Text Enhancement by PDE’s Based Methods

Abstract

In this work, we propose a new method to enhance text in document-image. Firstly, we introduce a classical model and a way to solve it by means of a non-convex optimization problem. So, a simoultaneaous estimation of the reflectance and the luminance is obtained when the non uniform illumination (also called luminance) is a smooth function and the reflectance is a function of bounded variation. We give an analyse of this problem and some conditions of existence and unicity. Then, we consider the "log" of the classical model. A new pde's model is proposed. This method is based on the resolution of an original partial differential equation (PDE) estimating the log of the luminance. We assume that the luminance is enough smooth and is the solution of a non classical second order's PDE.Then we deduce the reflectance from the estimated luminance and the acquired image. The effectiveness and the robustness of the proposed process are shown on numerical examples in real-world situation (images acquired from cameraphones). Then, we illustrate the ability of this method to improve an Optical Character Recognition (OCR) in text recognition.

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

“…The equation 6has demonstrated its robustness in the extraction of the variable luminance and it has given quite satisfactory results (see [32]). However, the theoretical aspect of this equation has not been investigated, which left a lack of information on the behavior and the existence of the solution.…”

“…In particular, we focus on extracting illumination I using a nonlocal PDE in a well posed functional framework. Our proposed model is considered as a nonlocal version of the PDE proposed in [32]. The idea behind this choice is related to recently developed nonlocal operators [16].…”

“…The method proposed in [32] which aims to resolve the equation (6) supposes that the document-image u has been acquired by a cameraphone. The authors consider two problem types; namely: image distortions and noise.…”

“…According to the theorem 2.1 and theorem 3.1 in [21], the results of comparison and existence of a unique viscosity solution is reached. � As demonstrated in [32], the used PDE (6) has given good results, but does not preserve well the fine details of the text. This can be interpreted by the use of a local image reconstruction algorithm using observations in a neighborhood of a pixel of the interest.…”

“…As discussed above, we propose a new model for document-image enhancing. Therefore, we intend to obtain a new nonlocal generalization of the local model presented in [32]. As a preliminary, we recall some definitions of nonlocal operators introduced by Gilboa and Osher [16].…”