A component tree is a graph representation that encodes the connected components of the upper or lower level sets of a grayscale image . Consequently, the nodes of a component tree represent binary images of the encoded connected components. There exist various algorithms that efficiently extract information and attributes of nodes of a component tree by incrementally exploiting the subset relation encoding in the tree. However, to the best of our knowledge, there is no such incremental approach to extract the contours of the nodes. In this paper, we propose an efficient incremental method to compute the contours of the nodes of a component tree by counting the edges (sides) of contour pixels. In addition, we discuss our method’s time complexity. We also experimentally show that our proposed method is faster than the standard approach based on node reconstruction.

The ability to edit an image using intuitive commands and primitives is a desired feature for any image editing software. In this paper, we combine recent results in medial axes with the well-established morphological tree representations to develop an interactive image editing tool that provides global and local image manipulation using high-level primitives. We propose a new way to render interactive morphological trees using icicle plots and introduce different ways of manipulating spline-based medial axis transforms for grayscale and colored image editing. Different applications of the tool, such as watermark removal, image deformation, dataset augmentation for machine learning, artistic illumination manipulation, image rearrangement, and clothing design, are described and showcased on examples.

Ultimate levelings are operators that extract important image contrast information from a scale-space based on levelings. Along with the residual extraction process, some residues usually come from undesirable regions, and they should be filtered out. For this, some strategies can be applied to filter these undesirable residues. In this paper, we introduce a new approach to detect desirable regions from ultimate levelings through a new hierarchical structure called residual tree. From this structure, we extract attribute vectors to build a machine learning model which gives a matching value between ground truth regions and residual tree nodes. Thus, from the selected residual tree nodes, we present a new approach to choose the best disjoint residual nodes which gives the regions of the ultimate levelings. Finally, from the ultimate levelings, we use its partition associated function to solve the segmentation problem. In order to evaluate our new approach, some experiments were carried out with a plant dataset and results report the state-of-the-art performance in plant segmentation.

Component tree is a full image representation which encodes all connected components from upper (resp. lower) level sets of a given image through the inclusion relation. Information from this representation can be used in many image processing and computational vision applications, e.g. connected filtering, image segmentation, feature extraction, among others. In general, each node of a component tree represents a connected component of a level set and stores attributes which describes features of this connected component. This paper presents a review of a previously published method to compute attributes such as area, perimeter, and number of Euler by incrementally counting patterns while traversing nodes of a component tree. This method foundation is further detailed in this paper by presenting a novel theoretical background and algorithm correctness intuition. We also present a novel approach for this algorithm showing improvements for run-time execution and precision analysis.

This work presents a new class of residual operators called ultimate levelings which are powerful image operators based on numerical residues. Within a multi-scale framework, these operators analyze a given image under a series of levelings. Thus, contrasted objects can be detected if a relevant residue is generated when they are filtered out by one of these levelings. Our approach consists of, firstly, (i) representing the input image as a morphological tree; then, (ii) showing that a certain operation on this tree results in a leveling operator; and finally (iii) demonstrating that a sequential application of this operation on the tree is able to produce a family of levelings that satisfies scale-space properties. Besides, other contributions of this paper include: (i) the statement of properties of ultimate levelings, (ii) the presentation of an efficient algorithm for their computation, (iii) the provision of strategies for choosing families of primitives, (iv) the presentation of strategies for filtering undesirable residues, and (v) the provision of some illustrative examples of application of ultimate levelings. Furthermore, ultimate levelings are computationally efficient and their performance evaluations are comparable to the state of art methods for filtering and image segmentation.

In this paper, we propose a collection of pattern sets to compute bit-quad matchings in component tree structures of grayscale images. The proposed patterns are designed to be used in an efficient algorithm which runs in linear time by counting incrementally each pattern matching per pixel. It is worth emphasizing that the proposed algorithm computes any attribute derived from 2×2 bit-quads such as area, perimeter, Euler number, among others. Finally, this algorithm is applied for circular object segmentation using shape ultimate opening with attribute of circularity computed efficiently by counting matchings from this collection of pattern sets.

