Article

ICPRAI 2018 SI: Descriptive Image Analysis. Foundations and Descriptive Image Algebras

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

The paper is devoted to Descriptive Image Analysis (DA) — a leading line of the modern mathematical theory of image analysis. DA is a logically organized set of descriptive methods, mathematical objects, and models and representations aimed at analyzing and evaluating the information represented in the form of images, as well as for automating the extraction from images of knowledge and data needed for intelligent decision-making. The basic idea of DA consists of embedding all processes of analysis (processing, recognition, understanding) of images into an image formalization space and reducing it to (1) construction of models/representations/formalized descriptions of images; (2) construction of models/representations/formalized descriptions of transformations over models and representations of images. We briefly discuss the basic ideas, methodological principles, mathematical methods, objects, and components of DA and the basic results determining the current state of the art in the field. Image algebras (IA) are considered in the context of a unified language for describing mathematical objects and operations used in image analysis (the standard IA by Ritter and the descriptive IA by Gurevich).

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... To date, this model and its generalizations were considered in many papers (see [8] and references thereafter). In particular, it found its place in the Descriptive Image Analysis [9]. Below we describe the main principles of the classical version of this model. ...
Article
In the paper some fuzzy classification algorithms based upon a nearest neighbor decision rule areconsidered in terms of the pattern recognition algorithms which are based on the computation of estimates (theso-called AEC model). It is shown that the fuzzy K nearest neighbor algorithm can be assigned to the AECclass. In turn, it is found that some standard AEC algorithms, which depend on a number of numericalparameters, can be used as fuzzy classification algorithms. Yet among them there exist algorithms extremalwith respect to these parameters. Such algorithms provide maximum values of the associated performancemeasures.
Chapter
This article is continued description of an original approach to the definition and description of a Turing machine (TM) for implementing descriptive image analysis methods based on an information structure for generating descriptive algorithmic schemes for automating image analysis. 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 image analysis. A necessary condition for such automation is a comparative analysis and optimization of the image analysis 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 image analysis is the study of models of image analysis processes. To do this, it is proposed to define and build an ‘‘Image Analysis Machine,’’ i.e., TMs specialized for processing spatial information. A method for determining a TM for modeling descriptive algorithmic schemes for image analysis is proposed and described. This machine can also be used to evaluate the mathematical characteristics of image analysis algorithms.Keywordsimage analysisdescriptive image analysisTuring Machine for Descriptive Image Analysismathematical theory of image analysisimage-miningdescriptive algorithmic schemesmathematical structuresinformation structures
Article
This article explores the use of computer vision for recognizing human fatigue by the eyes. The primary attention is paid to the development of a software package that can be used in the future as a system for monitoring the condition of drivers. Face detection is based on the Viola–Jones method and Haar cascades. This allows the algorithm to work in real time. However, convolutional neural networks are used to recognize eye conditions. Such networks training takes place on the eyes cut out from images of faces. Learning occurs in two eye states: open and closed. Moreover, the left and right eyes are analyzed separately. Different illumination characteristics have resulted in different accuracy rates for each eye. To develop the program, the Python programming language was used, the Jupyter Notebook was chosen as the development environment, and OpenCV was used as the main library, since it allows us to receive and process data from a USB camera. The developed software package allows us to detect closed eyes with precision and recall of about 90%. This uses a simple camera with a low resolution of 640 × 480 pixels. The proposed algorithm requires an additional increase in the accuracy and completeness of recognition of the closed eyes.
Chapter
This paper is devoted to the basic models of descriptive image analysis, which is the leading branch of the modern mathematical theory of image analysis and recognition. Descriptive analysis provides for the implementation of image analysis processes in the image formalization space, the elements of which are various forms (states, phases) of the image representation that is transformed from the original form into a form that is convenient for recognition (i.e., into a model), and models for converting data representations. Image analysis processes are considered as sequences of transformations that are implemented in the phase space and provide the construction of phase states of the image, which form a phase trajectory of the image translation from the original view to the model. Two types of image analysis models are considered: 1) models that reflect the general properties of the process of image recognition and analysis – the setting of the task, the mathematical and heuristic methods used, and the algorithmic content of the process: a) a model based on a reverse algebraic closure; b) a model based on the equivalence property of images; c) a model based on multiple image models and multiple classifiers; 2) models that characterize the architecture and structure of the recognition process: a) a multilevel model for combining algorithms and source data in image recognition; b) an information structure for generating descriptive algorithmic schemes for image recognition. A brief description, a comparative analysis of the relationships and specifics of these models are given. Directions for further research are discussed.
