Reduction of the non-uniform illumination using nonlocal variational models for document image analysis

Fatim Zahra Aït Bella (1) , Mohammed El Rhabi (2) , Abdelilah Hakim (1) , Amine Laghrib (3)

1 UCA - Université Cadi Ayyad [Marrakech]
2 ENPC - École des Ponts ParisTech
3 USMS - Université Sultan Moulay Slimane

In this paper, we investigate two new reflectance and illumination decomposition models based on a nonlocal partial differential equation (PDE) applied to text images. Taking into consideration the higher regularity level of the illumination compared to the reflectance, we propose a nonlocal PDE which deals with repetitive structures and textures that characterize the text image much better compared to the classical local PDEs. The aim of this approach is to use the repetitive features of the reflectance to efficiently extract it from the nonuniform illumination. This idea is motivated by extending the range of application of the nonlocal operators to such problem. Numerical experiments on both grayscale and color text images show the performance and strength of the proposed nonlocal PDE.

Keywords: Nonlocal operators; Partial differential equation; Text image; Viscosity solutions theory

Domains: Analysis of PDEs [math.AP]; Functional Analysis [math.FA]; Numerical Analysis [math.NA]; Signal and Image processing

Fatim Zahra Aït Bella, Mohammed El Rhabi, Abdelilah Hakim, Amine Laghrib. Reduction of the non-uniform illumination using nonlocal variational models for document image analysis. Journal of The Franklin Institute, inPress, ⟨10.1016/j.jfranklin.2018.08.012⟩. ⟨hal-01874941⟩