Name
Abstract | ||
|---|---|---|
Diffusion-type algorithms have been integrated successfully into the toolbox of image processing. We introduce a new more flexible and powerful family of parabolic-hyperbolic partial differential equations (PDEs) that somewhat resembles the structure of the parabolic diffusion equation, but incorporates the second order derivative in time. It is instructive intuitively to consider in this context the dynamics of image processing as the deformation of an `elastic sheet'. Indeed, our parabolic-hyperbolic PDE models elastic deformation. This analogy between a well-known physical system and process on one hand, and the dynamics of an image processing scheme on the other hand, contributes interesting and important insight about images and their processing. We explore and demonstrate the capabilities and advantages afforded by the application of the proposed family of equations in image enhancement, and highlight the importance of incorporating the second derivative in time. The problem of computational complexity is addressed, and efficient numeric schemes are also presented. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1109/ICIP.2009.5413809 | Image Processing |
Keywords | Field | DocType |
computational complexity,elastic deformation,hyperbolic equations,image denoising,image enhancement,parabolic equations,partial differential equations,computational complexity,damped elastic sheet deformation,diffusion type algorithms,image denoising,image enhancement,parabolic diffusion equation,parabolic hyperbolic partial differential equations,PDE image processing,Parabolic-hyperbolic equations,denoising,image edge analysis,image enhancement | Parabolic partial differential equation,Computer science,Physical system,Mathematical analysis,Image processing,Artificial intelligence,Computer vision,Second derivative,Algorithm,Partial differential equation,Diffusion equation,Computational complexity theory,Hyperbolic partial differential equation | Conference |
ISSN | ISBN | Citations |
1522-4880 E-ISBN : 978-1-4244-5655-0 | 978-1-4244-5655-0 | 0 |
PageRank | References | Authors |
0.34 | 5 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vadim Ratner | 1 | 12 | 7.20 |
| Zeevi, Y.Y. | 2 | 191 | 74.30 |