Chapter
The problem of detecting human fatigue by the state of the eyes is considered. A program for detecting the state of open/closed eyes has been developed. The Haar cascades were used to search for faces. Then the eyes were detected on the video from simple web-camera, which allowed us to accumulate a sufficient dataset. Training took place using convolutional neural networks, and due to different lighting conditions, different accuracy characteristics were obtained for the left and right eyes. Using Python programming language with the Jupyter Notebook functionality and the OpenCV library, a software package has been developed that allows us to highlight closed eyes when testing for a learning subject (certain person from whose images the model was trained) with an accuracy of about 90% on a camera with a low resolution (640 by 480 pixels). The proposed solution can be used in the tasks of monitoring driver’s state because one of the most frequent reasons of road accidents is driver fatigue.
Article
A high resolution microscope is designed for plasma hard X-ray (10–20[Formula: see text]keV) imaging diagnosis. This system consists of two toroidal mirrors, which are nearly parallel, with an angle twice that of the grazing incidence angle and a plane mirror for spectral selection and correction of optical axis offset. The imaging characteristics of single toroidal mirror and double mirrors are analyzed in detail by the optical path function. The optical design, parameter optimization, image quality simulation and analysis of the microscope are carried out. The optimized hard X-ray microscope has a resolution better than 5[Formula: see text][Formula: see text]m at 1[Formula: see text]mm object field of view. The experimental data shows that the variation of the resolution is smaller in the direction of incident angle decrease than that in the increasing direction.
Chapter
The study is continued investigation of mathematical and functional/physical interpretation of image analysis and processing operations used as sets of operations (ring elements) in descriptive image algebras (DIA) with one ring. The main result is the determination and characterization of interpretation domains of DIA operations: image algebras that make it possible to operate with both the main image models and main models of transformation procedures that ensure effective synthesis and realization of the basic procedures involved in the formal description, processing, analysis, and recognition of images. The applicability of DIAs in practice is determined by the realizability—the possibility of interpretation—of its operations. The interpretation is considered as a transition from a meaningful description of the operation to its mathematical or algorithmic implementation. The main types of interpretability are defined, and examples of interpretability of operations of the descriptive image algebras with one ring, are given.
Article
The study is devoted to mathematical and functional/physical interpretation of image analysis and processing operations used as sets of operations (ring elements) in descriptive image algebras (DIA) with one ring. The main result is the determination and characterization of interpretation domains of DIA operations: image algebras that make it possible to operate with both the main image models and main models of transformation procedures that ensure effective synthesis and realization of the basic procedures involved in the formal description, processing, analysis, and recognition of images. The applicability of DIAs in practice is determined by the realizability—the possibility of interpretation—of its operations. Since DIAs represent an algebraic language for the mathematical description of image processing, analysis, and understanding procedures using image transformation operations and their representations and models, the authors consider an algebraic interpretation. These procedures are formulated and implemented in the form of descriptive algorithmic schemes (DAS), which are correct expressions of the DIA language. The latter are constructed from the processing and transformation of images and other mathematical operations included in the corresponding DIA ring. The mathematical and functional properties of DIA operations are of considerable interest for optimizing procedures of processing and analyzing images and constructing specialized DAS libraries. Since not all mathematical operations have a direct physical equivalent, the construction of an efficient DAS for image analysis involves the problem of interpreting operations for DAS content. Research into this problem leads to the selection and study of interpretation domains of DIA operations. The proposed method for studying the interpretability of DIA operations is based on the establishment of correspondence between the content description of the operation function and its mathematical realization. The main types of interpretability are defined and examples given of the interpretability/uninterpretability of operations of a standard image algebra, which is a restriction of the DIA with one ring.
Article
Full-text available
The authors examine the set-theoretic interpretation of morphological filters in the framework of mathematical morphology and introduce the representation of classical linear filters in terms of morphological correlations, which involve supremum/infimum operations and additions. Binary signals are classified as sets, and multilevel signals as functions. Two set-theoretic representations of signals are reviewed. Filters are classified as set-processing (SP) or function-processing (FP). Conditions are provided for certain FP filters that pass binary signals to commute with signal thresholding because then they can be analyzed and implemented as SP filters.
