Abstract: Graph embeddings in vector spaces aim at assigning a pattern vector to every graph so that the problems of graph classification and clustering can be solved by using data processing algorithms originally developed for statistical feature vectors. An important requirement graph features should fulfil is that they reproduce as much as possible the properties among objects in the graph domain. In particular, it is usually desired that distances between pairs of graphs in the graph domain closely resemble those between their corresponding vectorial representations. In this work, we analyse relations between the edit distance in the graph domain and the L1 distance of the attribute statistics based embedding, for which good classification performance has been reported on various datasets. We show that there is actually a high correlation between the two kinds of distances provided that the corresponding parameter values that account for balancing the weight between node and edge based features are properly selected.

Abstract: Pattern recognition is the task that aims at distinguishing objects among different classes. When such a task wants to be solved in an automatic way a crucial step is how to formally represent such patterns to the computer. Based on the different representational formalisms, we may distinguish between statistical and structural pattern recognition. The former describes objects as a set of measurements arranged in the form of what is called a feature vector. The latter assumes that relations between parts of the underlying objects need to be explicitly represented and thus it uses relational structures such as graphs for encoding their inherent information. Vector spaces are a very flexible mathematical structure that has allowed to come up with several efficient ways for the analysis of patterns under the form of feature vectors. Nevertheless, such a representation cannot explicitly cope with binary relations between parts of the objects and it is restricted to measure the exact same number of features for each pattern under study regardless of their complexity. Graph-based representations present the contrary situation. They can easily adapt to the inherent complexity of the patterns but introduce a problem of high computational complexity, hindering the design of efficient tools to process and analyse patterns.
Solving this paradox is the main goal of this thesis. The ideal situation for solving pattern recognition problems would be to represent the patterns using relational structures such as graphs, and to be able to use the wealthy repository of data processing tools from the statistical pattern recognition domain. An elegant solution to this problem is to transform the graph domain into a vector domain where any processing algorithm can be applied. In other words, by mapping each graph to a point in a vector space we automatically get access to the rich set of algorithms from the statistical domain to be applied in the graph domain. Such methodology is called graph embedding.
In this thesis we propose to associate feature vectors to graphs in a simple and very efficient way by just putting attention on the labelling information that graphs store. In particular, we count frequencies of node labels and of edges between labels. Although their locality, these features are able to robustly represent structurally global properties of graphs, when considered together in the form of a vector. We initially deal with the case of discrete attributed graphs, where features are easy to compute. The continuous case is tackled as a natural generalization of the discrete one, where rather than counting node and edge labelling instances, we count statistics of some representatives of them. We encounter how the proposed vectorial representations of graphs suffer from high dimensionality and correlation among components and we face these problems by feature selection algorithms. We also explore how the diversity of different embedding representations can be exploited in order to boost the performance of base classifiers in a multiple classifier systems framework. An extensive experimental evaluation finally shows how the methodology we propose can be efficiently computed and compete with other graph matching and embedding methodologies.

Abstract: Historical documents suffer from different types of degradation and noise such as background variation, uneven illumination or dark spots. In case of double-sided documents, another common problem is that the back side of the document usually interferes with the front side because of the transparency of the document or ink bleeding. This effect is called the show through phenomenon. Many methods are developed to solve these problems, and in the case of show-through, by scanning and matching both the front and back sides of the document. In contrast, our approach is designed to use only one side of the scanned document. We hypothesize that show-trough are low contrast components, while foreground components are high contrast ones. A Multiresolution Contrast (MC) decomposition is presented in order to estimate the contrast of features at different spatial scales. We cancel the show-through phenomenon by thresholding these low contrast components. This decomposition is also able to enhance the image removing shadowed areas by weighting spatial scales. Results show that the enhanced images improve the readability of the documents, allowing scholars both to recover unreadable words and to solve ambiguities.

Abstract: Comic books constitute an important cultural heritage asset in many countries. Digitization combined with subsequent document understanding enable direct content-based search as opposed to metadata only search (e.g. album title or author name). Few studies have been done in this direction. In this work we detail a novel approach for the automatic text localization in scanned comics book pages, an essential step towards a fully automatic comics book understanding. We focus on speech text as it is semantically important and represents the majority of the text present in comics. The approach is compared with existing methods of text localization found in the literature and results are presented.

Abstract: Structural pattern recognition approaches offer the most expressive, convenient, powerful but computational expensive representations of underlying relational information. To benefit from mature, less expensive and efficient state-of-the-art machine learning models of statistical pattern recognition they must be mapped to a low-dimensional vector space. Our method of explicit graph embedding bridges the gap between structural and statistical pattern recognition. We extract the topological, structural and attribute information from a graph and encode numeric details by fuzzy histograms and symbolic details by crisp histograms. The histograms are concatenated to achieve a simple and straightforward embedding of graph into a low-dimensional numeric feature vector. Experimentation on standard public graph datasets shows that our method outperforms the state-of-the-art methods of graph embedding for richly attributed graphs.