Abstract. A classical approach to designing binary image operators is mathematical morphology (MM). We propose the Discrete Morphological Neural Networks (DMNN) for binary image analysis to represent W-operators and estimate them via machine learning. A DMNN architecture, which is represented by a morphological computational graph, is designed as in the classical heuristic design of morphological operators, in which the designer should combine a set of MM operators and Boolean operations based on prior information and theoretical knowledge. Then, once the architecture is fixed, instead of adjusting its parameters (i.e., structuring elements or maximal intervals) by hand, we propose a lattice descent algorithm (LDA) to train these parameters based on a sample of input and output images under the usual machine learning approach. We also propose a stochastic version of the LDA that is more efficient, is scalable, and can obtain small error in practical problems. The class represented by a DMNN can be quite general or specialized according to expected properties of the target operator, i.e., prior information, and the semantic expressed by algebraic properties of classes of operators is a differential relative to other methods. The main contribution of this paper is the merger of the two main paradigms for designing morphological operators: classical heuristic design and automatic design via machine learning. As a proof-of-concept, we apply the DMNN to recognize the boundary of digits with noise, and we discuss many topics for future research.

The U-curve optimization problem is characterized by a decomposable in U-shaped curves cost function over the chains of a Boolean lattice. This problem can be applied to model the classical feature selection problem in Machine Learning. In this paper, we point out that the firstly proposed algorithm to tackle the U-curve problem, the RBM algorithm, is in fact suboptimal. We also present two new algorithms: UCS, which is actually optimal to tackle this problem; and UCSR, a variation of UCS that solves a special case of the U-curve problem and relies on a reduced, ordered binary decision diagram to control the search space. We provide results of two computational assays with these new algorithms: first, W-operator design for filtering of binary images; second, linear SVM design for classification of data sets from the UCI Machine Learning Repository. We show that, in these assays, UCS and UCSR outperformed an exhaustive search and also three widely used heuristics: the SFFS sequential selection, the BFS graph-based search, and the CHCGA genetic algorithm. Finally, we analyze the obtained results and point out improvements that might enhance the performance of these two novel algorithms.

The inference of gene networks from gene expression data is an open problem due to the large dimensionality (number of genes) and the small number of data samples typically available, even considering the fact that the network is sparse (limited number of input genes per target gene). In this work we propose a method that alleviates the curse of dimensionality by grouping predictor gene configurations in their respective linear combination values. Each linear combination value results in an equivalence class. In this way, the number of configurations of predictor values becomes a linear function of the dimensionality (number of predictors) instead of an exponential function when considering the original configurations. The proposed method follows the probabilistic gene networks approach which applies local feature selection to obtain an adequate predictor gene set for each gene. Even considering that some information from the original configurations of predictors is lost after applying the grouping, the results indicate that the inference with linear grouping tends to provide networks with better topological similarities than those obtained without grouping in cases where the number of samples is quite limited and the inference involves a larger number of predictors per gene.

Histopathology is considered one of the most important tools for diagnosis in medical routine. It is characterized by the study of structural and morphological changes of the cells, caused by diseases in biological tissues. The use of computational techniques in the processing of histopathological images allows the identification of structural elements as well as the determination of inherent characteristics, supporting the study of the structural organization of tissues and their pathological changes. Within this perspective, the overall objective of this work includes the proposal, the implementation and the evaluation of a methodology for the analysis of cervical intraepithelial neoplasia (CIN) from histopathological samples through techniques based on Neighbourhood Graphs theory and Complex Networks. The proposed method was evaluated concerning the detection of the presence of lesions in the tissue. The maximum accuracy obtained in the evaluation of the detection of abnormalities was 88%. Since this method is generic, it can be applied to other types of lesions and tissues.

BACKGROUND: One goal of gene expression profiling is to identify signature genes that robustly distinguish different types or grades of tumors. Several tumor classifiers based on expression profiling have been proposed using microarray technique. Due to important differences in the probabilistic models of microarray and SAGE technologies, it is important to develop suitable techniques to select specific genes from SAGE measurements. RESULTS: A new framework to select specific genes that distinguish different biological states based on the analysis of SAGE data is proposed. The new framework applies the bolstered error for the identification of strong genes that separate the biological states in a feature space defined by the gene expression of a training set. Credibility intervals defined from a probabilistic model of SAGE measurements are used to identify the genes that distinguish the different states with more reliability among all gene groups selected by the strong genes method. A score taking into account the credibility and the bolstered error values in order to rank the groups of considered genes is proposed. Results obtained using SAGE data from gliomas are presented, thus corroborating the introduced methodology. CONCLUSION: The model representing counting data, such as SAGE, provides additional statistical information that allows a more robust analysis. The additional statistical information provided by the probabilistic model is incorporated in the methodology described in the paper. The introduced method is suitable to identify signature genes that lead to a good separation of the biological states using SAGE and may be adapted for other counting methods such as Massive Parallel Signature Sequencing (MPSS) or the recent Sequencing-By-Synthesis (SBS) technique. Some of such genes identified by the proposed method may be useful to generate classifiers.

We propose a new algorithm for optimal MAE stack filter design. It is based on three main ingredients. First, we show that the dual of the integer programming formulation of the filter design problem is a minimum cost network flow problem. Next, we present a decomposition principle that can be used to break this dual problem into smaller subproblems. Finally, we propose a specialization of the network Simplex algorithm based on column generation to solve these smaller subproblems. Using our method, we were able to efficiently solve instances of the filter problem with window size up to 25 pixels. To the best of our knowledge, this is the largest dimension for which this problem was ever solved exactly.

We propose an efficient parallel algorithm with simple static and dynamic scheduling for generating combinations. It can use any number of processors (NPlesn-m+1) in order to generate the set of all combinations of C(n,m). The main characteristic of this algorithm is to require no integer larger than n during the whole computation. The performance results show that even without a perfect load balance, this algorithm has very good performance, mainly when n is large. Besides, the dynamic algorithm presents a good performance on heterogeneous parallel platforms

A finite subset of Z/sup 2/ is called a structuring element. A decomposition of a structuring element A is a sequence of subsets of the elementary square (i.e., the 3/spl times/3 square centered at the origin) such that the Minkowski addition of them is equal to A. H. Park and R.T. Chin (see ibid., vol.17, no.1, p.2-15, 1995) developed an algorithm for finding the optimal decomposition of simply connected structuring elements (i.e., 8-connected structuring elements that contain no holes), imposing the restriction that all subsets in this decomposition are also simply connected. The authors show that there exist infinite families of simply connected structuring elements that have decompositions but are not decomposable according to Park and Chin's definition.

An important aspect of mathematical morphology is the description of complete lattice operators by a formal language, the Morphological Language (ML), whose vocabulary is composed of infimum, supremum, dilations, erosions, anti-dilations and anti-ero