Article
Full-text available
The work is devoted to the description of a new class of image algebras—descriptive image algebras (DIA). These algebras are intended for the structural description of possible algorithms for image analysis and understanding. Definitions of DIA and basic DIA are introduced. The choice of the algebra for refinement of the concept of DIA with one ring is discussed. Examples of operations, both resulting and not resulting in construction of DIA with one ring, are presented. Possible interpretations of operations of DIA are considered. By results of investigation of the standard Ritter’s image algebra used in construction of DIA with one ring are formulated. An illustrative example of an algorithmic scheme is described with the help of DIA.
Article
Full-text available
The brief review of main methods and features of the descriptive approach to image analysis (DAIA), viz. forming the system of concepts that characterize the initial information-images-in recognition problems, and descriptive image models designed for recognition problems, is given. At present, in terms of development of image analysis and recognition, it is critical to understand the nature of the initial information, viz. images, find methods of image representation and description to be used to construct image models designed for recognition problems, establish the mathematical language for the unified description of image models and their transformations that allow constructing image models and solving recognition problems, construct models to solve recognition problems in the form of standard algorithmic schemes that allow, in the general case, moving from the initial image to its model and from the model to the sought solution. The DAIA gives a single conceptual structure that helps develop and implement these models and the mathematical language. The main DAIA purpose is to structure and standardize different methods, operations and representations used in image recognition and analysis. The DAIA provides the conceptual and mathematical basis for image mining, with its axiomatic and formal configurations giving the ways and tools to represent and describe images to be analyzed and evaluated.
Book
Full-text available
Image algebra is a comprehensive, unifying theory of image transformations, image analysis, and image understanding. In 1996, the bestselling first edition of the Handbook of Computer Vision Algorithms in Image Algebra introduced engineers, scientists, and students to this powerful tool, its basic concepts, and its use in the concise representation of computer vision algorithms. Updated to reflect recent developments and advances, the second edition continues to provide an outstanding introduction to image algebra. It describes more than 80 fundamental computer vision techniques and introduces the portable iaC++ library, which supports image algebra programming in the C++ language. Revisions to the first edition include a new chapter on geometric manipulation and spatial transformation, several additional algorithms, and the addition of exercises to each chapter. The authors-both instrumental in the groundbreaking development of image algebra-introduce each technique with a brief discussion of its purpose and methodology, then provide its precise mathematical formulation. In addition to furnishing the simple yet powerful utility of image algebra, the Handbook of Computer Vision Algorithms in Image Algebra supplies the core of knowledge all computer vision practitioners need. It offers a more practical, less esoteric presentation than those found in research publications that will soon earn it a prime location on your reference shelf.
Article
Full-text available
This paper begins with analyzing the theoretical connections between levelings on lattices and scale-space erosions on reference semilattices. They both represent large classes of self-dual morphological operators that exhibit both local computation and global constraints. Such operators are useful in numerous image analysis and vision tasks including edge-preserving multiscale smoothing, image simplification, feature and object detection, segmentation, shape and motion analysis. Previous definitions and constructions of levelings were either discrete or continuous using a PDE. We bridge this gap by introducing generalized levelings based on triphase operators that switch among three phases, one of which is a global constraint. The triphase operators include as special cases useful classes of semilattice erosions. Algebraically, levelings are created as limits of iterated or multiscale triphase operators. The subclass of multiscale geodesic triphase operators obeys a semigroup, which we exploit to find PDEs that can generate geodesic levelings and continuous-scale semilattice erosions. We discuss theoretical aspects of these PDEs, propose discrete algorithms for their numerical solution which converge as iterations of triphase operators, and provide insights via image experiments.
Article
Full-text available
Associative Morphological Memories are the analogous construct to Linear Associative Memories defined on the lattice algebra R, +, ?, ?). They have excellent recall properties for noiseless patterns. However they suffer from the sensitivity to specific noise models, that can be characterized as erosive and dilative noise. To improve their robustness to general noise we propose a construction method that is based on the extrema point preservation of the Erosion/Dilation Morphological Scale Spaces. Here we report on their application to the tasks of face localization in grayscale images and appearance based visual self-localization of a mobile robot.
