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: : Edge-based color constancy methods make use of image derivatives to estimate the illuminant. However, different edge types exist in real-world images such as material, shadow and highlight edges. These different edge types may have a distinctive influence on the performance of the illuminant estimation. Therefore, in this paper, an extensive analysis is provided of different edge types on the performance of edge-based color constancy methods. First, an edge-based taxonomy is presented classifying edge types based on their photometric properties (e.g. material, shadow-geometry and highlights). Then, a performance evaluation of edge-based color constancy is provided using these different edge types. From this performance evaluation it is derived that specular and shadow edge types are more valuable than material edges for the estimation of the illuminant. To this end, the (iterative) weighted Grey-Edge algorithm is proposed in which these edge types are more emphasized for the estimation of the illuminant. Images that are recorded under controlled circumstances demonstrate that the proposed iterative weighted Grey-Edge algorithm based on highlights reduces the median angular error with approximately $25\%$. In an uncontrolled environment, improvements in angular error up to $11\%$ are obtained with respect to regular edge-based color constancy.

Abstract: When light is reflected off a surface, there is a linear relation between the three human photoreceptor responses to the incoming light and the three photoreceptor responses to the reflected light. Different colored surfaces have different linear relations. Recently, Philipona and O'Regan (2006) showed that when this relation is singular in a mathematical sense, then the surface is perceived as having a highly nameable color. Furthermore, white light reflected by that surface is perceived as corresponding precisely to one of the four psychophysically measured unique hues. However, Philipona and O'Regan's approach seems unrelated to classical psychophysical models of color constancy. In this paper we make this link. We begin by transforming cone sensors to spectrally sharpened counterparts. In sharp color space, illumination change can be modeled by simple von Kries type scalings of response values within each of the spectrally sharpened response channels. In this space, Philipona and O'Regan's linear relation is captured by a simple Land-type color designator defined by dividing reflected light by incident light. This link between Philipona and O'Regan's theory and Land's notion of color designator gives the model biological plausibility. We then show that Philipona and O'Regan's singular surfaces are surfaces which are very close to activating only one or only two of such newly defined spectrally sharpened sensors, instead of the usual three. Closeness to zero is quantified in a new simplified measure of singularity which is also shown to relate to the chromaticness of colors. As in Philipona and O'Regan's original work, our new theory accounts for a large variety of psychophysical color data.

Abstract: There are many works in color that assume illumination change can be modeled by multiplying sensor responses by individual scaling factors. The early research in this area is sometimes grouped under the heading “von Kries adaptation”: the scaling factors are applied to the cone responses. In more recent studies, both in psychophysics and in computational analysis, it has been proposed that scaling factors should be applied to linear combinations of the cones that have narrower support: they should be applied to the so-called “sharp sensors.” In this paper, we generalize the computational approach to spectral sharpening in three important ways. First, we introduce spherical sampling as a tool that allows us to enumerate in a principled way all linear combinations of the cones. This allows us to, second, find the optimal sharp sensors that minimize a variety of error measures including CIE Delta E (previous work on spectral sharpening minimized RMS) and color ratio stability. Lastly, we extend the spherical sampling paradigm to the multispectral case. Here the objective is to model the interaction of light and surface in terms of color signal spectra. Spherical sampling is shown to improve on the state of the art.

Abstract: With the ever-expanding volume of visual content available, the ability to organize and navigate such content by aesthetic preference is becoming increasingly important. While still in its nascent stage, research into computational models of aesthetic preference already shows great potential. However, to advance research, realistic, diverse and challenging databases are needed. To this end, we introduce a new large-scale database for conducting Aesthetic Visual Analysis: AVA. It contains over 250,000 images along with a rich variety of meta-data including a large number of aesthetic scores for each image, semantic labels for over 60 categories as well as labels related to photographic style. We show the advantages of AVA with respect to existing databases in terms of scale, diversity, and heterogeneity of annotations. We then describe several key insights into aesthetic preference afforded by AVA. Finally, we demonstrate, through three applications, how the large scale of AVA can be leveraged to improve performance on existing preference tasks

Abstract: Most works on image retrieval from text queries have addressed the problem of retrieving semantically relevant images. However, the ability to assess the aesthetic quality of an image is an increasingly important differentiating factor for search engines. In this work, given a semantic query, we are interested in retrieving images which are semantically relevant and score highly in terms of aesthetics/visual quality. We use large-margin classifiers and rankers to learn statistical models capable of ordering images based on the aesthetic and semantic information. In particular, we compare two families of approaches: while the first one attempts to learn a single ranker which takes into account both semantic and aesthetic information, the second one learns separate semantic and aesthetic models. We carry out a quantitative and qualitative evaluation on a recently-published large-scale dataset and we show that the second family of techniques significantly outperforms the first one.