Uma abordagem de agrupamento baseada na técnica de divisão e conquista e floresta de caminhos ótimos

Orientador: Alexandre Xavier FalcãoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: O agrupamento de dados é um dos principais desafios em problemas de Ciência de Dados. Apesar do seu progresso científico em quase um século de existência, algoritmos de agrupamento ainda falham na identificação de grupos (clusters) naturalmente relacionados com a semântica do problema. Ademais, os avanços das tecnologias de aquisição, comunicação, e armazenamento de dados acrescentam desafios cruciais com o aumento considerável de dados, os quais não são tratados pela maioria das técnicas. Essas questões são endereçadas neste trabalho através da proposta de uma abordagem de divisão e conquista para uma técnica de agrupamento única em encontrar um grupo por domo da função de densidade de probabilidade dos dados --- o algoritmo de agrupamento por floresta de caminhos ótimos (OPF - Optimum-Path Forest). Nesta técnica, amostras são interpretadas como nós de um grafo cujos arcos conectam os $k$-vizinhos mais próximos no espaço de características. Os nós são ponderados pela sua densidade de probabilidade e um mapa de conexidade é maximizado de modo que cada máximo da função densidade de probabilidade se torna a raiz de uma árvore de caminhos ótimos (grupo). O melhor valor de $k$ é estimado por otimização em um intervalo de valores dependente da aplicação. O problema com este método é que um número alto de amostras torna o algoritmo inviável, devido ao espaço de memória necessário para armazenar o grafo e o tempo computacional para encontrar o melhor valor de $k$. Visto que as soluções existentes levam a resultados ineficazes, este trabalho revisita o problema através da proposta de uma abordagem de divisão e conquista com dois níveis. No primeiro nível, o conjunto de dados é dividido em subconjuntos (blocos) menores e as amostras pertencentes a cada bloco são agrupadas pelo algoritmo OPF. Em seguida, as amostras representativas de cada grupo (mais especificamente as raízes da floresta de caminhos ótimos) são levadas ao segundo nível, onde elas são agrupadas novamente. Finalmente, os rótulos de grupo obtidos no segundo nível são transferidos para todas as amostras do conjunto de dados através de seus representantes do primeiro nível. Nesta abordagem, todas as amostras, ou pelo menos muitas delas, podem ser usadas no processo de aprendizado não supervisionado, sem afetar a eficácia do agrupamento e, portanto, o procedimento é menos susceptível a perda de informação relevante ao agrupamento. Os resultados mostram agrupamentos satisfatórios em dois cenários, segmentação de imagem e agrupamento de dados arbitrários, tendo como base a comparação com abordagens populares. No primeiro cenário, a abordagem proposta atinge os melhores resultados em todas as bases de imagem testadas. No segundo cenário, os resultados são similares aos obtidos por uma versão otimizada do método original de agrupamento por floresta de caminhos ótimosAbstract: Data clustering is one of the main challenges when solving Data Science problems. Despite its progress over almost one century of research, clustering algorithms still fail in identifying groups naturally related to the semantics of the problem. Moreover, the advances in data acquisition, communication, and storage technologies add crucial challenges with a considerable data increase, which are not handled by most techniques. We address these issues by proposing a divide-and-conquer approach to a clustering technique, which is unique in finding one group per dome of the probability density function of the data --- the Optimum-Path Forest (OPF) clustering algorithm. In the OPF-clustering technique, samples are taken as nodes of a graph whose arcs connect the $k$-nearest neighbors in the feature space. The nodes are weighted by their probability density values and a connectivity map is maximized such that each maximum of the probability density function becomes the root of an optimum-path