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The Possibilities of Diagnosis and Prediction of Cardiac Disorders Based on the Results of mathematical Modeling of the Myocardium and Regulation of Action of the Heart

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pattern RECOGNITION AND image analysis 2023年第4期33卷 1293-1308页

作者： Makhortykh, S. A. Moskalenko, A. V. Russian Acad Sci Keldysh Inst Appl Math Inst Math Problems Biol Pushchino 142290 Moscow Russia

Theoretical approaches to solving problems of diagnosing and predicting cardiac dysfunctions within the framework of modern mathematical physics of the heart (cardiophysics) are presented. The possibilities for diagnostic purposes of using recognition of patterns of behavior of autowave vortices that arise in the heart during dangerous disturbances in its functioning are considered. The prospects for the development of new methods for diagnosing patterns of the basic heart rhythm in the development of already recognized methods for analyzing heart rate variability are discussed.

关键词： diagnostics prognosis spectral analysis cardiophysics bifurcation memory mathematical modeling excitable media autowaves action of the heart heart rate variability

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Retrieving urban areas on Google Earth images: application to towns of West Africa

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INTERNATIONAL JOURNAL OF REMOTE SENSING 2010年第22期31卷 5867-5877页

作者： Mering, Catherine Baro, Johanna Upegui, Erika Univ Paris Diderot Pole Rech Org & Diffus lInformat Geog Paris France

This article presents original stepwise image processing providing spatial delimitation of urban areas from Google Earth images in West Africa. In such images, converted to grey level images, urban areas are distinguished from their surroundings thanks to a specific textural aspect that may be retrieved by means of relevant morphological filters. Extraction of urban patterns consists of image analysis based on methods of mathematical morphology. The morphological filters used in the stepwise processing are chosen according to the spatial resolution, the visual quality of the original images and the environmental characteristics of the towns under study. Results are then compared with spatial data provided by a public geographical database.

关键词： original image morphological filters image analysis topsoil Earth spatial data West Africa image processing urban pattern urban area Google images Outcome Studies Towns

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A projection local image descriptor

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pattern Recognition and image analysis 2012年第2期22卷 380-385页

作者： Sorokin, D.V. Krylov, A.S. Centre for Biomedical Image Analysis Faculty of Informatics Masaryk University Botanická 68a Brno Czech Republic Laboratory of Mathematical Methods of Image Processing Faculty of Computational Mathematics and Cybernetics Moscow State University Moscow Russia

This paper presents a projection local image descriptor. The projection local image descriptor construction is based on the local image expansion into the set of Gauss-Laguerre circular harmonic functions in the support region of a keypoint. The keypoints detection method is considered. It is also based on the analysis of image projections on the set of Gauss-Laguerre circular harmonic functions. The efficient technique for descriptors elements computation is introduced. The 2D Hermite projection method is used to accelerate the local image descriptors construction. The proposed approach is tested on the task of image points matching. The test results approved the ability of acceleration of descriptors construction process up to several times. © 2012 Pleiades Publishing, Ltd.

关键词： Gaussian distribution

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Morphological reversible contour representation

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IEEE TRANSACTIONS ON pattern analysis AND MACHINE INTELLIGENCE 2000年第3期22卷 227-240页

作者： Hasan, YMY Karam, LJ Arizona State Univ Dept Elect Engn Ctr Telecommun Res Tempe AZ 85287 USA

In this paper, a novel morphological reversible contour representation of discrete binary images is proposed. A binary image is represented by a set of nonoverlapping multilevel contours and a residual image. In this proposed representation, the total number of pixels representing an image is far less than the total number of pixels obtained by the seed-based morphological contour-skeleton lossless representation. The proposed contour representation is simple, unique. and general without restrictions on the binary image to be represented. Moreover, it requires fewer number of operations to compute the proposed representation compared with other lossless morphological representation methods. The resulting multicontour image component is also robust to noise. An efficient differential chain contour coding scheme is employed to further compress the represented image. The proposed method yields very low bit rates compared to the existing morphological techniques. To exactly reconstruct an original image, an automatic filling procedure, which properly fills a proper multicontour image according to its topological structure without need of seed points, is proposed. The morphological unique contour representation and its lossless reconstruction techniques have been tested on images with varying size and complexity. Examples are presented to illustrate the performance of the proposed method.