BACKGROUND: Complex diseases are characterized as being polygenic and multifactorial, so this poses a challenge regarding the search for genes related to them. With the advent of high-throughput technologies for genome sequencing, gene expression measurements (transcriptome), and protein-protein interactions, complex diseases have been sistematically investigated. Particularly, Protein-Protein Interaction (PPI) networks have been used to prioritize genes related to complex diseases according to its topological features. However, PPI networks are affected by ascertainment bias, in which more studied proteins tend to have more connections, degrading the results quality. Additionally, methods using only PPI networks can provide only static and non-specific results, since the topologies of these networks are not specific of a given disease. RESULTS: The goal of this work is to develop a methodology that integrates PPI networks with disease specific data sources, such as GWAS and gene expression, to find genes more specific of a given complex disease. After the integration of PPI networks and gene expression data, the resulting network is used to connect genes related to the disease through the shortest paths that have the greatest concordance between their gene expressions. Both case and control expression data are used separately and, at the end, the most altered genes between the two conditions are selected. To evaluate the method, schizophrenia was adopted as case study. CONCLUSION: Results show that the proposed method successfully retrieves differentially coexpressed genes in two conditions, while avoiding the bias from literature. Moreover we were able to achieve a greater concordance in the selection of important genes from different microarray studies of the same disease and to produce a more specific gene set related to the studied disease.

Many methods have been published to prioritize genes using network theory. By using protein-protein interaction (PPI) data, it is possible to use mathematical features to rank and prioritize genes products in the network. Taking into account that genes related to the same diseases tend to connect, in the network structure, the prioritization methods search for candidate genes in the neighborhood of other genes already known to be related to a specific phenotype. Unfortunately, some existing algorithms can not deal well with highly connected genes, and some of them end up being related by chance to the disease being studied. We propose a pure method, with no need of adjustments, based on the hitting time of a random walk in PPI networks. This method captures information of the whole network and can equally prioritize genes regardless of its degree. We tested the efficiency of our method prioritizing candidate genes for Attention-Deficit/Hyperactivity Disorder (ADHD). The proposed method was able to give a good rank to genes that have genetic association with ADHD and was able to prioritize a large proportion of genes prioritized by other random-walk-based methods.

Various statistical and machine learning based algorithms have been proposed in literature for selecting an informative subset of genes from micro array data sets. The recent trend is to use functional knowledge to aid the gene selection process. In this paper we propose a clustering algorithm which generates multiple views (clusters) from the micro array expression profiles, each representing a particular facet of the data. Such multiple clusters are found to represent strongly connected regions of the known protein -- protein interaction (PPI) networks, perhaps corresponding to those responsible for certain biological processes. Thus we integrate micro array data clustering with PPI knowledge to obtain enriched gene sets. Results on benchmark micro array data sets demonstrate the competitiveness of our method compared to gene selection techniques.

This work introduces a residual operator called ultimate grain filter which is a powerful image operator based on numerical residues. With a multi-scale approach, the ultimate grain filter analyzes an image under a series of grain filters of increasing grain sizes. Thus, contrasted objects can be detected if a relevant residue is generated when they are filtered out by one of these grain filters. We also present an efficient algorithm for ultimate grain filter computation by using a structure called tree of shapes. In fact, since the result of a given grain filter can be obtained by pruning the corresponding tree and reconstructing it, we show that the result of the ultimate grain filter (which is based on numerical residues from a family of grain filters) can be obtained by the computation of the difference (remaining nodes) of the corresponding pruned trees. Finally, we propose the use of ultimate grain filter to extract contrasted objects using a priori knowledge of an application.