Article
Full-text available
This paper examines the set-theoretic interpretation of morphological filters in the framework of mathematical morphology and introduces the representation of classical linear filters in terms of morphological correlations, which involve supremum/infimum operations and additions. Binary signals are classified as sets, and multilevel signals as functions. Two set-theoretic representations of signals are reviewed. Filters are classified as set-processing (SP) or function-processing (FP). Conditions are provided for certain FP filters that pass binary signals to commute with signal thresholding because then they can be analyzed and implemented as SP filters. The basic morphological operations of set erosion, dilation, opening, and closing are related to Minkowski set operations and are used to construct FP morphological filters. Emphasis is then given to analytically and geometrically quantifying the similarities and differences between morphological filtering of signals by sets and functions; the latter case allows the definition of morphological convolutions and correlations. Toward this goal, various properties of FP morphological filters are also examined. Linear shift-invariant filters (due to their translation-invariance) are uniquely characterized by their kernel, which is a special collection of input signals. Increasing linear filters are represented as the supremum of erosions by their kernel functions. If the filters are also discrete and have a finite-extent impulse response, they can be represented as the supremum of erosions only by their minimal (with respect to a signal ordering) kernel functions. Stable linear filters can be represented as the sum of (at most) two weighted suprema of erosions. These results demonstrate the power of mathematical morphology as a unifying approach to both linear and nonlinear signal-shaping strategies.
Chapter
This chapter discusses pattern recognition and organization of information. Developments in pattern recognition over the past decade or so have been characterized more by the proliferation of effort involving various motivations and different approaches than by concrete realization of practical working systems. A great deal of stress has been laid on the necessity for integration of the various functions to be able to make effective use of the sensory, perceptive, behavioral and procedural capabilities necessary, and on adequate knowledge of the world. The advantages of a conceptual organization of information have been put forward as a good basis on which to build the requisite information, both innate and acquired through interaction with the environment. It has been argued that because processing tasks may require the identification of sub-tasks and accordingly demand complex organizational, structural and procedural capabilities for planning solution, it seems profitable to view a pattern recognition machine as an integrated artificial intelligence system.
Article
This paper is devolved to descriptive image analysis, an important, if not a leading, direction in the modern mathematical theory of image analysis. Descriptive image analysis is a logically organized set of descriptive methods and models meant for analyzing and estimating the information represented in the form of images, as well as for automating the extraction (from images) of knowledge and data needed for intelligent decision making about the real-world scenes reflected and represented by images under analysis. The basic idea of descriptive image analysis consists in reducing all processes of analysis (processing, recognition, and understanding) of images to (1) construction of models (representations and formalized descriptions) of images; (2) definition of transformations over image models; (3) construction of models (representations and formalized descriptions) of transformations over models and representations of images; and (4) construction of models (representations and formalized descriptions) of schemes of transformations over models and representations of images that provide the solution to image analysis problems. The main fundamental sources that predetermined the origination and development of descriptive image analysis, or had a significant influence thereon, are considered. In addition, a brief description of the current state of descriptive image analysis that reflects the main results of the descriptive approach to analysis and understanding of images is presented. The opportunities and limitations of algebraic approaches to image analysis are discussed. During recent years, it was accepted that algebraic techniques, particularly, different kinds of image algebras, are the most promising direction of construction of the mathematical theory of image analysis and of the development of a universal algebraic language for representing image analysis transforms, as well as image representations and models. The main goal of the algebraic approaches is designing a unified scheme for representation of objects under recognition and its transforms in the form of certain algebraic structures. This makes it possible to develop the corresponding regular structures ready for analysis by algebraic, geometrical, and topological techniques. The development of this line of image analysis and pattern recognition is of crucial importance for automatic image mining and application problems solving, in particular, for diversification of the classes and types of solvable problems, as well as for significant improvement of the efficiency and quality of solutions. The main subgoals of the paper are (1) to set forth the-state-of-the-art of the mathematical theory of image analysis; (2) to consider the algebraic approaches and techniques suitable for image analysis; and (3) to present a methodology, as well as mathematical and computational techniques, for automation of image mining on the basis of the descriptive approach to image analysis (DAIA). The main trends and problems in the promising basic researches focused on the development of a descriptive theory of image analysis are described.
Article
Edge operators based on grayscale morphologic operations are introduced. These operators can be efficiently implemented in near real time machine vision systems which have special hardware support for grayscale morphologic operations. The simplest morphologic edge detectors are the dilation residue and erosion residue operators. The underlying motivation for these is discussed. Finally, the blur minimum morphologic edge operator is defined. Its inherent noise sensitivity is less than the dilation or the erosion residue operators.
