Vol 27, No 3 (2017)

The work considers the mathematical aspects of one of the most fundamental problems of data analysis: search (choice) among a collection of objects for a subset of similar ones. In particular, the problem appears in connection with data editing and cleaning (removal of irrelevant (not similar) elements). We consider the model of this problem, i.e., the problem of searching for a subset of maximal cardinality in a finite set of points of the Euclidean space for which quadratic variation of points with respect to its unknown centroid does not exceed a given fraction of the quadratic variation of points of the input set with respect to its centroid. It is proved that the problem is strongly NP-hard. A polynomial 1/2-approximation algorithm is proposed. The results of the numerical simulation demonstrating the effectiveness of the algorithm are presented.

The problem of discriminant analysis under mild conditions is reduced to a system of linear inequalities. However, this system can turn out to be inconsistent, which happens rather frequently. This is when the method of committees is used. The quality of a committee is improved as the number of its members drops. A method of reducing the number of members of committees, if this is fundamentally possible, is considered.

In this paper, we present a detailed study and comparison of different classification algorithms. Our main purpose is the study of the Vicinal Support Vector Classifier (VSVC) and its relations to the other state-of-the-art classifiers. To this end, we start by the historical development of each classifier, derivation of the mathematics behind it and describing the relations that exist between some of them, in particular the relation between the VSVC and the other classifiers. Thereafter, we apply them to two famous learning datasets very used by the research community, namely the MIT-CBCL face and the Wisconsin Diagnostic Breast Cancer (WDBC) datasets. We show that despite its simplicity compared to the other state-of-the-art classifiers, the VSVC leads to very robust classification results and provide some practical advantages compared to the other classifiers.

Mathematical science in tight integration with the natural and life sciences provide sophisticated models and algorithms of knowledge acquisition. Overall rapid development of nowadays science and technologies is a direct consequence of such interdisciplinary developments. The same time, there exist particular research domains, e.g., the biological research domain, that appears as a semi-exact discipline (except of its genomics part). This is due to insufficient level of readiness of mathematical, physical and chemical sciences, being in power to provide the proper interpretation of the real size biological interrelations. Enrichment of mathematics to this new sophisticated level may be a long lasting but unavoidable process. Current series of studies is driven by a number of applied problems that are focused around the unique integrative technique of getting knowledge from fragmented data and descriptions. A large number of links connect these ideas to the problems of: artificial intelligence, intelligent information management, high performance computation, and other research domains. Our objective is in provision of integrated solutions of inverse type combinatorial problems that will help to sustain a set of applied problems. The base set of applied problems we consider involves the radiation therapy planning, the wireless sensor network integrated-connectivity-coverage protocols with its decentralized management, and the network tomography scenario devoted to the issue of energy minimization in networks. As we will see the necessary mathematical technique of solving these problems is focused around the model description by the sets of constraints and relations, by integration of the partial knowledge about these models. Two scenarios have been considered. One is based on the use of projections and their interpretation, and the second is based on the local neighbourhood analysis (generic projections). Given projections and/or neighbourhoods (in inverse manner), it is to analyse the consistency issue; to know the properties of the set of solutions; and to reconstruct one or all solutions of these problems. In mathematical level the problem is related to the well-known open problems such as the Berge’s hypothesis about the simple hypergraphic degree sequences. The technique to be used in investigations involves Boolean domain studies and the n-cube geometry, Lagrangean relaxation together with integer linear programming, Minkowski geometry, Voronoi diagrams, and the Constraint satisfaction mathematics. Prototype solutions and demonstrations to the mentioned applied problems will be provided.

We describe a subpixel edge detection approach in images. The proposed approach is based on the algebraic moments of the brightness function of halftone images. For an ideal two-dimensional edge, we consider a model with the following four parameters: the edge orientation, the distance from the edge to the center of the mask, and the brightness values from both sides of the edge. To obtain all subpixel parameters of the edge, six algebraic moments are used. To compute the moments rapidly, masks are used. The specificity of the proposed approach is as follows: masks of almost all sizes can be used and they are computed by means of explicit relations provided in the present paper as well. Increasing mask sizes, one can increase the accuracy of the detection of subpixel edge parameters, which is especially important for high-definition images. We present experiments displaying the efficiency of the proposed approach.

