# Bayesian Feature Fusion Using Factor Graph in Reduced Normal Form
## 1 Introduction  
Data Fusion techniques are becoming increasingly important in many application contexts, such as defence, energy, biomedicine, manufacturing, etc. Fusion methods lead to better understanding of a phenomenon and of the decisions to be taken, especially in terms of robustness and accuracy with respect to what we would obtain using separate sources of information [1]. We can identify three increasing abstraction levels of Data Fusion models: Data Level, Feature Level and Decision Level. [PERSON] [2] has proposed five fusion modes : Data In-Data Out (DaI-DaO) Fusion, Data In-Feature Out (Dal-FeO) Fusion, Feature In-Feature Out (Fel-FeO) Fusion, Feature In-Decision Out (Fel-DeO) Fusion, Decision In-Decision Out (Del-DeO) Fusion. In this work, we investigate the application of a Bayesian approach to the Fel-DeO Fusion, which can be considered one of the most common fusion paradigms. The input features, coming from different sensors, are merged to produce a more informed decision. The data, retrieved from each sensor, can have missing, or wrong values, and the proposed Bayesian approach permits to manage them in a robust and flexible way. In the following, we apply the Bayesian Data Fusion methodology to the Classification of Documents in a Maritime Port scenario, limiting our attention to documents such as Passports, Identity Cards and Fiscal Codes from different countries. The general architecture of such system is similar to Automated Border Control (ABC) [3], which is a self-service barrier that permits the identification of the passengers through the comparison between biometrics information stored in the passport's chip and the face, fingerprint, or iris (or a combination of them). These automatic systems have improved the efficiency, rapidity and security of the identification process. A simplified scheme of an ABC is presented in Figure 1.  
In our applications, each document is scanned in its front and back, and three specialized detectors extract face, text, and barcode, possibly present in it. The related content is also stored for a Document Verification, or for other steps of the overall Border Control as: Authenticity Check, Identity Verification, etc. The document classification has been emerging as an important task for its application in several real scenarios where a huge number of documents has to be managed. In this context, many different solutions have been proposed that use the layout, the contained text, the visual contents or a combination of them as the more recent solutions [4; 5]. In the recent years some approaches based on the Graph Convolutional Networks have demonstrated to be very promising [6; 7] given their capability to describe the relations among different part of the document. The identity document classification can be considered a particular type of more generic document classification task but the layout is not discriminant enough because the identity documents have similar layouts, the textual information is not so easy to extract and the available datasets are small and with critical privacy and legal issues. In the years the identity document classification task has been tackled using different approaches. Some solutions have used the visual features extracted from the document image itself in order to train a classifier [8; 9]; other works have used the template matching approach comparing the observed document with some reference models [10]; finally different deep learning approaches have been investigated as [8; 11; 12]. In our work, instead of focusing on the strength and weakness of the particular classifiers and/or features, we describe a general architecture where information from different detectors (in general feature extractors or different classifiers), are fused together in order to infer the type of the presented document. The technique is based on the Naive Bayes model represented as Factor Graph in Reduced Normal Form (FGrn) [13].