Conference Paper
Survey. The main goal of the Algebraic Approach is the design of a unified scheme for the representation of objects for the purposes of their recognition and the transformation of such representations in the suitable algebraic structures. It makes possible to develop corresponding regular structures ready for analysis by algebraic, geometrical and topological techniques. Development of this line of image analysis and pattern recognition is of crucial importance for automated image mining and application problems solving. It is selected and briefly characterized main aspects of current state of the image analysis algebraization. Special attention is paid to the recent results of the Russian mathematical school.
Chapter
This chapter discusses some techniques for recognizing structures in pictures. The research aims to develop techniques whereby a machine may observe its surroundings and then use its observations to achieve goals in an effective and efficient manner. To fulfill such requirements, the machine will inevitably use knowledge gained from past experience and observation to plan its activities, and also to interpret its sensory data. The chapter discusses the idea of a finite relational structure, that is, a set of elements with given properties and relations among them, as a useful mathematical tool for describing pictures, and to describe general techniques for matching such structures against each other. The matching process for relational structures attempts to find whether one structure occurs in or is a substructure of another structure. More precisely one need a function that assigns to each element of the first structure a distinct element of the second structure in such a way as to preserve the properties and relations which subsist in the first structure.
Article
The work is devoted to computer science. The subject, fundamental research problems, methodology, structure, and applied problems are defined and analyzed. The mathematical apparatus of computer science and its main methods—formalization, algorithmization, mathematical modeling, and programming—are considered. A characterization is given to the main fields of computer science pattern recognition, image analysis, artificial intelligence, intelligent data analysis, and information technologies. An in-depth analysis is carried out of the relationship and interaction between computer science and cybernetics. The role and the subject of informatics are discussed.
Article
The paper describes the possibilities and main results of mathematical and informational approaches to automating the analysis, recognition, and evaluation of images in brain research. The latter are conducted in such essential sectors of neuroscience as molecular and cellular neuroscience, behavioral neuroscience, systemic neuroscience, developmental neuroscience, cognitive neuroscience, theoretical and computational neuroscience, neurology and psychiatry, neural engineering, neurolinguistics, and neurovisualization. An important direction in simulating diseases, including diseases of the brain and their diagnoses, is the obtaining, storage, processing, and analysis of data extracted from digital images. The theoretical and methodical basis of automating the processing, analysis, and evaluation of experimental data obtained in brain research consists of the mathematical theory of image recognition and mathematical theory of image analysis. The paper presents examples of mathematical and informational approaches to automate the processing, analysis, and evaluation of microimages of neurons for constructing preclinical models of Parkinson’s disease.
Article
An indirect way of reconstructing the coordinates of points on the surface of a 3D object by its planar parallel projections is proposed. The approach is based on the substitution of the object by another (virtual) object, for which this operation can be carried out simply, whereas the correctness of the obtained results is controlled. The specificities of obtaining a mathematical model of reconstructed objects with a polyhedral shape, the issues of normalization of the angular discrepancies between the recognized and the etalon objects, and the solution of the problem of their recognition based on the introduced model are considered.
Article
The paper presents and discusses the main results obtained using the descriptive approach to analyzing and understanding images when solving fundamental problems of the formalization and systematization of the methods and forms of representing information in the problems of the analysis, recognition, and understanding of images, in particular that arise in connection with the automation of information extraction from images in order to make intelligent decisions (diagnosis, prediction, detection, evaluation, and identification of patterns). In this direction, so far, the following results have been obtained: (1) the conceptualization of a system of concepts that describe the initial information (images) in recognition problems has been carried out; (2) descriptive models of images focused on the recognition problem have been defined; (3) the image-formalization space has been introduced, the elements of which include different forms (states, phases) of representing the image transformed from the original form into the recognizable one, i.e., into the image model; (4) the basic axioms of the descriptive approach were introduced. Axiomatics and its formal structures provide the methods and tools of representation and the description of images for their subsequent analysis and evaluation.
Article
A cellular logic image processor employing 192 cells in a 16 by 12 hexagonal array is described. The processor has been constructed and its performance assessed. The various classes of functions which can be implemented in the cellular array are discussed and sample programs explained in detail.