Models of gene regulatory networks (GRN) have been proposed along with algorithms for inferring their structure. By structure, we mean the relationships among the genes of the biological system under study. Despite the large number of genes found in the genome of an organism, it is believed that a small set of genes is responsible for maintaining a specific core regulatory mechanism (small subnetworks). We propose an algorithm for inference of subnetworks of genes from a small initial set of genes called seed and time series gene expression data. The algorithm has two main steps: First, it grows the seed of genes by adding genes to it, and second, it searches for subnetworks that can be biologically meaningful. The seed growing step is treated as a feature selection problem and we used a thresholded Boolean network with a perturbation model to design the criterion function that is used to select the features (genes). Given that the reverse engineering of GRN is a problem that does not necessarily have one unique solution, the proposed algorithm has as output a set of networks instead of one single network. The algorithm also analyzes the dynamics of the networks which can be time-consuming. Nevertheless, the algorithm is suitable when the number of genes is small. The results showed that the algorithm is capable of recovering an acceptable rate of gene interactions and to generate regulatory hypotheses that can be explored in the wet lab.

This paper presents a new supervised machine learning technique based on distances between points and straight lines segments. Basically, given a training data set, this technique estimates a function where its value is calculated using the distance between points and two sets of straight line segments. A training algorithm has been developed to find these sets of straight line segments that minimizes the mean square error. This technique has been applied on two real pattern recognition problems: (1) breast cancer data set to classify tumors as benign or malignant; (2) wine data set to classify wines in one of the three different cultivators from which they could be derived. This technique was also tested with two artificial data sets in order to show its ability to solve approximation function problems. The obtained results show that this technique has a good performance in all of these problems and they indicate that it is a good candidate to be used in Machine Learning applications.

MOTIVATION: Ranking gene feature sets is a key issue for both phenotype classification, for instance, tumor classification in a DNA microarray experiment, and prediction in the context of genetic regulatory networks. Two broad methods are available to estimate the error (misclassification rate) of a classifier. Resubstitution fits a single classifier to the data, and applies this classifier in turn to each data observation. Cross-validation (in leave-one-out form) removes each observation in turn, constructs the classifier, and then computes whether this leave-one-out classifier correctly classifies the deleted observation. Resubstitution typically underestimates classifier error, severely so in many cases. Cross-validation has the advantage of producing an effectively unbiased error estimate, but the estimate is highly variable. In many applications it is not the misclassification rate per se that is of interest, but rather the construction of gene sets that have the potential to classify or predict. Hence, one needs to rank feature sets based on their performance. RESULTS: A model-based approach is used to compare the ranking performances of resubstitution and cross-validation for classification based on real-valued feature sets and for prediction in the context of probabilistic Boolean networks (PBNs). For classification, a Gaussian model is considered, along with classification via linear discriminant analysis and the 3-nearest-neighbor classification rule. Prediction is examined in the steady-distribution of a PBN. Three metrics are proposed to compare feature-set ranking based on error estimation with ranking based on the true error, which is known owing to the model-based approach. In all cases, resubstitution is competitive with cross-validation relative to ranking accuracy. This is in addition to the enormous savings in computation time afforded by resubstitution.

MOTIVATION: A number of models have been proposed for genetic regulatory networks. In principle, a network may contain any number of genes, so long as data are available to make inferences about their relationships. Nevertheless, there are two important reasons why the size of a constructed network should be limited. Computationally and mathematically, it is more feasible to model and simulate a network with a small number of genes. In addition, it is more likely that a small set of genes maintains a specific core regulatory mechanism. RESULTS: Subnetworks are constructed in the context of a directed graph by beginning with a seed consisting of one or more genes believed to participate in a viable subnetwork. Functionalities and regulatory relationships among seed genes may be partially known or they may simply be of interest. Given the seed, we iteratively adjoin new genes in a manner that enhances subnetwork autonomy. The algorithm is applied using both the coefficient of determination and the Boolean-function influence among genes, and it is illustrated using a glioma gene-expression dataset. AVAILABILITY: Software for the seed-growing algorithm will be available at the website for Probabilistic Boolean Networks: http://www2.mdanderson.org/app/ilya/PBN/PBN.htm

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.