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Miquel Ferrer, Ernest Valveny, F. Serratosa, K. Riesen, & Horst Bunke. (2010). Generalized Median Graph Computation by Means of Graph Embedding in Vector Spaces. PR - Pattern Recognition, 43(4), 1642–1655.
Abstract: The median graph has been presented as a useful tool to represent a set of graphs. Nevertheless its computation is very complex and the existing algorithms are restricted to use limited amount of data. In this paper we propose a new approach for the computation of the median graph based on graph embedding. Graphs are embedded into a vector space and the median is computed in the vector domain. We have designed a procedure based on the weighted mean of a pair of graphs to go from the vector domain back to the graph domain in order to obtain a final approximation of the median graph. Experiments on three different databases containing large graphs show that we succeed to compute good approximations of the median graph. We have also applied the median graph to perform some basic classification tasks achieving reasonable good results. These experiments on real data open the door to the application of the median graph to a number of more complex machine learning algorithms where a representative of a set of graphs is needed.
Keywords: Graph matching; Weighted mean of graphs; Median graph; Graph embedding; Vector spaces
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Oriol Ramos Terrades, Ernest Valveny, & Salvatore Tabbone. (2009). Optimal Classifier Fusion in a Non-Bayesian Probabilistic Framework. TPAMI - IEEE Transactions on Pattern Analysis and Machine Intelligence, 31(9), 1630–1644.
Abstract: The combination of the output of classifiers has been one of the strategies used to improve classification rates in general purpose classification systems. Some of the most common approaches can be explained using the Bayes' formula. In this paper, we tackle the problem of the combination of classifiers using a non-Bayesian probabilistic framework. This approach permits us to derive two linear combination rules that minimize misclassification rates under some constraints on the distribution of classifiers. In order to show the validity of this approach we have compared it with other popular combination rules from a theoretical viewpoint using a synthetic data set, and experimentally using two standard databases: the MNIST handwritten digit database and the GREC symbol database. Results on the synthetic data set show the validity of the theoretical approach. Indeed, results on real data show that the proposed methods outperform other common combination schemes.
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Josep Llados, Horst Bunke, & Enric Marti. (1997). Finding rotational symmetries by cyclic string matching. PRL - Pattern recognition letters, 18(14), 1435–1442.
Abstract: Symmetry is an important shape feature. In this paper, a simple and fast method to detect perfect and distorted rotational symmetries of 2D objects is described. The boundary of a shape is polygonally approximated and represented as a string. Rotational symmetries are found by cyclic string matching between two identical copies of the shape string. The set of minimum cost edit sequences that transform the shape string to a cyclically shifted version of itself define the rotational symmetry and its order. Finally, a modification of the algorithm is proposed to detect reflectional symmetries. Some experimental results are presented to show the reliability of the proposed algorithm
Keywords: Rotational symmetry; Reflectional symmetry; String matching
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Sergio Escalera, Alicia Fornes, O. Pujol, Petia Radeva, Gemma Sanchez, & Josep Llados. (2009). Blurred Shape Model for Binary and Grey-level Symbol Recognition. PRL - Pattern Recognition Letters, 30(15), 1424–1433.
Abstract: Many symbol recognition problems require the use of robust descriptors in order to obtain rich information of the data. However, the research of a good descriptor is still an open issue due to the high variability of symbols appearance. Rotation, partial occlusions, elastic deformations, intra-class and inter-class variations, or high variability among symbols due to different writing styles, are just a few problems. In this paper, we introduce a symbol shape description to deal with the changes in appearance that these types of symbols suffer. The shape of the symbol is aligned based on principal components to make the recognition invariant to rotation and reflection. Then, we present the Blurred Shape Model descriptor (BSM), where new features encode the probability of appearance of each pixel that outlines the symbols shape. Moreover, we include the new descriptor in a system to deal with multi-class symbol categorization problems. Adaboost is used to train the binary classifiers, learning the BSM features that better split symbol classes. Then, the binary problems are embedded in an Error-Correcting Output Codes framework (ECOC) to deal with the multi-class case. The methodology is evaluated on different synthetic and real data sets. State-of-the-art descriptors and classifiers are compared, showing the robustness and better performance of the present scheme to classify symbols with high variability of appearance.
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Albert Gordo, Alicia Fornes, & Ernest Valveny. (2013). Writer identification in handwritten musical scores with bags of notes. PR - Pattern Recognition, 46(5), 1337–1345.
Abstract: Writer Identification is an important task for the automatic processing of documents. However, the identification of the writer in graphical documents is still challenging. In this work, we adapt the Bag of Visual Words framework to the task of writer identification in handwritten musical scores. A vanilla implementation of this method already performs comparably to the state-of-the-art. Furthermore, we analyze the effect of two improvements of the representation: a Bhattacharyya embedding, which improves the results at virtually no extra cost, and a Fisher Vector representation that very significantly improves the results at the cost of a more complex and costly representation. Experimental evaluation shows results more than 20 points above the state-of-the-art in a new, challenging dataset.
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