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

Example of scale-space technique Example: Figure 1. Character N

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 Koenderink motivates the diffusion equation by stating these criteria - Causality - Homogeneity and Isotropy

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

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

Alternative scheme presented in paper An anisotropic diffusion process Intraregion smoothing in preference to interregion smoothing Objectives – Causality, Immediate Localization, Piecewise Smoothing

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 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 Isotropic (Heat equation) Anisotropic

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 Locality: neighborhood where smoothing occurs are determined locally Simplicity: simple, fewer steps, less expensive scheme Parallelism: cheaper when run on parallel processors

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 Efficient and reliable scheme Interesting benefits Questions???

References pdf pdf pt#403,85,Current pt#403,85,Current sop.inria.fr/epidaure/personnel/Pierre.Fillard/research/tensors/ten sors.php sop.inria.fr/epidaure/personnel/Pierre.Fillard/research/tensors/ten sors.php htm htm Scale-Space and Edge Detection Using Anisotropic Diffusion - Pietro Perona & Jitendra Malik