tree (cluster). The best value of $k$ is estimated by optimization within an application-specific interval of values. The problem with this method is that a high number of samples makes the algorithm prohibitive, due to the required memory space to store the graph and the computational time to obtain the clusters for the best value of $k$. Since the existing solutions lead to ineffective results, we decided to revisit the problem by proposing a two-level divide-and-conquer approach. At the first level, the dataset is divided into smaller subsets (blocks) and the samples belonging to each block are grouped by the OPF algorithm. Then, the representative samples (more specifically the roots of the optimum-path forest) are taken to a second level where they are clustered again. Finally, the group labels obtained in the second level are transferred to all samples of the dataset through their representatives of the first level. With this approach, we can use all samples, or at least many samples, in the unsupervised learning process without affecting the grouping performance and, therefore, the procedure is less likely to lose relevant grouping information. We show that our proposal can obtain satisfactory results in two scenarios, image segmentation and the general data clustering problem, in comparison with some popular baselines. In the first scenario, our technique achieves better results than the others in all tested image databases. In the second scenario, it obtains outcomes similar to an optimized version of the traditional OPF-clustering algorithmMestradoCiência da ComputaçãoMestre em Ciência da ComputaçãoCAPE

Supervised pattern classification using optimum path forest

Orientador: Alexandre Xavier FalcãoTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Padrões são geralmente representados por vetores de atributos obtidos através de amostras em uma base de dados, a qual pode estar totalmente, parcialmente ou não rotulada. Dependendo da quantidade de informação disponível dessa base de dados, podemos aplicar três tipos de técnicas para identificação desses padrões: supervisionadas, semisupervisionadas ou não-supervisionadas. No presente trabalho, estudamos técnicas supervisionadas, as quais caracterizam-se pelo total conhecimento dos rótulos das amostras da base de dados. Propusemos também um novo método para classificação supervisionada de padrões baseada em Floresta de Caminhos Ótimos (OPF - Optimum-Path Forest), a qual modela o problema de reconhecimento de padrões como sendo um grafo, onde os nós são as amostras e os arcos definidos por uma relação de adjacência. Amostras mais relevantes (protótipos) são identificadas e um processo de competição entre elas é iniciado, as quais tentam oferecer caminhos de custo ótimo para as demais amostras da base de dados. Apresentamos aqui duas abordagens, as quais diferem na relação de adjacência, função de custo de caminho e maneira de identificar os protótipos. A primeira delas utiliza como relação de adjacência o grafo completo e identifica os protótipos nas regiões de fronteira entre as classes, os quais oferecem caminhos de custo ótimo que são computados como sendo o valor do maior peso de arco do caminho entre esses protótipos e as demais amostras da base de dados, sendo o peso do arco entre duas amostras dado pela distância entre seus vetores de características. O algoritmo OPF tenta minimizar esses custos para todas as amostras. A outra abordagem utiliza como relação de adjacência um grafo k-nn e identifica os protótipos como sendo os máximos de uma função de densidade de probabilidade, a qual é computada utilizando os pesos dos arcos. O valor do custo do caminho é dado pelo menor valor de densidade ao longo do caminho. Neste caso, o algoritmo OPF tenta agora maximizar esses custos. Apresentamos também um algoritmo de aprendizado genérico, o qual ensina o classificador através de seus erros em um conjunto de validação, trocando amostras classificadas incorretamente por outras selecionadas através de certas restrições. Esse processo é repetido