Graph-based morphological processing of multivariate microscopy images and data bases

International audienceThe extension of lattice based operators to manifolds is still a challenging theme in mathematical morphology. In this paper, we propose to explicitly construct complete lattices and replace each element of a manifold by its rank suitable for classical morphological processing. Manifold learning is considered as the basis for the construction of a complete lattice. The whole processing of multivariate functions is expressed on graphs to have a formalism that can be applied on images, region adjacency graphs, and image databases. Several examples in microscopy do illustrate the benefits of the proposed approach

Vector ordering and multispectral morphological image processing

International audienceThis chapter illustrates the suitability of recent multivariate ordering approaches to morphological analysis of colour and multispectral images working on their vector representation. On the one hand, supervised ordering renders machine learning no-tions and image processing techniques, through a learning stage to provide a total ordering in the colour/multispectral vector space. On the other hand, anomaly-based ordering, automatically detects spectral diversity over a majority background, al-lowing an adaptive processing of salient parts of a colour/multispectral image. These two multivariate ordering paradigms allow the definition of morphological operators for multivariate images, from algebraic dilation and erosion to more advanced techniques as morphological simplification, decomposition and segmentation. A number of applications are reviewed and implementation issues are discussed in detail

Stochastic spectral-spatial permutation ordering combination for nonlocal morphological processing

International audienceThe extension of mathematical morphology to mul-tivariate data has been an active research topic in recent years. In this paper we propose an approach that relies on the consensus combination of several stochastic permutation orderings. The latter are obtained by searching for a smooth shortest path on a graph representing an image. The construction of the graph can be based on both spatial and spectral information and naturally enables patch-based nonlocal processing

Cellular neural networks, Navier-Stokes equation and microarray image reconstruction

Copyright @ 2011 IEEE.Although the last decade has witnessed a great deal of improvements achieved for the microarray technology, many major developments in all the main stages of this technology, including image processing, are still needed. Some hardware implementations of microarray image processing have been proposed in the literature and proved to be promising alternatives to the currently available software systems. However, the main drawback of those proposed approaches is the unsuitable addressing of the quantification of the gene spot in a realistic way without any assumption about the image surface. Our aim in this paper is to present a new image-reconstruction algorithm using the cellular neural network that solves the Navier–Stokes equation. This algorithm offers a robust method for estimating the background signal within the gene-spot region. The MATCNN toolbox for Matlab is used to test the proposed method. Quantitative comparisons are carried out, i.e., in terms of objective criteria, between our approach and some other available methods. It is shown that the proposed algorithm gives highly accurate and realistic measurements in a fully automated manner within a remarkably efficient time

Adaptive Markov random fields for joint unmixing and segmentation of hyperspectral image

Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm

The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch

Recent and forthcoming advances in instrumentation, and giant new surveys, are creating astronomical data sets that are not amenable to the methods of analysis familiar to astronomers. Traditional methods are often inadequate not merely because of the size in bytes of the data sets, but also because of the complexity of modern data sets. Mathematical limitations of familiar algorithms and techniques in dealing with such data sets create a critical need for new paradigms for the representation, analysis and scientific visualization (as opposed to illustrative visualization) of heterogeneous, multiresolution data across application domains. Some of the problems presented by the new data sets have been addressed by other disciplines such as applied mathematics, statistics and machine learning and have been utilized by other sciences such as space-based geosciences. Unfortunately, valuable results pertaining to these problems are mostly to be found only in publications outside of astronomy. Here we offer brief overviews of a number of concepts, techniques and developments, some "old" and some new. These are generally unknown to most of the astronomical community, but are vital to the analysis and visualization of complex datasets and images. In order for astronomers to take advantage of the richness and complexity of the new era of data, and to be able to identify, adopt, and apply new solutions, the astronomical community needs a certain degree of awareness and understanding of the new concepts. One of the goals of this paper is to help bridge the gap between applied mathematics, artificial intelligence and computer science on the one side and astronomy on the other.Comment: 24 pages, 8 Figures, 1 Table. Accepted for publication: "Advances in Astronomy, special issue "Robotic Astronomy

A new method to calculate mathematical morphology using associative memory and cellular learning automata

Abstract: The methods presented in this paper include using auto-associative memory which can be defined as a supervised organizing method which is a specific type of h-sorting which is compatible with the morphologic operators over multi-variables data. Mathematical morphologies for multi-variable images require appropriate sort descriptions that allow us to define and use primitive morphologies operators without any wrong results such as wrong color. All the required calculations are defined with lattice algebra (+,^ and ∨); therefore, the proposed method will be faster with less computation overhead than the previous methods. This method does not use any assumptions of the stochastic process which means that this method is independent of the model. The presented method uses cellular learning automata which results in fewer errors than the mathematical methods due to the feedback from the network

Classifying the suras by their lexical semantics :an exploratory multivariate analysis approach to understanding the Qur'an

PhD ThesisThe Qur'an is at the heart of Islamic culture. Careful, well-informed interpretation of it is fundamental both to the faith of millions of Muslims throughout the world, and also to the non-Islamic world's understanding of their religion. There is a long and venerable tradition of Qur'anic interpretation, and it has necessarily been based on literary-historical methods for exegesis of hand-written and printed text. Developments in electronic text representation and analysis since the second half of the twentieth century now offer the opportunity to supplement traditional techniques by applying the newly-emergent computational technology of exploratory multivariate analysis to interpretation of the Qur'an. The general aim of the present discussion is to take up that opportunity. Specifically, the discussion develops and applies a methodology for discovering the thematic structure of the Qur'an based on a fundamental idea in a range of computationally oriented disciplines: that, with respect to some collection of texts, the lexical frequency profiles of the individual texts are a good indicator of their semantic content, and thus provide a reliable criterion for their conceptual categorization relative to one another. This idea is applied to the discovery of thematic interrelationships among the suras that constitute the Qur'an by abstracting lexical frequency data from them and then analyzing that data using exploratory multivariate methods in the hope that this will generate hypotheses about the thematic structure of the Qur'an. The discussion is in eight main parts. The first part introduces the discussion. The second gives an overview of the structure and thematic content of the Qur'an and of the tradition of Qur'anic scholarship devoted to its interpretation. The third part xvi defines the research question to be addressed together with a methodology for doing so. The fourth reviews the existing literature on the research question. The fifth outlines general principles of data creation and applies them to creation of the data on which the analysis of the Qur'an in this study is based. The sixth outlines general principles of exploratory multivariate analysis, describes in detail the analytical methods selected for use, and applies them to the data created in part five. The seventh part interprets the results of the analyses conducted in part six with reference to the existing results in Qur'anic interpretation described in part two. And, finally, the eighth part draws conclusions relative to the research question and identifies directions along which the work presented in this study can be developed