Deterministic and Bayesian orthogonal nonnegative matrix factorization: application to blind decomposition of multispectral document images

Abstract

This thesis addresses the problem of blind decomposition of spectral document images into layers of their constituent materials (e.g., inks, paper, pigments). The aim is to develop advanced processing tools that enable the effective use of spectral imaging technologies for document analysis and simplify their processing. Since spectral imaging provides more information on several acquisition wavelengths, for such images, observations of document scenes are considered as a mixture of some latent signals of their constituent objects, where neither the mixing operator nor the mixed sources are known. Therefore, we resort to Blind Source Separation (BSS) techniques to estimate these two unknown operators. Specifically, we consider nonnegative matrix factorization (NMF), one of the powerful techniques for the analysis of high-dimensional data. NMF provides a lower-rank approximation of the data that is easier to interpret. The problem is then inverted, and NMF seeks to estimate the two unknown factors based only on a set of observations. Formally, this problem turns into an algebraic operation of the form X ≈ MA, where X represents the observations reshaped into an m × n matrix, M is an m × k matrix of sources, and A is a k × n matrix of coefficients. This problem is far from being a simple image segmentation task. Indeed, many challenges owing to the high-dimensionality of data, lack of labeled samples, and other ambiguities related to BSS methods should be considered to handle this problem appropriately. Hence, to tackle the aforementioned challenges, this thesis investigates the orthogonal constraint over the Stiefel manifold as a key feature for NMF. Consequently, this study proposes new orthogonal NMF (ONMF) models ranging from deterministic to probabilistic settings. We first proposed a new ONMF formulation over the Stiefel manifold. Therefore, according to which factor matrix is constrained to be orthogonal, we developed three new ONMF models. Then, to account for the non-linearity inherent in the feature space of spectral data and the intrinsic geometrical structure lost by the vectorization required by NMF, we proposed a new non-linear ONMF model with a graph-based total variation regularization. The new model is immune against the pre-image issue and preserves the structure of the data. Finally, we reformulated the problem from a Bayesian perspective to address limitations of deterministic frameworks, such as model parameters uncertainty and model order selection. The performance of the proposed algorithms has been evaluated on synthetic and real-world datasets. The results demonstrate their efficiency in handling unsupervised separation of components in spectral document images. The contribution and impact of this research work are two folds. On the one hand, it provides several practical algorithms to handle spectral document images decomposition based on orthogonal NMF. On the other hand, it promotes the benefit of spectral imaging technologies for analyzing documents through concrete use-cases ranging from inks differentiation to materials separation based on their optical properties only. The developed framework opens the doors toward new applications that could not be handled using traditional document images processing approaches. Some of the potential applications include writing materials identification and differentiation, forgery detection, and content change detection, to name a few. Ultimately, this will enable extensive and efficient use of spectral technology in the field of document image analysis.

Date	7 Feb 2022
Original language	American English
Awarding Institution	École de technologie supérieure
Supervisor	Mohamed Cheriet (Supervisor)