at'e um critério de erro ser estabelecido. Comparações com os classificadores SVM, ANN-MLP, k-NN e BC foram feitas, tendo o OPF demonstrado ser similar ao SVM, porém bem mais rápido, e superior aos restantes.Abstract: Patterns are usually represented by feature vectors obtained from samples of a dataset, which can be fully, partially or non labeled. Depending on the amount of available information of these datasets, three kinds of pattern identification techniques can be applied: supervised, semi-supervised or non supervised. In this work, we addressed the supervised ones, which are characterized by the fully knowledge of the labels from the dataset samples, and we also proposed a novel idea for supervised pattern recognition based on Optimum-Path Forest (OPF), which models the pattern recognition problem as a graph, where the nodes are the samples and the arcs are defined by some adjacency relation. The most relevant samples (prototypes) are identified and a competition process between them is started, which try to offer optimum-path costs to the remaining dataset samples. We presented here two approaches, which differ from each other in the adjacency relation, path-cost function and the prototypes identification procedure. The first ones uses as the adjacency relation the complete graph and identify the prototypes in the boundaries of the classes, which offer optimum-path costs that are computed as been the maximum path arc-weight between these prototypes and the other dataset samples, in which the arc-weight is given by the distance between their feature vectors. In this case, the OPF algorithm tries to minimize these costs for each sample of the dataset. The other approach uses as the adjacency relation a k-nn graph and identifies the prototypes as the maxima of a probability density function, which is computed using the arc-weigths. The path-cost value is given by the lowest density value among it. The OPF algorithm now tries to maximize these costs. We also presented a generic learning algorithm, which tries to teach a classifier through its erros in a validation set, replacing the misclassified samples by other selected using some constraints. This process is repeated until an error criterion is satisfied. Comparisons with SVM, ANN-MLP, k-NN and BC classifiers were also performed, being the OPF similar to SVM, but much faster, and superior to the remaining classifiers.DoutoradoMetodologia e Tecnicas da ComputaçãoDoutor em Ciência da Computaçã

A Comparative Study Among Pattern Classifiers In Interactive Image Segmentation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Edition of natural images usually asks for considerable user involvement, being segmentation one of the main challenges. This paper describes an unified graph-based framework for fast, precise and accurate interactive image segmentation. The method divides segmentation into object recognition, enhancement and extraction. Recognition is done by the user when markers are selected inside and outside the object. Enhancement increases the dissimilarities between object and background and Extraction separates them. Enhancement is done by a fuzzy pixel classifier and it has a great impact in the number of markers required for extraction. In view of minimizing user involvement, we focus this paper on a comparative study among popular classifiers for enhancement, conducting experiments with several natural images and seven users. © 2009 IEEE.268275Petrobras,CNPq,CAPES,INCTMat,FAPERJConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Spina, T.V., Montoya-Zegarra, J.A., Falcão, A.X., Miranda, P.A.V., Fast interactive segmentation of natural images using the image foresting transform (2009) DSP (International Conference on Digital Signal Processing), , Santorini, Greece: IEEE, JulFalcão, A.X., Udupa, J.K., Miyazawa, F.K., An ultra-fast user-steered image segmentation paradigm: Live-wire-on-the-fly (2000) IEEE Trans. on Medical Imaging, 19 (1), pp. 55-62Falcão, A.X., Stolfi, J., Lotufo, R.A., The image foresting transform: