection Using Anisotropic Diffusion - Pietro Perona & Jitendra Malik


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