Pattern Recognition and Image Analysis

The vessel structures of the blood circulatory system are one of the most complex structures of the human body. Modern computed tomography techniques allow acquiring high resolution images, but at the same time, the number of artifacts in output images is quite high. They may affect diagnostic result and may obscure or simulate pathology. The idea of our method is to represent a 3D computed tomography image as a combination of vascular structure and background that has normal distribution in some neighborhood. Locally adaptive non-linear filters decrease global difference between bright and dark voxels, even if it produces better local contrast. Luminosity and contrast are observed from image background and are used for normalization of the whole image. After making background normalization at each layer, we merge layers and reconstruct vessels structure. The proposed method has been tested on real cardiac CT images, the test results show that high quality 3D structures are reconstructed, without requiring a priori knowledge or user interaction. The tested dataset has been made publicly available. The proposed approach can be applied to denoising computed tomography images, enhancing of contrast in lesion areas without changing topology of initial vessel structures.

In this paper, a Particle Swarm Optimization proposition is presented to solve the Homography problem. We tested our technique with several datasets. Also a comparison with existing technique (SVD) is done. PSO shows a significant superiority comparing to classic approach (SVD). The main gain of this technique is the accuracy of results and easiness of implementation.

A new method of image restoration based on the quasi-solution method for a compact set of functions with bounded total variation is introduced. Application of this method does not require estimation of the noise level, which is necessary to choose the regularization parameter in the Tikhonov regularization method. The approbation of this method with test images shows its effectiveness for image deringing.

In order to reconstruct a nonlinear dependence of the refractive index of a medium on the wavelength, a set of inductively generated models for choosing the optimal one is considered. An algorithm for the inductive generation of admissible nonlinear models is applied. A criterion for determining the error in the coefficients of the generated models, which is referred to as stability, and a method for estimating the stability of the solution are proposed. The results of numerical simulation on the data obtained in an experiment on determining the composition of a mixture from its total dispersion are presented.

The publication presents an introductory paper to the Special issue of the international journal Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications of the Russian Academy of Sciences. The main scientific results of the 8th International Workshop “Image Mining: Theory and Applications,” held on August 21, 2022, Montreal, Canada, are presented. Historical information is given on this series of international workshops, and their significant role in the development of the theory and practice of automation of image analysis, pattern recognition, and artificial intelligence is emphasized. The list of papers of the Special issue of PRIA, prepared based on the invited and regular papers selected and recommended for publication by the Program Committee of the IMTA-VIII-2022, is presented.

In the versatile advanced world, diseases due to the cardiovascular disease (CVD) play a major role in human health disorders event leads to death. CVD deaths accounts for 80% in males and 75% in females. Cardiovascular diseases are the leading cause of death globally. By 2030, over 23 million people will die from CVD every year. Up to 90% of cardiovascular disease may be preventable if they are properly recognized and correct treatment should be given at the earlier stage. This paper undergoes one of the key factors to find CVD is through retinal vessels, the processes involved in those measurements could predict the presence of diseases. The main function that is involved in the retinal vessels is the extraction of information present inside the tissues which is used in the case of recognition and treatment towards cardiovascular diseases such as stroke, blood pressure, hyper tension, glaucoma etc. The retinal image taken is filtered and then segmented. Their result is used for arteries and vein classification through the support vector machine (SVM). By detecting the optic cup and optic disc measurement, cup-to-disc ratio (CDR) is calculated here. By using artificial neural networks (ANN), the presence of CVD is recognized and their parameters are measured. Hence, the presence of CVD is recognized through the retinal images are detected in this paper.

Adequate formalization of problems is the most important task that has to be solved in order to apply the modern methods of so-called “machine learning” to real problems. The effective application of the metric, logical, regression, and other algorithms of machine learning becomes possible only when feature generation procedures and classes of objects are adequately defined. In this study, the theory of topological analysis of poorly formalized problems and the theory of analysis of labeled graphs were applied to the problem of predicting numerical characteristics of crystalline materials. The methods developed were tested on the problem of predicting the critical temperature of superconducting transition (Tc) of high-temperature cuprate superconductors (1450 structures). As a result, in a tenfold 6 : 1 cross-validation, the best model with a linear recognition operator yielded quite high average value of the correlation coefficient (r = 0.77) between the predicted and experimentally determined values of Tc.

The article is the second in a series on the current state and prospects of Descriptive Image Analysis, which is the leading branch of the modern mathematical theory of image analysis. Descriptive image analysis is a logically organized set of descriptive methods and models for analyzing and evaluating information in the form of images and for automating knowledge and data extraction from images necessary for making intelligent decisions about real-world scenes displayed and represented in an analyzed image. Problems on making intelligent decisions based on data analysis require formal representation of the source information, ideally, a mathematical model. Image modeling has a long, but not very productive history. Therefore, in the Descriptive Approach to image analysis and understanding (DA), the primary problem is bringing an image to a form suitable for recognition. The DA interprets the sought representation in the form of a descriptive image model (DIM). Due to the extremely complex informational nature and technical features involved in the digital representation of an image, it is impossible to construct a classical mathematical model of an image as an information object. To overcome this complexity and regularize the problem of bringing an image to a form convenient for recognition, a new mathematical object, a DIM is introduced and used in the DA. Models of recognition objects—images—and definitions of transformations over image models are considered. A formalized concept of descriptive image models is proposed. The results can be used to create a basis for methods of transforming and understanding an image as a mathematical object. The article’s main contribution to developing the mathematical theory of image analysis is understanding of an image as an information object and mathematical object.