Article
CONTENTSIntroduction Chapter I. Linear algebra in superspaces § 1. Linear superspaces § 2. Modules over superalgebras § 3. Matrix algebra § 4. Free modules § 5. Bilinear forms § 6. The supertrace § 7. The Berezinian (Berezin function) § 8. Tensor algebras § 9. Lie superalgebras and derivations of superalgebras Chapter II. Analysis in superspaces and superdomains § 1. Definition of superspaces and superdomains § 2. Vector fields and Taylor series § 3. The inverse function theorem and the implicit function theorem § 4. Integration in superdomains Chapter III. Supermanifolds § 1. Definition of a supermanifold § 2. Subsupermanifolds § 3. Families Notes References
Article
Many of the basic theorems about general “algebras” derived in [1, Ch. 6] are extended to a class of heterogeneous algebras which includes automata, state machines, and monoids acting on sets. It is shown that some algebras can be fruitfully studied, using different interpretations, both as (homogeneous) algebras and as heterogeneous algebras, and a non-trivial “free machine” is constructed as an application. The extent of the overlap with previous work of Higgins [9] is specified.
Article
This paper introduces a complete matrix classification of a family of image processing transforms called lattice transformations. Lattice transformations are nonlinear and include mathematical morphology transforms as a subclass. A matrix algebraic structure called minimax algebra provides a rigorous mathematical environment for lattice transforms as used in image processing. This is the first application of minimax algebra to image processing. Minimax algebra was originally developed for solving machine scheduling and other problems in operations research. The relationship between minimax algebra, mathematical morphology, and image algebra, a high-level image processing language, is presented in this paper, and a theoretical foundation in which to analyze image lattice transformations in context of matrices is established. Several examples are presented to exemplify the power of these relationships.
Article
Article
This chapter discusses the potentialities and problems of descriptive pattern-analysis techniques. The limitations inherent in the ability of the classical model to treat complex patterns are based on its inability to cope with what is thought of intuitively as the structure of a pattern and to concentrate its attention as necessary on the subpatterns whose relationships form this structure. The model is a global one, capable only of computing a set of properties defined on the whole input pattern and then making a choice based on them. That the model lends itself well to mathematical treatment is inadequate recompense for its failure in this respect. The classical pattern-classification model is a special (two-stage) case of pattern analysis, so defined, where the output of each feature extractor, usually a single number, is a very simple form of description of the input pattern, and the decision-making stage consolidates these descriptions into one description of the input pattern, a single number of specifying one of n categories. Thus, the entire effect is a mapping of a class of patterns into one of n possible descriptions.
Article
The authors present a broad overview of grayscale morphological image processing with particular emphasis on algorithms. They have shown that grayscale morphology is a natural extension of binary morphology where the operations of min and max replace intersection and union. Grayscale openings and closings have been described using the analogy of sliding solid geometric structures across gray level topologies. From this analogy the authors derived the rolling ball algorithm. Background normalization by the rolling ball algorithm is an excellent way of preprocessing a grayscale image prior to thresholding. Morphological filters implemented as iterative sequences of successively larger openings and closings exhibit desirable properties for image enhancement and noise suppression. Distance related transformations of binary images, like skeletons and perceptual graphs, can be implemented directly in the grayscale morphology.
Article
The paper examines an approach to parallel recognition of noisy signals (images) of different classes during their simultaneous entry at the input of a recognition device as an additive mixture. The idea of the approach is that the synthesized device is originally parallel in terms of its operation. It is a structure of interconnected channels, each transparent to signals of its class and rejecting signals of all other classes. For this system, it is important to stick to the following condition. Standard signals of the alphabet should be the basis. At the learning stage, the alphabet of standard signals is transformed so as to make these signals independent of information. In processing the mixture of recognized noisy signals, the problems of their resolution, display, and parameterization are also being solved.
Article
This paper is devoted to the study of the key concepts of the mathematical theory of image recognition—the invariance and equivalence of images. To provide a computer-aided choice of invariants for constructing partial descriptions of images, a classification of invariants is proposed that takes into account the basic features of invariants and systematizes their properties. Group invariants, methods for constructing invariants, and various image invariants are described. Various methods for determining equivalence on the set of images are considered. The relation between equivalence and invariance of images is analyzed. It is proved that, under certain constraints on image transformations, the problem of image recognition in the standard statement can be reduced to a problem for which there exists a correct algorithm within the algebraic closure of algorithms for calculating estimates.