Theory, algorithms, and applications (2004) IEEE Trans. on Pattern Analysis and Machine Intelligence, 26 (1), pp. 19-29Falcão, A.X., Bergo, F.P.G., Interactive volume segmentation with differential image foresting transforms (2004) IEEE Trans. on Medical Imaging, 23 (9), pp. 1100-1108J. P. Papa, A. X. Falcão, C. T. N. Suzuki, and N. D. A. Mascarenhas, A discrete approach for supervised pattern recognition, in 12th International Workshop on Combinatorial Image Analysis, 4958. LNCS Springer Berlin/Heidelberg, 2008, pp. 136-147Portilla, J., Simoncelli, E.P., A parametric texture model based on joint statistics of complex wavelet coefficients (2000) Intl. Journal of Computer Vision, 40 (1), pp. 49-70Meyer, F., Levelings, image simplification filters for segmentation (2004) Journal of Mathematical Imaging and Vision, 20 (1-2), pp. 59-72J. P. Papa, A. X. Falcão, C. T. N. Suzuki, and N. D. A. Mascarenhas, A discrete approach for supervised pattern recognition, in Proc. of the 12th Intl. Workshop on Combinatorial Image Analysis, LNCS 4958. Buffalo, NY, USA: Springer, Apr 7th-9th 2008, pp. 136-147C.-W. Hsu, C.-C. Chang, and C.-J. Lin, A practical guide to support vector classification, Department of Computer Science, National Taiwan University, Tech. Rep., 2009. [Online]. Available: http://www.csie.ntu.edu.tw/ ~cjlin/papers/guide/guide.pdfChang, C.C., Lin, C.J., (2001) LIBSVM: A library for support vector machines, , http://www.csie.ntu.edu.tw/~cjlin/libsvm, Online, AvailableHaykin, S., (1999) Neural Networks, A Comprehensive foundation, , Prenticer Hall, IncHecht-Nielsen, R., (1989) Neurocomputing, , Boston, MA, USA: Addison-Wesley Longman Publishing Co, IncMiranda, P.A.V., Falcão, A.X., Rocha, A., Bergo, F.P.G., Object delineation by K-connected components (2008) EURASIP Journal on Advances in Signal Processing, pp. 1-14. , doi: 10.1155/2008/467928Bradski, G., The OpenCV Library (2000) Dr. Dobbs Journal of Software ToolsMartin, D., Fowlkes, C., Tal, D., Malik, J., Berkeley segmentation dataset and benchmark, , http://www.eecs.berkeley.edu/Research/Projects/CS/vision/grouping, Online, AvailableRother, C., Kolmogorov, V., Blake, A., Brown, M., Image and video editing: Grabcut, , http://research.microsoft.com/enus/um/cambridge/projects/visionimagevideoediting/segmentation/grabcut.htm, Online, Availablevan Rijsbergen, C., (1979) Information retrieval, , 2nd ed. London: Wiley Inter-scienc

Improving User Control With Minimum Involvement In User-guided Segmentation By Image Foresting Transform

The image foresting transform (IFT) can divide an image into object and background, each represented by one optimum-path forest rooted at internal and external markers selected by the user. We have considerably reduced the number of markers (user involvement) by separating object enhancement from its extraction. However, the user had no guidance about effective marker location during extraction, losing segmentation control. Now, we pre-segment the image automatically into a few regions. The regions inside the object are selected and merged from internal markers. Regions with object and background pixels are further divided by IFT. This provides more user control with minimum involvement, as validated on two public datasets. © 2009 Springer Berlin Heidelberg.5702 LNCS971978Falcão, A., Udupa, J., Miyazawa, F., An ultra-fast user-steered image segmentation paradigm: Live-wire-on-the-fly (2000) IEEE Trans. on Medical Imaging, 19, pp. 55-62Spina, T., Montoya-Zegarra, J., Falcão, A., Miranda, P., Fast interactive segmentation of natural images using the image foresting transform (2009) DSP (International Conference on Digital Signal Processing), , Santorini, Greece. IEEE, Los Alamitos , accepted for publicationRother, C., Kolmogorov, V., Blake, A., grabcut: Interactive foreground extraction using iterated graph cuts (2004) ACM Transactions on Graphics, 23, pp. 309-314Protiere, A., Sapiro, G., Interactive image segmentation via adaptive weighted distances (2007) IEEE Transactions on Image Processing, 16, pp. 