Spatio-temporal regularized shock-diffusion filtering with local entropy for restoration of degraded document images

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Highlights

  • Propose a novel model for restoration of document images with degraded background.

  • The model is formulated as a system PDE coupling shock filter and indirect diffusion.

  • Source term is responsible to generate a sequence of images with “gradually clean” background.

  • Proposed method is effective for restoration of document images with degraded background.

Abstract

This paper proposes a novel model for restoration of document images with degraded background caused by show-through/smear or deteriorated documents. The model is formulated as a partial differential equation (PDE) that consists of spatio-temporal regularization of shock filtering and diffusion process, as well as local entropy. Shock filtering is employed to enhance the brightness contrast between texts and background according to image gradients adaptively. Diffusion process is not only responsible for removing selectively noise in the input image, but also suppressing the amplified noise by the shock filtering. Local entropy based source term serves as degradation-corrected term that is responsible for reducing the influence of degradation. A splitting-based algorithm is developed to solve the proposed model numerically, where two typical splitting methods and finite difference are combined. We test the proposed model and numerical scheme on DIBCO 2009–2014 and 2016 datasets. Experimental results indicate that the proposed method works well in restoring document images with degraded background, and achieves comparable performances compared to seven relevant methods for seven DIBCO datasets.

Introduction

Binarization of document images is a critical step which is really performed in advance of performing optical character recognition (OCR). The role of binarization is to separate the texts from the background of a document image. However, document images, especially historical document images, usually suffer from numerous degradations including smear or show through, uneven illumination, contrast variation, bleed-through, faded ink or faint characters, thin or weak text, blur, deteriorated documents and other factors [1], [2]. In this case, direct binarization has difficulty in extracting the texts from the degraded document image accurately. Thus, degradation restoration of degraded document images for binarization is a basic but challenging task in OCR system.

In recent decades, some methods based on partial differential equation (PDE) have been applied in the field of degraded document image restoration/binarization. PDE-based models are appealing for profound physical background and some unique properties, especially for smoothness, continuity, and so on [3], [4]. The basic idea behind PDE-based binarization methods is that, for different types of degradations, to design a PDE for degradation restoration, and then follow by a binary projection for binarization.

In [5], Cheriet presented a generalized shocking model for degraded gray-level character images, which is a quasi-linear hyperbolic partial differential equation with discontinuous coefficients. In [6], Nwogu et al. exploited the regional smoothing that occurs in a nonlinear diffusion process to enhance low quality documents. To eliminate the inherent corner rounding, Drira et al. [7] proposed an anisotropic diffusion by adding new constraints to the Weickert coherence-enhancing diffusion filter to control the diffusion process. In [8], Mahani et al. introduced two methods to enhance text in document-image. One is a classical model and the other is obtained by a way to solve it by considering the “log” of the classical model. To address irregular boundaries and noise, Kumar et al. [9] employed edge enhancement diffusion and level set method to separate text/image region from scanned document images. In [10], Guemri and Drira proposed an adaptive shock filter for image characters enhancement and denoising, in which a filter is introduced to sharpen image features like edges and singularities while an anisotropic diffusion process is used to remove noise. Recently, to deal with degraded document images with blur, noise and bleed-through, Guo and He [11] presented an adaptive restoration model with selective smoothing, involving an adaptive shock filter and a nonlinear isotropic diffusion process. In [12], Du et al. proposed a nonlinear diffusion equation with selective source for restoration of degraded document images, followed by a binary projection for binarization. Jacobs and Celik [13] presented an unsupervised document image binarization method using a system of nonlinear PDEs, wherein the thresholding parameter are governed by an additional PDE.

In addition, some variational level set models have been proposed in literature. For example, in [14], Feng presented a convex variational level set model for document image binarization, in which binarization results are generated by the sign of level set function. In fact, minimization problems can be converted into a diffusion equation with source by gradient descent. Therefore, to some extent, such models can also be seen as binarization techniques in the PDE framework.

The restoration and binarization methods above have obtained achievements for one specific or a few document degradations issues. However, document images suffer from various forms of degradations, and challenges may still come up in the form of some typical degradations, such as degraded background appearing over the documents (see Fig. 1) which are caused by show-through/smear, deteriorated documents [1]. There are the compelling needs to develop accepted PDE-based restoration methods that can provide robust results to deal with specific kinds of document degradations.

In this paper, we propose a PDE-based restoration model to handle the document images with degraded background, as shown in Fig. 1. The model is composed of a spatio-temporal regularized shock filtering and selective diffusion, together with a source term based on local entropy. The shock filtering enhances the brightness contrast between texts and background according to image gradients adaptively. The role of diffusion term is to selectively remove noise in the input degraded document image, while reducing amplified noise by the shock filtering. The source serves as degradation-corrected term that is responsible for reducing the influence of smear/show-through on the degraded background. We develop a splitting-based algorithm to solve the proposed model numerically. The proposed model with algorithm is tested on six publicly available datasets, i.e., DIBCO 2009 to 2014 and 2016 and is compared with seven closely related models [7], [9], [10], [11], [12], [13], [14].

The remainder of this paper is organized as follows. Section 2 introduces briefly some related works. Section 3 describes and analyses the proposed restoration model. Section 4 gives numerical scheme and Section 5 presents experimental results qualitatively and quantitatively. This paper is summarized in Section 6.

Section snippets

Related works

In this section, we briefly give a review of the related works which motivate us to develop a new model for the restoration of some degraded document images.

Proposed method and discussion

In what follows, we give and discuss the proposed model for restoration of document images with degraded background.

Numerical scheme

The proposed model can be implemented by using the simple explicit finite differencing. However, to ensure numerical stability, a very small timestep is usually needed because of Courant-Friedrichs-Lewy condition. Besides, it can also be implemented by the implicit scheme, but this always requires solving a large-scale nonlinear system of equations on each iteration. To solve our model more efficiently and effectively, in this section, we design a splitting-based algorithm,which combines

Experimental results

Our model is firstly assessed on six degraded document images with smear or show through, which are shown in Fig. 1. It is not easy to understand the nature of defects and degradations in these document images [1]. In this paper, they are referred to as document images with degraded background. These images are all chosen from public DIBCO datasets. Then, we test our model on all images in these datasets and compared it with four PDE-based restoration models: DLE [7], KRPS [9], GD [10], GH [11]

Conclusions

For restoration of document images with degraded backgrounds, we propose a partial differential equation (PDE) that couples spatio-temporal regularized shock filtering and diffusion process. We show experimentally that it has comparable performance on document images with degraded background caused by show-through/smear or deteriorated documents, compared to several relevant PDE-based restoration models and binarization models, qualitatively and quantitatively.

Acknowledgments

This work is partially supported by National Natural Science Foundation of China (No. 11901071, 31971113), and the Natural Science Foundation Project of CQCSTC (No. cstc2019jcyj-msxmX0219).

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