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- Evaluating Intelligent Methods for Decision Making Support in Dermoscopy Based on Information Gain and EnsemblePublication . Spolaôr, Newton; Fonseca-Pinto, Rui; Mendes, Ana I.; Ensina, Leandro A.; Takaki, Weber S. R.; Parmezan, Antonio R. S.; Nogueira, Conceição V.; Coy, Claudio S. R.; Wu, Feng C.; Lee, Huei D.Melanoma, the most dangerous skin cancer, is sometimes associated with a nevus, a relatively common skin lesion. To find early melanoma, nevus, and other lesions, dermoscopy is often used. In this context, intelligent methods have been applied in dermoscopic images to support decision making. A typical computer-aided diagnosis method comprises three steps: (1) extraction of features that describe image properties, (2) selection of important features previously extracted, (3) classification of images based on the selected features. In this work, traditional data mining approaches underexploited in dermoscopy were applied: information gain for feature selection and an ensemble classification method based on gradient boosting. The former technique ranks image features according to data entropy, while the latter combines the outputs of single classifiers to predict the image class. After evaluating these approaches in a public dataset, we can observe that the results obtained are competitive with the state-of-the-art. Moreover, the presented approach allows a reduction of the total number of features and types of features to produce similar classification scores.
- On the geometric modulation of skin lesion growth: a mathematical model for melanomaPublication . Mendes, Ana Isabel; Nogueira, Conceição; Pereira, Jorge; Fonseca-Pinto, RuiIntroduction: Early detection of suspicious skin lesions is critical to prevent skin malignancies, particularly the melanoma, which is the most dangerous form of human skin cancer. In the last decade, image processing techniques have been an increasingly important tool for early detection and mathematical models play a relevant role in mapping the progression of lesions. Methods: This work presents an algorithm to describe the evolution of the border of the skin lesion based on two main measurable markers: the symmetry and the geometric growth path of the lesion. The proposed methodology involves two dermoscopic images of the same melanocytic lesion obtained at different moments in time. By applying a mathematical model based on planar linear transformations, measurable parameters related to symmetry and growth are extracted. Results: With this information one may compare the actual evolution in the lesion with the outcomes from the geometric model. First, this method was tested on predefined images whose growth was controlled and the symmetry known which were used for validation. Then the methodology was tested in real dermoscopic melanoma images in which the parameters of the mathematical model revealed symmetry and growth rates consistent with a typical melanoma behavior. Conclusions: The method developed proved to show very accurate information about the target growth markers (variation on the growth along the border, the deformation and the symmetry of the lesion trough the time). All the results, validated by the expected phantom outputs, were similar to the ones on the real images.
- Interactive and Multimedia Contents Associated with a System for Computer-Aided AssessmentPublication . Paiva, Rui; Ferreira, S. Milton; Mendes, G. Ana; Eusébio, M. J. AugustoThis article presents a research study addressing the development, implementation, evaluation, and use of Interactive Modules for Online Training (MITO) of mathematics in higher education. This work was carried out in the context of the MITO project, which combined several features of the learning and management system Moodle, the computer-aided assessment for mathematics STACK, the mathematical software GeoGebra, several packages from the type-setting program LaTeX, and tutorial videos. A total of 1,962 students participated in this study. Two groups of students taking a calculus course were selected for a deeper analysis. With regard to usability and functionality, the results indicate that MITO scored well in almost all aspects, which is fundamental for their introduction into formal university courses. The analysis of the data reveals that the use of MITO educational contents by students mainly occurs about 1 week and a half prior to the evaluations. Moreover, there is a strong correlation between the results of online assessments on MITO in a continuous assessment model and the final grade on the course.
- Dynamics and interpretation of some integrable systems via matrix orthogonal polynomialsPublication . Branquinho, A.; Moreno, A. Foulquié; Mendes, A.In this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a com plex matrix measure. In order to study the solution of this dynamical system, we give explicit expressions for the Weyl function, general ized Markov function, and we also obtain, under some conditions, a representation of the vector of linear functionals associated with this system. We show that the orthogonality is embedded in these structure and governs the high-order Toda lattice. We also present a Lax-type theorem for the point spectrum of the Jacobi operator associated with a Toda-type lattice.
- Vector Interpretation of the Matrix Orthogonality on the Real LinePublication . Branquinho, A.; Marcellán, F.; Mendes, A.In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials satisfy three-term recurrence relations with matrix coefficients that do not obey to any type of symmetry. In this sense the vectorial reinterpretation allows us to study a non-symmetric case of the matrix orthogonality. We also prove that our systems of polynomials are indeed orthonormal with respect to a complex measure of orthogonality. Approximation problems of Hermite-Padé type are also discussed. Finally, a Markov's type theorem is presented.
- Relative asymptotics for orthogonal matrix polynomialsPublication . Branquinho, A.; Marcellán, F.; Mendes, A.In this paper we study sequences of matrix polynomials that satisfy a non-symmetric recurrence relation. To study this kind of sequences we use a vector interpretation of the matrix orthogonality. In the context of these sequences of matrix polynomials we introduce the concept of the generalized matrix Nevai class and we give the ratio asymptotics between two consecutive polynomials belonging to this class. We study the generalized matrix Chebyshev polynomials and we deduce its explicit expression as well as we show some illustrative examples. The concept of a Dirac delta functional is introduced. We show how the vector model that includes a Dirac delta functional is a representation of a discrete Sobolev inner product. It also allows to reinterpret such perturbations in the usual matrix Nevai class. Finally, the relative asymptotics between a polynomial in the generalized matrix Nevai class and a polynomial that is orthogonal to a modification of the corresponding matrix measure by the addition of a Dirac delta functional is deduced. © 2012 Elsevier Ltd. All rights reserved.