A new method for fast computation of the camera/robot local displacement (6 DOF) based on matched 3D point clouds obtained from images using computer vision methods is proposed. According to the method, the local geometric transformation matrix is computed based on the combination of external coordinate systems generated from random sample points. Comparative estimates of the efficiency of the method are made using data of computational experiments.

Textures and patterns are the distinguishing characteristics of objects. Texture classification plays fundamental role in computer vision and image processing applications. In this paper, texture classification using PDE (partial differential equation) approach and wavelet transform is presented. The proposed method uses wavelet transform to obtain the directional information of the image. A PDE for anisotropic diffusion is employed to obtain texture component of the image. The feature set is obtained by computing different statistical features from the texture component. The linear discriminant analysis (LDA) enhances separability of texture feature classes. The features obtained from LDA are class representatives. The proposed approach is experimented on three gray scale texture datasets: VisTex, Kylberg, and Oulu. The classification accuracy of the proposed method is evaluated using k-NN classifier. The experimental results show the effectiveness of the proposed method as compared to the other methods in the literature.

This paper aims at addressing a challenging research in both fields of the wavelet neural network theory and the pattern recognition. A novel architecture of the wavelet network based on the multiresolution analysis (MRWN) and a novel learning algorithm founded on the Fast Wavelet Transform (FWTLA) are proposed. FWTLA has numerous positive sides compared to the already existing algorithms. By exploiting this algorithm to learn the MRWN, we suggest a pattern recognition system (FWNPR). We show firstly its classification efficiency on many known benchmarks and then in many applications in the field of the pattern recognition. Extensive empirical experiments are performed to compare the proposed methods with other approaches.

The paper describes a research support system named “MSM Tools” that can be used for stochastic modelling of real processes in various information systems and implements the heterogeneous computing paradigm. The proposed approach to data mining is based on method of moving separation of probability mixtures. To obtain statistical estimations of the unknown parameters of mixed probability models, the system implements several modifications of so-called EM algorithm (including grid modifications for the NVIDIA CUDA architecture) that are commonly used in such areas as pattern recognition, clustering, classification, processing of censored and/or truncated data. An example of real data analysis via “MSM Tools” service is given.

Conventional gait recognition schemes has poor recognition accuracies in presence of covariates. It is mainly due to ineffective and inefficient representation and discriminative feature extraction schemes. The paper presents new technique to extract discriminative features from masked gait energy image based on curvelet transform and PCANet. The binary gait silhouette video sequence obtained from pre-processing of video sequence is converted in to masked gait energy image and then direction and edge representation ability of fast discrete curvelet transform is employed. Nonlinear and non invertible, image space to feature space mapping scheme of PCANet is used to extract discriminative robust features. The suitability and effectiveness of newly proposed scheme is demonstrated by experimentation on standard publicly available benchmark USF HumanID database.

A new mathematical method is presented for identifying the state of the lipid layer from images of the intermarginal space of human eyelids. As initial data, we use images of imprints of the intermarginal space of eyelids on a millipore filter after their staining with osmium vapor. Each image is a grey-scale photograph in which the dark regions represent imprints of the sebaceous secretions from the orifices of the excretory ducts of the meibomian glands. The proposed method is designed for extracting morphometric data from images of intermarginal space imprints. The method yields the following statistical characteristics: expectation and rootmean- square deviation of the imprint’s intensity on a line drawn and in a selected region, the imprint’s intensity along a line drawn, and variations in the imprint’s thickness. The proposed approach is based on the combined use of the techniques of mathematical morphology and mathematical statistics. The software implementation of the developed method, as well as the results of its experimental testing, are presented.

Documents may contain multiscript and recognition of those documents is really a challenging task. Earlier OCR (Optical Character Recognition) was developed for documents containing only English or regional languages. Documents containing multiple scripts are also needed to be kept protected for later use. So it needs more effort of the OCR designers for improving the accuracy rate for multi script OCR. In this paper we describe the character recognition process for printed documents containing Roman and Odia texts. The separation of the script has been performed at line level. We discuss a detailed description on the segmentation scheme using X-Y-Cut algorithm which isolates the text image into individual Odia and Roman line. To distinguish between the Roman and the Odia script, along with line height, we have considered the features of both the scripts. Most of the Roman character is linear as well as circular in nature and Odia characters are circular occupying more width as compared to Roman characters. We emphasize on Upper and lower Matras associated with Odia and absent in English. After extracting the individual scripts from the bilingual documents line wise, we send them to their individual OCR for recognition. Thus an algorithm has been proposed for identification of Odia and Roman scripts.