1046-1057Vicente, S., Kolmogorov, V., Rother, C., Graph cut based image segmentation with connectivity priors (2008) IEEE Proc. of CVPR, pp. 1-8. , Anchorage, Alaska, ppBeucher, S., Meyer, F., The morphological approach to segmentation: The watershed transformation (1993) Mathematical Morphology in Image Processing, pp. 433-481. , M. Dekker, New YorkLotufo, R., Falcão, A., The ordered queue and the optimality of the watershed approaches (2000) Mathematical Morphology and its Applications to Image and Signal Processing, 18, pp. 341-350. , Kluwer, DordrechtFalcão, A., Stolfi, J., Lotufo, R., The image foresting transform: Theory, algorithms, and applications (2004) IEEE Trans. on Pattern Analysis and Machine Intelligence, 26, pp. 19-29Portilla, J., Simoncelli, E.P., A parametric texture model based on joint statistics of complex wavelet coefficients (2000) Intl. Journal of Computer Vision, 40, pp. 49-70Meyer, F., Levelings, image simplification filters for segmentation (2004) Journal of Mathematical Imaging and Vision, 20, pp. 59-72Papa, J.P., Falcão, A.X., Suzuki, C.T.N., Mascarenhas, N.D.A.: A discrete approach for supervised pattern recognition. In: Brimkov, V.E., Barneva, R.P., Hauptman, H.A. (eds.) IWCIA 2008. LNCS, 4958, pp. 136-147. Springer, Heidelberg (2008)Salembier, P., Oliveras, A., Guarrido, L., Antiextensive connected operators for image and sequence processing (1998) IEEE Transactions on Image Processing, 7, pp. 555-570Van Rijsbergen, C., (1979) Information retrieval, , 2nd edn. Wiley Interscience, Londo

Optimum Path Forest Classifier Applied To Laryngeal Pathology Detection

Optimum path forest-based classifiers are a novel approach for supervised pattern recognition. The OPF classifier differs from traditional approaches by not estimating probability density functions of the classes neither assuming samples linearity, and creates a discrete optimal partition of the feature space, in which the decision boundary is obtained by the influence zones of the most representative samples of the training set. Due to the large number of applications in biomedical signal processing involving pattern recognition techniques, specially voice disorders identification, we propose here the laryngeal pathology detection by means of OPF. Experiments were performed in three public datasets against SVM, and a comparison in terms of accuracy rates and execution times was also regarded.249252A.A. Spadotto, J.P. Papa, A.R. Gatto, P.C. Cola, J.C. Pereira, R.C. Guido, and A.O. Schelp, Denoising swallowing sound to improve the evaluators qualitative analysis., Computers and Electrical Engineering: Advances on Computer-based Biological Signal Processing Techniques, 34, no. 2, pp. 148-153, 2008Spadotto, A.A., Pereira, J.C., Guido, R.C., Papa, J.P., Falcão, A.X., Gatto, A.R., Cola, P.C., Shelp, A.O., Oropharyngeal dysphagia identification using wavelets and optimum path forest (2008) Proceedings of the 3th IEEE International Symposium on Communications, Control and Signal Processing, , to appearHadjitodorov, S.T., Boyanov, B., Teston, B., Laryngeal pathology detection by means of class-specific neural maps (2000) IEEE Transactions on Information Technology in Biomedicine, 4 (1), pp. 68-73Boyanov, B., Hadjitodorov, S.T., Acoustic analysis of pathological voices. a voice analysis systemfor the screening of laryngeal diseases (1997) IEEE Transactions on Engineering in Medicine and Biology Magazine, 16 (4), pp. 74-82Godino-Llorente, J.I., Vilda, P.G., Senz-Lechn, N., Blanco-Velasco, M., Craz-Roldn, F., Ferrer-Ballester, M.A., (2005) Support vector machines applied to the detection of voice disorders, 3817, pp. 219-230Perrin, E., Berger-Vachon, C., Kauffmann, I., Collet, L., (2006) Acoustical recognition of laryngeal pathology using the fundamental frequency and the first three formants of vowels, 35 (4), pp. 361-368Mezzalama, M., Prinetto, P., Morra, B., (2006) Experiments in automatic classification of laryngeal pathology, 21 (5), pp. 603-611Hadjitodorov, S.T., Ivanov, T., Boyanov, B., Analysis of dysphony using objective voice