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: 5Y Impact Factor: 2.99 / 1st (Ophthalmology)
An achromatic stimulus is defined as a patch of light that is devoid of any hue. This is usually achieved by asking observers to adjust the stimulus such that it looks neither red nor green and at the same time neither yellow nor blue. Despite the theoretical and practical importance of the achromatic locus, little is known about the variability in these settings. The main purpose of the current study was to evaluate whether achromatic settings were dependent on the task of the observers, namely the navigation direction in color space. Observers could either adjust the test patch along the two chromatic axes in the CIE u*v* diagram or, alternatively, navigate along the unique-hue lines. Our main result is that the navigation method affects the reliability of these achromatic settings. Observers are able to make more reliable achromatic settings when adjusting the test patch along the directions defined by the four unique hues as opposed to navigating along the main axes in the commonly used CIE u*v* chromaticity plane. This result holds across different ambient viewing conditions (Dark, Daylight, Cool White Fluorescent) and different test luminance levels (5, 20, and 50 cd/m2). The reduced variability in the achromatic settings is consistent with the idea that internal color representations are more aligned with the unique-hue lines than the u* and v* axes.

Abstract: The importance of logos and trademarks in nowadays society is indisputable, variably seen under a positive light as a valuable service for consumers or a negative one as a catalyst of ever-increasing consumerism. This chapter discusses the technical approaches for enabling machines to work with logos, looking into the latest methodologies for logo detection, localization, representation, recognition, retrieval, and spotting in a variety of media. This analysis is presented in the context of three different applications covering the complete depth and breadth of state of the art techniques. These are trademark retrieval systems, logo recognition in document images, and logo detection and removal in images and videos. This chapter, due to the very nature of logos and trademarks, brings together various facets of document image analysis spanning graphical and textual content, while it links document image analysis to other computer vision domains, especially when it comes to the analysis of real-scene videos and images.