Scale-Space and Edge Detection Using Anisotropic Diffusion

1. Scale-Space and Edge Detection Using Anisotropic Diffusion Presented By:Deepika Madupu Reference: Pietro Perona & Jitendra Malik

2. 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.

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

4. Heat Diffusion • Scale-space can be viewed as the solution of the heat conduction, or diffusion as With the initial condition , the original image.

5. Criteria • Koenderink motivates the diffusion equation by stating these criteria • Causality • Homogeneity and Isotropy

6. 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

7. Example of scale-space • Fig 3 shows that the region boundaries are generally quite diffuse instead of being sharp.

8. 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

9. Edge Detection at different scale levels

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

11. 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

12. 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

13. Anisotropic Diffusion Isotropic (Heat equation) Anisotropic

14. Experiments • Numerical experiments • Utilize a square lattice • Each of 4-neighbors’ brightness contributing to the discretization of the Laplacian • Different values of c

15. 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

16. 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

17. Conclusions • Efficient and reliable scheme • Interesting benefits • Questions???

18. 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