This paper proposes a novel Nonlinear Orthogonal NMF model with Graph-based Total Variation regularization (GTV) for Multispectral document images decomposition. In this model, a GTV regularization is incorporated to preserve the intrinsic geometrical structure of document content lost by the vectorization of spectral images. A spatial orthogonality constraint over the Stiefel manifold is imposed to improve the sparsity of the solution and ensure its uniqueness. The kernel trick is involved to account for the non-linear correlation inherent to spectral data. We devised an efficient algorithm to solve the formulated problem using the Alternating Direction Method of Multipliers (ADMM). The experimental results on real-world data show that the proposed model achieves better decomposition performance than recent competitive methods and outperforms some traditional state-of-the-art methods.

Nonnegative matrix factorization (NMF) is one of the best-known multivariate data analysis techniques. The NMF uniqueness and its rank selection are two major open problems in this field. The solutions uniqueness issue can be addressed by imposing the orthogonality condition on NMF. This constraint yields sparser part-based representations and improved performance in clustering and source separation tasks. However, existing orthogonal NMF algorithms rely mainly on non-probabilistic frameworks that ignore the noise inherent in real-life data and lack variable uncertainties. Thus, in this work, we investigate a new probabilistic formulation of orthogonal NMF (ONMF). In the proposed model, we impose the orthogonality through a directional prior distribution defined on the Stiefel manifold called von Mises-Fisher distribution. This manifold consists of a set of directions that comply with the orthogonality condition that arises in many applications. Moreover, our model involves an automatic relevance determination (ARD) prior to address the model order selection issue. We devised an efficient variational Bayesian inference algorithm to solve the proposed ONMF model, which allows fast processing of large datasets. We evaluated the proposed model, called VBONMF, on the task of blind decomposition of real-world multispectral images of ancient documents. The numerical experiments demonstrate its efficiency and competitiveness compared to the state-of-the-art approaches.

As a nonlinear extension of the standard nonnegative matrix factorization (NMF), kernel-based variants have demonstrated to be more effective for discovering meaningful latent features from raw data. However, many existing kernel methods allow only obtaining the basis matrix in the projected feature space, which prevents its inverse mapping back to the original space as requested in many applications. In this work, we propose a new kernel orthogonal NMF method that does not suffer from the pre-image issue. We incorporate the orthogonality constraint as an optimization problem over the Stiefel manifold to improve the sparsity and the model’s clustering properties. We solve the proposed model with an efficient optimization approach based on the alternating direction method of multipliers (ADMM) scheme and the projected gradients method. We validate our model on the task of blind decomposition of real-world Multispectral (MS) document images. Our experiments demonstrate the competitiveness of our proposed model in comparison to the state-of-the-art techniques.

This paper addresses the challenge of Multispectral (MS) document image segmentation, which is an essential step for subsequent document image analysis. Most previous studies have focused only on binary (text/non-text) separation. They also rely on handcrafted features and techniques dedicated to conventional images that do not take advantage of MS images' spectral richness. In this work, we reformulate this task as a source separation problem, whereby we target the blind decomposition of entire MS document images via a new orthogonal nonnegative matrix factorization (ONMF). On the one hand, we incorporate orthogonality constraint as a Riemannian optimization on the Stiefel manifold. On the other hand, based on which factor we impose the orthogonality constraint, i.e., either on the endmember matrix, abundance matrix, or both, we propose three ONMF models to investigate this issue and determine which model is more suitable for this study. Minimizing the three models subject to nonnegativity and orthogonality constraints simultaneously is very challenging. Therefore, we extend the alternating direction method of multipliers scheme to solve them. We evaluated our models on synthetic Hyperspectral (HS) images and real-world MS document images. The experimental results confirm the effectiveness of the proposed models and demonstrate their generalization power compared to state-of-the-art techniques.

In this paper, we propose a novel method for Multispectral document image binarization (MSdB) through the Non-negative Matrix Factorization (NMF) approach. We propose a three-step MSdB-NMF framework: i) NMF-based feature extraction algorithm by introducing a new optimization problem; ii) post-processing method iii); apply any existing gray/RGB binarization scheme. In the first step, we extract N features out of B spectral bands (N < B) and their corresponding coefficient matrix. We introduce a novel objective formulation that considers the robustness (related to the noise and various types of degradations) and sparseness (related to the ratio of text pixels versus the background). We employ the multiplicative updating rules to solve the proposed minimization problem and prove the convergence of the proposed feature extraction algorithm. In the next step, we select an appropriate feature vector, equivalently the corresponding coefficient vector. We propose to select it either visually or automatically via a post-processing method, which uses the benchmark binarization methods as baseline. In the last step, we apply some existing binarization methods such as Sauvola and Howe over the selected coefficient vector. Our proposed binarization framework is applicable for any kind of MS or hyperspectral (HS) document image without considering any prior knowledge such as the side information about the spectral bands of MS/HS document image. We evaluate our proposed binarization framework over two MS document image datasets. The experimental results confirm that our proposed framework outperforms several state-of-theart binarization schemes including the winner of the contest in MS-TEx-2015.

In this paper, we propose a novel Blind Source Separation (BSS) based framework for multispectral (MS) document images binarization. This framework takes advantage of the multidimensional data representation of MS images and makes use of the Graph regularized Non-negative Matrix Factorization (GNMF) to decompose MS document images into their different constituting components, i.e., foreground (text, ink), background (paper, parchment), degradation information, etc. The proposed framework is validated on two different real-world data sets of manuscript images showing a high capability of dealing with: variable numbers of bands regardless of the acquisition protocol, different types of degradations, and illumination non-uniformity while outperforming the results reported in the state-of-the-art. Although the focus was put on the binary separation (i.e., foreground/background), the proposed framework is also used for the decomposition of document images into different components, i.e., background, text, and degradation, which allows full sources separation, whereby further analysis and characterization of each component can be possible. A comparative study is performed using Independent Component Analysis (ICA) and Principal Component Analysis (PCA) methods. Our framework is also validated on another third dataset of MS images of natural objects to demonstrate its generalizability beyond document samples.