Article
This study has been conducted in the framework of developing one of the directions of descriptive approach to image analysis and recognition, and it is devoted to one of the main tools of this approach, namely, the use of formal image models in solving recognition problems. We systematized the image features widely used in solving applied problems of image analysis and recognition. It is well known that the mathematical nature and functional meaning of these features, as well as computational and measurement methods employed, are extremely various. The main results are the following: different approaches to the classification of image features are introduced, comparative analysis of them is performed, and the aspect of descriptivity is realized by numerous examples of the considered classifications being filled in by features (descriptors). On the basis of these results, certain recommendations and criteria for choosing the features in applied problems of image analysis and recognition are derived. The considered classifications of image features enable the construction of multiple-aspect image representations that preserve information essential to an applied problem. As a tool for choosing the features that depend on specific characteristics of a given problem and the initial data, we propose using parametrical generating descriptive trees, which support the creation and use of multiple-aspect image representation on the basis of different classifications of image features.
Article
The work is devoted to developing the main results in solving the fundamental problem of formalization and systematization of methods and forms of information representation in image analysis, recognition, and understanding tasks. This problem arises in connection with development of the descriptive approach to image analysis and understanding. The main result is the concept of image spatial formalization, including a set of image states and a set of states of image transformation schemes. We consider the construction of algorithmic schemes generating phase trajectories for solving problems of image analysis and recognition. We present axioms defining the properties and structure of the image formalization space. The introduced system of concepts constitute the basis for standardizing methods for synthesizing image models oriented to image analysis and understanding tasks.
Article
Edge operators based on gray-scale morphologic operations are introduced. These operators can be efficiently implemented in near real time machine vision systems which have special hardware support for gray-scale morphologic operations. The simplest morphologic edge detectors are the dilation residue and erosion residue operators. The underlying motivation for these and some of their combinations are discussed and justified. Finally, the blur-minimum morphologic edge operator is defined. Its inherent noise sensitivity is less than the dilation or the erosion residue operators. Some experimental results are provided to show the validity of these morphologic operators. When compared with the enhancement/thresholding edge detectors and the cubic facet second derivative zero-crossing edge operator, the results show that all the edge operators have similar performance when the noise is small. However, as the noise increases, the second derivative zero-crossing edge operator and the blur-minimum morphologic edge operator have much better performance than the rest of the operators. The advantage of the blur-minimum edge operator is that it is less computationally complex than the facet edge operator.
Article
There are now a wide variety of image segmentation techniques, some considered general purpose and some designed for specific classes of images. These techniques can be classified as: measurement space guided spatial clustering, single linkage region growing schemes, hybrid linkage region growing schemes, centroid linkage region growing schemes, spatial clustering schemes, and split-and-merge schemes. In this paper, each of the major classes of image segmentation techniques is defined and several specific examples of each class of algorithm are described. The techniques are illustrated with examples of segmentations performed on real images.
Article
Computational mathematical-morphology has been developed to provide a directly computable alternative to classical gray-scale morphology that is range preserving and compatible with the design of statistically optimal filters based on morphological representation. It serves as an image algebra because of the expressive capability of its image-operator representations. Because representations are based on binary comparators used in conjunction with AND and OR operations, it provides a low-level, efficient computational environment that is a direct extension of the finite Boolean operational environment. The paper focuses on development of the comparator-based representation, providing the relevant representation theory for lattice operators and lattice-vector operators. Computational lattice-operator theory represents a comparator-based alternative to the classical morphological lattice theory, one that is directly implementable in logic. For totally ordered valuation spaces, the lattice theory reduces to a simplified form appropriate to straightforward optimization. The present paper treats architectural considerations and a second part considers the implications for latticevalued image operators.
Article
In this paper we establish a relationship between regularization theory and morphological shared-weight neural networks (MSNN). We show that a certain class of morphological shared-weight neural networks with no hidden units can be viewed as regularization neural networks. This relationship is established by showing that this class of MSNNs are solutions of regularization problems. This requires deriving the Fourier transforms of the min and max operators. The Fourier transforms of min and max operators are derived using generalized functions because they are only defined in that sense.