关键词： shape analysis binary images mathematical morphology shape representation homotopy topology contour coding contour filling

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image REPRESENTATION USING BLOCK pattern MODELS AND ITS image-PROCESSING APPLICATIONS

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IEEE TRANSACTIONS ON pattern analysis AND MACHINE INTELLIGENCE 1993年第4期15卷 321-336页

作者： WANG, Y MITRA, SK UNIV CALIF SANTA BARBARA DEPT ELECT & COMP ENGN SANTA BARBARA CA 93106 USA

An image representation scheme using a set of block pattern models (BPM's) is introduced. These models consist of three categories (constant, oriented, and irregular), with the last one consisting of two subgroups: textured and mixed. They are constructed to represent three basic types of image patterns: shade, edge, and texture. image representation using these models requires considerably fewer bits than the original pixel-wise description and yet characterizes perceptually significant features more effectively. In particular, the parameterization of the oriented model using oriented basis functions lays a mathematical foundation for designing directional operators that are desirable in many image processing applications. Algorithms for model classification, model parameter estimation, and image reconstruction from model parameters are presented, and these provide the necessary vehicles for applying the proposed representation scheme to various image processing tasks. The applications of the proposed models in image coding, image zooming, and image smoothing are described. The coding system approximates each image block by a BPM and further quantizes the model parameters. Satisfactory coded images have been obtained at bit rates between 0.5 - 0.6 bpp (bits per pixel) with a high-rate realization and between 0.3 - 0.5 bpp with a low-rate realization. The high-rate realization has a simple structure suitable for real-time implementation. The methods for image zooming and smoothing are similar, where both adapt the processing for each pixel according to the model of its neighborhood. By using directional filters in oriented regions, edges and lines are rendered sharper in a smoother manner than with conventional linear filtering approaches, which leads to significant improvement in perceived image quality.

关键词： image CODING image INTERPOLATION image MODELING image SMOOTHING

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analysis OF AN INVERSE PROBLEM ARISING IN PHOTOLITHOGRAPHY

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mathematical MODELS & methods IN APPLIED SCIENCES 2012年第5期22卷 1150026-1-1150026-30页

作者： Rondi, Luca Santosa, Fadil Univ Trieste Dipartimento Matemat & Informat I-34127 Trieste Italy Univ Minnesota Sch Math Minneapolis MN 55455 USA

We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship between the target shape and the unknown is modeled through diffractive optics. We develop a variational formulation that is well-posed and propose an approximation that can be shown to have convergence properties. The approximate problem can serve as a foundation to numerical methods, much like the Ambrosio-Tortorelli's approximation of the Mumford-Shah functional in image processing.

关键词： Photolithograpy shape optimization sets of finite perimeter Gamma-convergence

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Evaluation of polynomial image deformation using anatomical landmarks for matching of 3D-abdominal MR-images and for atlas construction

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 1999年第4期46卷 1110-1113页

作者： Kimiaei, S Noz, M Jonsson, E Crafoord, J Maguire, GQ Karolinska Inst Dept Med Radiat Phys S-17176 Stockholm Sweden NYU Dept Radiol New York NY 10012 USA Karolinska Inst Dept Radiol S-17176 Stockholm Sweden KTH Dept Teleinformat S-10044 Stockholm Sweden

While a variety of different deformation algorithms have been implemented for matching of skull, few attempts in matching areas in abdomen have been reported. In this study we evaluate the usability of first and second order polynomial 3D-warping for this purpose. We match abdominal MR-images from different individuals using manually picked anatomical landmarks. Generation of transformation coefficients was done through a linear regression technique that employs a least square fit using the reference landmarks. The landmarks were picked in a predefined order, well spread over the entire data set, by a radiologist. The image resampling was done using linear interpolation and the evaluation was performed visually as well as by calculating the cross correlation and the normalized least squared error between the original image and the transformed image. Our preliminary results reveal that the second order polynomial transformation using landmarks is a robust and efficient method. It is also superior to the second order one, for image deformation in the abdominal region and it may be used in atlas generation as well as in multimodality image coregistration and fusion.