parameter (1993) Proceedings of the II Balkan Conference on Operational Research, pp. 911-917Schlotthauer, G., Torres, M.E., Jackson-Menaldi, C., Automatic diagnosis of pathological voices (2006) Proceedings of the 6th WSEAS International Conference on Signal, Speech and Image Processing, pp. 150-155Boser, B.E., Guyon, I.M., Vapnik, V.N., A training algorithm for-optimal margin classifiers (1992) Proc. 5th Workshop on Computational Learning Theory, pp. 144-152. , New York, NY, USA, ACM PressDuan, K., Keerthi, S.S., Which is the best multiclass svm method? an empirical study (2005) Multiple Classifier Systems, pp. 278-285Papa, J.P., Falcão, A.X., Miranda, P.A.V., Suzuki, C.T.N., Mascarenhas, N.D.A., Design of robust pattern classifiers based on optimum-path forests (2007) Mathematical Morphology and its Applications to Signal and Image Processing (ISMM), pp. 337-348. , MCT/INPEPapa, J.P., Falcão, A.X., Suzuki, C.T.N., Mascarenhas, N.D.A., A discrete approach for supervised pattern recognition (2008) 12th International Workshop on Combinatorial Image Analysis (IWCIA), 4958, pp. 136-147. , SpringerJ.A. Montoya-Zegarra, J.P. Papa, N.J. Leite, R.S. Torres, and A.X. Falcão, Rotation-invariant texture recognition, in 3rd International Symposium on Visual Computing, Lake Tahoe, Nevada, CA, USA, Nov 2007, Part II, LNCS 4842, pp. 193-204, SpringerFalcão, A.X., Stolfi, J., Lotufo, R.A., The image foresting transform: Theory, algorithms, and applications (2004) IEEE Trans. on PAMI, 26 (1), pp. 19-29. , JanAllène, C., Audibert, J.Y., Couprie, M., Cousty, J., Keriven, R., Some links between min-cuts, optimal spanning forests and watersheds (2007) Proceedings of the ISMM'08, pp. 253-264Hadjitodorov, S.T., Mitev, P., Boyanov, B., (2005) Laryngeal databases, , http://www.informatics.bangor.ac.uk/~kuncheva, Available inCohen, J., A coefficient of agreement for nominal scales (1960) Educational and Psychological Measurement, 20, pp. 37-46Chang, C.C., Lin, C.J., (2001) LIBSVM: A library for support vector machines, , http://www.csie.ntu.edu.tw/~cjlin/libsvm, Software available at ur

Oropharyngeal Dysphagia Identification Using Wavelets And Optimum Path Forest

The swallowing disturbers are defined as oropharyngeal dysphagia when present specifies signals and symptoms that are characterized for alterations in any phases of swallowing. Early diagnosis is crucial for the prognosis of patients with dysphagia and the potential to diagnose dysphagia in a noninvasive manner by assessing the sounds of swallowing is a highly attractive option for the dysphagia clinician. This study proposes a new framework for oropharyngeal dysphagia identification, having two main contributions: a new set of features extract from swallowing signal by discrete wavelet transform and the dysphagia classification by a novel pattern classifier called OPF. We also employed the well known SVM algorithm in the dysphagia identification task, for comparison purposes. We performed the experiments in two sub-signals: the first was the moment of the maximal peak (MP) of the signal and the second is the swallowing apnea period (SAP). The OPF final accuracy obtained were 85.2% and 80.2% for the analyzed signals MP and SAP, respectively, outperforming the SVM results. ©2008 IEEE.735740Logemann, J.A., (1983) Evaluation and treatment of swallowing disorders, , College- Hill PressPlatt, J., (2001) Dysphagia Management for Long-Term Care: A Manual for Nurses and Other Healthcare Professionals, Clinical and Educational ServicesFurkim, A.M., Silva, R.G., (1999) Programas de reabilitacão em disfagia neurogênica, , Frôntis EditorialChen, M.Y.M., Ott, D.J., Peele, V.N., Gelfand, D.W., Oropharynx in pacients with cerebrovascular disease: Evaluation with videofluoroscopy (1990) Radiology, 176, pp. 38-47J.B. Palmer and A.S. Duchane, Rehabilitation of swallowing disorders due to stroke, hys. Med. Rehab.Clin. N. Amer, 2, 1991Horner, J., Buoyer, F.G., Alberts, M.J., Helms, M.J., Dysphagia folowing brain stem stroke: Clinical correlates and outcome (1991) Arch Neurol, 