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# Scale-Space and Edge Detection Using Anisotropic Diffusion - PowerPoint PPT Presentation

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

Reference: Pietro Perona & Jitendra Malik

• 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:

Figure 1. Character N

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

With the initial condition ,

the original image.

• Koenderink motivates the diffusion equation by stating these criteria

• Causality

• Homogeneity and Isotropy

• 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

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

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

• Causality

• Immediate Localization

• Piecewise Smoothing

• An anisotropic diffusion process

• Intraregion smoothing in preference to interregion smoothing

• Objectives – Causality, Immediate Localization, Piecewise Smoothing

• 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

• 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

Isotropic

(Heat equation)

Anisotropic

• Numerical experiments

• Utilize a square lattice

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

• Different values of c

• Locality: neighborhood where smoothing occurs are determined locally

• Simplicity: simple, fewer steps, less expensive scheme

• Parallelism: cheaper when run on parallel processors

• 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

• Efficient and reliable scheme

• Interesting benefits

• Questions???

• 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