关键词： Magnetic resonance imaging Medical imaging image analysis pattern recognition Polynomials mathematical transformations Regression analysis Least squares approximations Interpolation Computational methods Optical correlation Error analysis image warping computational methods regression analysis Polynomial Medical imaging anatomical landmarks image Interpolation image warping Optical correlation pattern recognition landmarks image analysis

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image Intensity Variation Information for Interest Point Detection

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IEEE TRANSACTIONS ON pattern analysis AND MACHINE INTELLIGENCE 2023年第8期45卷 9883-9894页

作者： Zhang, Weichuan Sun, Changming Gao, Yongsheng Xian Polytech Univ Coll Elect & Informat Xian 710048 Peoples R China CSIRO Data61 Epping NSW 1710 Australia Griffith Univ Inst Integrated & Intelligent Syst Nathan Qld 4111 Australia

Interest point detection methods are gaining more attention and are widely applied in computer vision tasks such as image retrieval and 3D reconstruction. However, there still exist two main problems to be solved: (1) from the perspective of mathematical representations, the differences among edges, corners, and blobs have not been convincingly explained and the relationships among the amplitude response, scale factor, and filtering orientation for interest points have not been thoroughly explained;(2) the existing design mechanism for interest point detection does not show how to accurately obtain intensity variation information on corners and blobs. In this paper, the first- and second-order Gaussian directional derivative representations of a step edge, four common genres of corners, an anisotropic-type blob, and an isotropic-type blob are analyzed and derived. Multiple interest point characteristics are discovered. The characteristics for interest points that we obtained help us describe the differences among edges, corners, and blobs, explain why the existing interest point detection methods with multiple scales cannot properly obtain interest points from images, and present novel corner and blob detection methods. Extensive experiments demonstrate the superiority of our proposed methods in terms of detection performance, robustness to affine transformations, noise, image matching, and 3D reconstruction.

关键词： image edge detection Interest point detection mathematical models Detectors Blob detection Feature extraction Corner detection Blob detection corner detection first-and second-order Gaussian directional derivative representations interest point characteristics multiple scales

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Reconstruction of three-dimensional anisotropic media based on analysis of morphological completeness

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COMPUTATIONAL MATERIALS SCIENCE 2019年 167卷 123-135页

作者： Gao, MingLiang Li, XiangQun Xu, YongSheng Wu, Tao Wang, JianHua Northwest Univ Nationalities Coll Elect Engn Lanzhou 730030 Gansu Peoples R China

The physical properties of porous media can be more effectively observed and understood when analyzing three-dimensional (3D) structures. The use of computer-based mathematical modeling methods has been proven effective for reconstructing 3D structures of porous media from two-dimensional (2D) images. However, reconstructing a heterogeneous 3D structure from a single 2D image is currently challenging for computer-based mathematical modeling methods. Focusing on the reconstruction of heterogeneous 3D structures from a single anisotropic training image (TI), this paper first introduces a morphological completeness analysis method, which presents a completely new approach to reconstruction in which only two sections are controlled. Then, to enhance the constraint on the simulation points in this new approach to reconstruction, a double-layer and multi-grid system (DLMGS) is proposed. The updated pattern density function simulation, based on the DLMGS, is then taken as the specific reconstruction algorithm in this work. Finally, our reconstruction method is tested using a core image, and the performance of the reconstruction result is assessed using multiple functions. Detailed experiments show that our method can successfully reconstruct a heterogeneous 3D structure from a single anisotropic image, which reduces the required dimensionality of input data for 3D reconstruction and extends the applicable scope.

关键词： Heterogeneous media Morphological completeness Double-layer and multi-grid system pattern density function simulation 3D reconstruction

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Bayesian models for medical image biology using Monte Carlo Markov chains techniques

Bayesian models for medical image biology using Monte Carlo ...

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International Conference on Computational methods in Sciences and Engineering

作者： Zimeras, S Gerogiakodis, F Univ Aegean Dept Stat & Actuarial Financial Math GR-83200 Karlovassi Samos Greece Univ Piraeus Dept Stat & Insurance Sci Piraeus 18534 Greece

The objective of Bayesian modelling in pattern analysis is aimed to extract the important characteristics of the pattern using a few parameters so as to represent the pattern effectively. The use of Bayesian methods in medical biology and modelling is an approach, which seeks to provide a unified framework within many different image processes. Markov random fields (M.r.f.) modelling are a very popular pattern analysis methods and it plays an important role in pattern recognition and computer vision. In this work, Bayesian models would be presented to illustrate biological phenomena using the Gibbs sampler technique. Finally, methods for estimating model parameters using likelihood techniques are examined, and a model selection procedure is proposed for classifying the neighbourhood structure of the image. The techniques are investigated using simulated and real data from the area of biology. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： mathematical models

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