48, pp. 1170-1173Buchhloz, D.W., (1997) Neurologic disordes of swallowing, pp. 37-62. , ppVeis, S.L., Logemann, J.A., Swallowing disorders in persons with cerebrovascular accident (1985) Arch Phys Med Rehabil, 66, pp. 372-376Gordon, C., Hewer, R.L., Wade, D.T., Dysphagia in acute stroke (1987) Brazilian Medical Journal, pp. 3411-3414Silva, R.G., Disfagia neurogênica em adultos: Uma proposta para avaliacão clínica (1999) Disfagias Orofaríngeas, pp. 35-47Cichero, J.A.Y., Murdoch, B.E., The physiologic cause of swallowing sounds: Answers from heart sounds and vocal tract acoustics (1998) Dysphagia, 13, pp. 39-52Youmans, S.R., Stierwalt, J.A.G., The physiologic cause of swallowing sounds: Answers from heart sounds and vocal tract acousticsan acoustic profile of normal swallowing (2005) Dysphagia, 20, pp. 195-209Lazareck, L.J., Moussavi, Z., Classification of normal and dysphagic swallows by acoustical means (2004) IEEE Transactions on Biomedical Engineering, 51Kuncheva, L.I., (2004) Combining Pattern Classifiers: Methods and Algorithms, , Wiley-InterscienceAboofazeli, M., Moussavi, Z., Automated extraction of swallowing sounds using a wavelet-based filter (2006) Engineering in Medicine and Biology Society, 2006. EMBS '06. 28th Annual International Conference of the IEEE, pp. 5607-5610Papa, J.P., Falcão, A.X., Miranda, P.A.V., Suzuki, C.T.N., Mascarenhas, N.D.A., Design of robust pattern classifiers based on pptimum-path forests (2007) Mathematical Morphology and its Applications to Signal and Image Processing (ISMM), pp. 337-348. , MCT/INPEPapa, J.P., Falcão, A.X., Suzuki, C.T.N., Mascarenhas, N.D.A., A discrete approach for supervised pattern recognition (2008) Proceedings of the 12th International Workshop on Combinatorial Image Analysis, , Accepted for publicationBoser, B.E., Guyon, I.M., Vapnik, V.N., A training algorithm for optimal margin classifiers (1992) Proc. 5th Workshop on Computational Learning Theory, pp. 144-152. , New York, NY, USA, ACM PressJ.A. Montoya-Zegarra, J.P. Papa, N.J. Leite, R.S. Torres, and A.X. Falcão, Rotation-invariant texture recognition, in 3rd International Symposium on Visual Computing, Lake Tahoe, Nevada, CA, USA, Nov 2007, Part II, LNCS 4842, pp. 193-204, SpringerVapnik, V.N., An overview of statistical learning theory (1999) Neural Networks, IEEE Transactions on, 10 (5), pp. 988-999Bazaraa, M.S., Sherali, H.D., Shetti, C.M., (2006) Nonlinear programming theory and algorithms, , Wiley-InterscienceBurges, C.J.C., A tutorial on support vector machines for pattern recognition (1998) Data Mining and Knowledge Discovery, 2 (2), pp. 121-167Falcão, A.X., Stolfi, J., Lotufo, R.A., The image foresting transform: Theory, algorithms, and applications (2004) IEEE Trans. on PAMI, 26 (1), pp. 19-29. , JanCormen, T., Leiserson, C., Rivest, R., (1990) Introduction to Algorithms, , MITAllène, C., Audibert, J.Y., Couprie, M., Cousty, J., Keriven, R., Some links between min-cuts, optimal spanning forests and watersheds (2007) Proceedings of the 8th Int. Symposium on Mathematical Morphology, pp. 253-264Addison, P.S., (2002), Institute of Physics Publishing Bristol and PhiladelphiaMallat, S.G., A theory for multiresolution signal decomposition: The wavelet representation (1989) IEEE Transactions on Pattern Analysis and Machine Intelligence, 11 (7), pp. 674-693Daubechies, I., The wavelet transform, time-frequency localization and signal analysis (1990) IEEE Transactions on Information Theory, 36 (5), pp. 961-1005I. Daubechies, Philadelphia, PA: Soc. Indus. Applied Math., 1992Daubechies, I., Orthonormal bases of compactly supported wavelets ii, variations on a theme (1993) SIAM J. Math. Anal, 24 (2), p. 499519Spadotto, A.A., Papa, J.P., Gatto, A.R., Cola, P.C., Pereira, J.C., Guido, R.C., Schelp, A.O., Denoising swallowing sound to improve the evaluators qualitative analysis (2007) Computers and Electrical Engineering, , accepted for publicationChang, C.C., Lin, C.J., (2001) LIBSVM: A library for support vector machines, , http://www.csie.ntu.edu.tw/~cjlin/libsvm, Software available at ur