Kidney stone detection is one of the sensitive topic now-a-days. There are various problem associates with this topic like low resolution of image, similarity of kidney stone and prediction of stone in the new image of kidney. Ultrasound images have low contrast and are difficult to detect and extract the region of interest. Therefore, the image has to go through the preprocessing which normally contains image enhancement. The aim behind this operation is to find the out the best quality, so that the identification becomes easier. Medical imaging is one of the fundamental imaging, because they are used in more sensitive field which is a medical field and it must be accurate. In this paper, we first proceed for the enhancement of the image with the help of median filter, Gaussian filter and un-sharp masking. After that we use morphological operations like erosion and dilation and then entropy based segmentation is used to find the region of interest and finally we use KNN and SVM classification techniques for the analysis of kidney stone images.

The paper discusses an algorithm for spectral density estimation in the frequency domain using wavelet-based smoothing by wavelet thresholding techniques. The suggested algorithm can be applied to vibrational and hydroacoustic signal processing in order to estimate signal parameters in the frequency domain. The algorithm can be applied to the Fourier periodogram without using signal samples in the time domain. We also propose a technique aimed at working with signals of arbitrary length by applying the maximal overlap discrete wavelet transform. We also study software-hardware implementation of the developed algorithms.

The paper proposes an elastic grid technique to separate satellite target image into some intersections of characteristic rows and columns, which can extract more local texture features. Then, the relevant statistics of gray level co-occurrence matrix (GLCM) reflected the regional global texture features are used to generate some feature cells, which can be merged into a fingerprint array. The fingerprint can preserve the global and local features of the target satellite image. Because these cells have different ranges and variances, each cell can be projected into a Gauss kernel space by using its relevant Gauss function. The similarity of fingerprint cell components can be calculated by the product of fingerprint cells by using Gauss measure. The similarity of fingerprint array can be calculated as the sum of similarities of fingerprint cells. The area algorithm and shape algorithm can be used to preliminary separate the dwelling targets from village satellite images, and the preliminary detection accurate rate is higher. When the dwelling fingerprint algorithm based on elastic grid and GLCM features is used, the accurate chronicle classification rate can reach more than 85.2%.

The situation when uncertainty rules the circumstances some inefficiency of crisp set can be observed. This was overcome by application of fuzzy set for solving different real life problems. Intuitionistic fuzzy set was introduced to handle complex circumstances and to provide better result. Fuzzy set proves its efficiency in field data processing. Minimal structure fuzzy oscillation can be efficiently applied for image processing, especially for face recognition. In this paper we introduce the concept of Intuitionistic fuzzy set or IF Set based minimal structure oscillation. A face database which may be considered as training set, is used to form IF set minimal structure. Again non membership pixel values are also calculated with those pixel values which are used to form IF set minimal structure accordingly. The pixels from membership and nonmembership images are applied to compute two new oscillatory operators. We introduce four new conditions according to the values of the oscillatory operators, which is used for recognition of the face. This new concept can be applied in different types of real life data analysis such as data mining. Along with the theoretical explanation we also presented some experimental results which proves the precision of the face recognition algorithm. In this paper proposed new face recognition algorithm executed and tested using MATLAB 7.9 software and experiments are performed on Face fix Database and ORL database. Accuracy of the results describes the application of IF set minimal structure oscillation in the field of face recognition.

Face alignment has been an indispensable procedure in face application. It is still a challenge to locate facial landmarks in unconstrained scene. In this paper, we propose an algorithm to perform accurately face alignment. A method based on human retinal information processing principle is proposed to enhance the images and remove the illumination noise. According to the image’s locality principle, the distance constrains is imposed on the pixel difference features around the landmark to achieve robustness. And then, the random forest is used to map the pixel difference features to local binary features. The obtained local binary features are used to jointly learn a linear regression for the final output. In addition, the inherent data structure is utilized to reduce the computational burden when preform maximum variance reduction on the split node in random forest. Extensive experiments on public datasets show that the proposed approach can locate facial landmarks accurately and rapidly.