Fingerprint recognition has found a reliable application for verification or identification of people in biometrics. Globally, fingerprints can be viewed as valuable traits due to several perceptions observed by the experts; such as the distinctiveness and the permanence on humans and the performance in real applications. Among the main stages of fingerprint recognition, the automated matching phase has received much attention from the early years up to nowadays. This paper is devoted to review and categorize the vast number of fingerprint matching methods proposed in the specialized literature. In particular, we focus on local minutiae-based matching algorithms, which provide good performance with an excellent trade-off between efficacy and efficiency. We identify the main properties and differences of existing methods. Then, we include an experimental evaluation involving the most representative local minutiae-based matching models in both verification and evaluation tasks. The results obtained will be discussed in detail, supporting the description of future directions.

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Orientation map 35 Singular points 36 3 7 a b s t r a c t 38 This paper reviews the fingerprint classification literature looking at the problem from a double perspec-39 tive. We first deal with feature extraction methods, including the different models considered for singular 40 point detection and for orientation map extraction. Then, we focus on the different learning models con-41 sidered to build the classifiers used to label new fingerprints. Taxonomies and classifications for the fea-42 ture extraction, singular point detection, orientation extraction and learning methods are presented. A 43 critical view of the existing literature have led us to present a discussion on the existing methods and 44 their drawbacks such as difficulty in their reimplementation, lack of details or major differences in their 45 evaluations procedures. On this account, an experimental analysis of the most relevant methods is car-46 ried out in the second part of this paper, and a new method based on their combination is presented.47

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We investigate the problem of averaging values on lattices and, in particular, on discrete product lattices. This problem arises in image processing when several color values given in RGB, HSL, or another coding scheme need to be combined. We show how the arithmetic mean and the median can be constructed by minimizing appropriate penalties, and we discuss which of them coincide with the Cartesian product of the standard mean and the median. We apply these functions in image processing. We present three algorithms for color image reduction based on minimizing penalty functions on discrete product lattices.

In the first part of this paper we reviewed the fingerprint classification literature from two different perspectives: the feature extraction and the classifier learning. Aiming at answering the question of which among the reviewed methods would perform better in a real implementation we end up in a discussion which showed the difficulty in answering this question. No previous comparison exists in the literature and comparisons among papers are done with different experimental frameworks. Moreover, the difficulty in implementing published methods was stated due to the lack of details in their description, parameters and the fact that no source code is shared. For this reason, in this paper we will go through a deep experimental study following the proposed double perspective. In order to do so, we have carefully implemented some of the most relevant feature extraction methods according to the explanations found in the corresponding papers and we have tested their performance with different classifiers, including those specific proposals made by the authors. Our aim is to develop an objective experimental study in a common framework, which has not been done before and which can serve as a baseline for future works on the topic. This way, we will not only test their quality, but their reusability by other researchers and will be able to indicate which proposals could be considered for future developments. Furthermore, we will show that combining different feature extraction models in an ensemble can lead to a superior performance, significantly increasing the results obtained by individual models.

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In this paper we present a new fuzzy reasoning method in which the Choquet integral is used as aggregation function. In this manner, we can take into account the interaction among the rules of the system. For this reason, we consider several fuzzy measures, since it is a key point on the subsequent success of the Choquet integral, and we apply the new method with the same fuzzy measure for all the classes. However, the relationship among the set of rules of each class can be different and therefore the best fuzzy measure can change depending on the class. Consequently, we propose a learning method by means of a genetic algorithm in which the most suitable fuzzy measure for each class is computed. From the obtained results it is shown that our new proposal allows the performance of the classical fuzzy reasoning methods of the winning rule and additive combination to be enhanced whenever the fuzzy measure is appropriate for the tackled problem.