Research projects stimulating the formation of new independent young research teams
PN-II-RU-TE-2014-4-0083
ARHIMEDES
Hybrid Image Restoration Algorithms based on Diffusion and Stochastic Equation Models
Algoritmi de Restaurare Hibridă a Imaginilor pe baza Modelelor cu Ecuaţii de Difuzie şi Ecuaţii Stocastice
CONTRACT # : |
126/01.10.2015 |
CONTRACTOR : |
Romanian Academy - Iaşi Branch |
TIME PERIOD : |
01.11.2015 - 30.09.2017 |
DURATION : |
24 months |
FINANCED BY : |
Executive Agency for Higher Education, Research, Development and Innovation (UEFISCDI) |
DIRECTOR : |
TUDOR BARBU, PhD, Habil, SR I Institute of Computer Science Iaşi |
PROJECT PURPOSE
Our Project ARHIMEDES is located at the confluence of Computer Science and Mathematics. Its purpose is to develop an effective image restoration system based on deterministic and stochastic differential models. The restoration process enhances the degraded images by performing both smoothing and reconstruction (missing region filling) operations. It represents a very important image pre-processing step that facilitates many image analysis and computer vision tasks. Image restoration results are applied in some important domains, like medicine, law enforcement, art conservation or cinematography.
Since mathematical models have been increasingly and succesfully used in all the image processing domains, our restoration system based on partial differential equations (PDEs), aiming to outperform existing PDE-based models, has scientific motivation. Also, the ARHIMEDES goal is not only to model and implement novel diffusion equation-based denoising and inpainting techniques, but also to integrate them into hybrid and combined restoration schemes that provide much better results.
The existing linear PDE denoising methods are equivalent to 2D Gaussian filters and have some drawbacks like producing the blurring effect and dislocating edges when moving from finer to coarser scales. We intend to construct improved linear diffusion based restoring models that alleviate the undesired effects and provide a better feature-preserving denoising. Also, we will derive nonlinear PDE filters from our linear denoising models and combine the latter with 2D conventional filters to improve smoothing.
More important, we intend to develop PDE-based hybrid restoration architectures that combine both 2nd and 4th order nonlinear diffusions. Such a combined anisotropic diffusion-based denoising framework would produce more natural restored images and overcome all the unintended effects. The variational models associated to these hybrid restoration schemes are also considered and investigated.
Besides these deterministic models, another important category of differential models used increasingly in the image enhancement area is that of the stochastic models. These probability models are based on stochastic differential equations (SDEs) and provide effective image restoration. We propose some robust SDE-based restoration techniques that could be reduced to novel diffusion models through the associated Kolmogorov equations.
We also intend to integrate our inpainting algorithms into more effective hybrid restoration schemes performing texture reconstruction or enhancing images affected by both noise and missing zones. While many PDE methods use the inconsistent and not so mathematically correct P-M discretization, we propose consistent numerical approximation schemes using the finite-difference method to discretize continuous models. An important part of the research conducted within this project will focus on performing robust mathematical treatments for developed PDE and SDE models. They will be rigorously investigated, their well-posedness, stability and consistency being seriously treated.