The possibilities of research on mathematical models with a large number of parameters using pattern recognition methods are discussed in this paper. Research of models through construction of phase and parametric por...
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This article is devoted to an original approach to the definition and description of a Turing machine (TM) for implementing descriptive imageanalysismethods based on an information structure for generating descripti...
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This article is devoted to an original approach to the definition and description of a Turing machine (TM) for implementing descriptive imageanalysismethods based on an information structure for generating descriptive algorithmic schemes for automating imageanalysis. The fundamental problem, to which the subject of the study belongs, is the automation of extracting information from images that is necessary for making intelligent decisions. One of the important and promising areas of research in this problem is the automation of the choice of a method for solving the problem of imageanalysis. A necessary condition for such automation is a comparative analysis and optimization of the imageanalysis algorithms, which, in turn, requires estimates of the complexity and efficiency of algorithms and a universal calculator to obtain them. One of the strategic goals for the development of descriptive imageanalysis is the study of models of imageanalysis processes. To do this, it is proposed to define and build an imageanalysis Machine, i.e., TMs specialized for processing spatial information. A method for determining a TM for modeling descriptive algorithmic schemes for imageanalysis is proposed and described. This machine can also be used to evaluate the mathematical characteristics of imageanalysis algorithms. The main concepts and objects of descriptive analysis necessary for defining and constructing a TM for modeling and studying procedures for the descriptive analysis of images are recalled. An example is given of modeling, on a TM specialized for imageanalysis, information processing procedures implemented in an information structure to generate descriptive algorithmic schemes for imageanalysis when solving imageanalysis problems. The fundamental importance of the results of these studies for the development of the mathematical theory of imageanalysis and their scientific novelty are related to the formulation of problems and the development of methods fo
The possibilities of using a new approach to study specific multivariate dynamic systems based on applying methods of pattern recognition and statistical modeling are demonstrated in the paper using the example of the...
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We develop a mathematical framework for quantifying and understanding multidimensional frequency modulations in digital images. We begin with the widely accepted definition of the instantaneous frequency vector ( IF) ...
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We develop a mathematical framework for quantifying and understanding multidimensional frequency modulations in digital images. We begin with the widely accepted definition of the instantaneous frequency vector ( IF) as the gradient of the phase and define the instantaneous frequency gradient tensor ( IFGT) as the tensor of component derivatives of the IF vector. Frequency modulation bounds are derived and interpreted in terms of the eigendecomposition of the IFGT. Using the IFGT, we derive the ordinary differential equations ( ODEs) that describe image flowlines. We study the diagonalization of the ODEs of multidimensional frequency modulation on the IFGT eigenvector coordinate system and suggest that separable transforms can be computed along these coordinates. We illustrate these new methods of imagepatternanalysis on textured and fingerprint images. We envision that this work will find value in applications involving the analysis of image textures that are nonstationary yet exhibit local regularity. Examples of such textures abound in nature.
Practical use of mathematicalmethods of pattern recognition in medicine and psychology faces a number of problems, caused by the peculiarities of data and users. The author, a doctor by education, analyzes these prob...
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In the speckle metrology, the processing of speckle image is very important. A method of morphological image processing is proposed in this paper. The theory of mathematical morphology and some basic morphological ope...
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In the speckle metrology, the processing of speckle image is very important. A method of morphological image processing is proposed in this paper. The theory of mathematical morphology and some basic morphological operations are introduced. In the experiment of laser speckle double-exposure, we get the specklegram which contains the information of micro-displacement. Then we employ the device of point-to-point analysis and get the image of laser speckle pattern interference fringes. Using the theory of speckle, the formula of micro-displacement is obtained. In the image processing, we first use grey-level transformation and histogram equalisation. Then we use the method of dynamic local threshold to get the binary image of laser speckle pattern interference fringes. In order to extract the fringe spacing, the image is processed by the operations of mathematical morphology in this work, such as the operations of opening, closing, skeletonisation and deburring. After that, the image can be used to extract the average fringe spacing by which the micro-displacement can be calculated finally. We get a more accurate result than traditional methods. The deviation may be less than 1% and the order of magnitude can reach 1 mm. The method of morphological image processing used in the speckle metrology has some advantages such as fast processing, easiness and high precision.
The evaluation of surface roughness is crucial to the hydrochemical and mechanical description of fractured rockmasses. Surface roughness contains information on rock strength, deformability, permeability, etc. Recent...
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The evaluation of surface roughness is crucial to the hydrochemical and mechanical description of fractured rockmasses. Surface roughness contains information on rock strength, deformability, permeability, etc. Recent years have witnessed a rapid development of new methods for measuring the surface of rock fracture using state-of-the-art technologies. Currently available measuring instruments, such as profilometers and confocal microscopes, provide information about hundreds of thousands of even millions measurement points which represent the investigated surface. The key problem, therefore, is to work out methods to adequately interpret such large packets of data. This study attempts a thorough analysis of this type of data using image processing and mathematical morphology methods. The paper presents the results received from morphological gradients, analyses of the results obtained from the water shed as well as the analyses of variograms. Furthermore, it proposes the application of morphological filtering for selecting the roughness component of a rock fracture. These results have been used in classifying the investigated rock. This classification was based on pattern recognition methods. By the definition of the 6D features space and the definition of learning sets, a successful classification of investigated rocks has been obtained, with upto ca. 95% correct recognitions. (C) 2009 Elsevier Ltd. All rights reserved.
In this paper we present a generalization on the notion of image connectivity similar to that modeled by second-generation connections. The connected operators based on this new type of connection make use of image pa...
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In this paper we present a generalization on the notion of image connectivity similar to that modeled by second-generation connections. The connected operators based on this new type of connection make use of image partitions aided by mask images to extract path-wise connected regions that were previously treated as sets of singletons. This leads to a redistribution of image power which affects texture descriptors. These operators find applications in problems involving contraction-based connectivities, and we show how they can be used to counter the over-segmentation problem of connected filters. Despite restrictions which prevent extensions to gray-scale, we present a method for gray-scale spectral analysis of biomedical images characterized by filamentous details. Using connected pattern spectra as feature vectors to train a classifier we show that the new operators outperform the existing contraction-based ones and that the classification performance competes with, and in some cases outperforms methods based on the standard 4- or 8-connectivity. Finally, combining the two methods we enrich the texture description and increase the overall classification rate. (C) 2009 Elsevier Ltd. All rights reserved.
The paper presents a new method to find areas related to typical artifacts of image enhancements methods. Two artifacts are analyzed: edge blur and ringing effect. The method is based on the analysis of basic edges-th...
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Poissonian image deconvolution is a key issue in various applications, such as astronomical imaging, medical imaging, and electronic microscope imaging. Alarge amount of literature on this subject is analysis-based me...
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Poissonian image deconvolution is a key issue in various applications, such as astronomical imaging, medical imaging, and electronic microscope imaging. Alarge amount of literature on this subject is analysis-based methods. These methods assign various forward measurements of the image. Meanwhile, synthesis-based methods are another well-known class of methods. These methods seek a reconstruction of the image. In this paper, we propose an approach that combines analysis with synthesis methods. The method is proposed to address Poissonian image deconvolution problem by minimizing the energy functional, which is composed of a sparse representation prior over a learned dictionary, the data fidelity term, and framelet based analysis prior constraint as the regularization term. The minimization problem can be efficiently solved by the split Bregman technique. Experiments demonstrate that our approach achieves better results than many state-of-the-art methods, in terms of both restoration accuracy and visual perception.
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