Article
In this second part of a two-part study, the lattice-based computational representational structure is applied to image operators. The computational representations are first applied to some common non-linear window (vector) operators used in image processing — for instance, flat erosion, flat dilation, fuzzy erosion, and flat filters, in general. For these, application of the representations is direct. Representations are then developed for gray-to-binary and gray-to-gray image operators. In all cases, images are assumed to be lattice-valued. It is shown that under appropriate circumstances the representations can be viewed as structural generalizations of classical representations. Flat (stack) filters are treated in their own fight (as operators on lattice-valued images) and it is seen that for these the lattice representations can be interpreted in terms of threshold decomposition.
Conference Paper
A discussion is presented of the design of a system that can input a vision task specification and use its knowledge of the operations of mathematical morphology to automatically construct a procedure that can execute the task. To do this, the authors develop a predicate calculus representation to describe the essence of the states of all the images that are created during the execution of the morphological procedure and the states of the relationships among them. The authors translate the English descriptions of morphological procedures into predicate logic. In so doing they gain an understanding of the goal of each procedure and the exact conditions under which a procedure achieves its goal. With this knowledge of the operations of mathematical morphology represented in predicate logic, a search procedure can be used to automatically produce vision procedures
Conference Paper
The presentation is devoted to the research of mathematical fundamentals for image analysis and recognition procedures. The final goal of this research is automated image mining: a) automated design, test and adaptation of techniques and algorithms for image recognition, estimation and understanding; b) automated selection of techniques and algorithms for image recognition, estimation and understanding; c) automated testing of the raw data quality and suitability for solving the image recognition problem. The main instrument is the Descriptive Approach to Image Analysis, which provides: 1) standardization of image analysis and recognition problems representation; 2) standardization of a descriptive language for image analysis and recognition procedures; 3) means to apply common mathematical apparatus for operations over image analysis and recognition algorithms, and over image models. It is shown also how and where to link theoretical results in the foundations of image analysis with the techniques used to solve application problems.
Article
This paper presents a hybrid model of integrating the synergy of two superior classifiers: Convolutional Neural Network (CNN) and Support Vector Machine (SVM), which have proven results in recognizing different types of patterns. In this model, CNN works as a trainable feature extractor and SVM performs as a recognizer. This hybrid model automatically extracts features from the raw images and generates the predictions. Experiments have been conducted on the well-known MNIST digit database. Comparisons with other studies on the same database indicate that this fusion has achieved better results: a recognition rate of 99.81% without rejection, and a recognition rate of 94.40% with 5.60% rejection. These performances have been analyzed with reference to those by human subjects.
Article
Morphological neural networks (MNNs) are a class of artificial neural networks whose operations can be expressed in the mathematical theory of minimax algebra. In a morphological neural net, the usual sum of weighted inputs is replaced by a maximum or minimum of weighted inputs (in this context, the weighting is performed by summing the weight and the input). We speak of a max product, a min product respectively. In recent years, a number of different MNN models and applications have emerged. The emphasis of this paper is on morphological associative memories (MAMs), in particular on binary autoassociative morphological memories (AMMs). We give a new set theoretic interpretation of recording and recall in binary AMMs and provide a generalization using fuzzy set theory.
Conference Paper
Conventional computers do not readily lend themselves to picture processing. Digital image manipulation by conventional computer is accomplished only at a tremendous cost in time and conceptual distraction. Computer image processing is the activity of modifying a picture such that retrieval of relevant pictorially encoded information becomes trivial. Algorithm development for image processing is an alternating sequence of inspired creative visualizations of desired processed results and the formal procedures implementing the desired process on a particular image processing system. But our process of creative visualization is of pictures as a whole. Implementation of the visualized image manipulation by conventional computer requires fragmentation of the pictorial concept into information units matched to the word oriented capabilities of general purpose machines. Conventional computer image processing could be broadly categorized as manipulation of pixel states rather than pictorial content.
Article
A general purpose digital computer can, in principle, solve any well defined problem. At many tasks, such as the solution of systems of linear equations, these machines are thousands of times as fast as human beings. However, they are relatively inept at solving many problems where the data is arranged naturally in a spatial form. For example, when it comes to playing chess or recognizing sophisticated patterns, present day machines cannot match the performance of their designers. The difficulty in such cases appears to be that conventional computers can actively cope with only a small amount of information at any one time. (This circumstance is aptly illustrated by the title of an article by Samuel, "Computing Bit by Bit.") It appears that efficient handling of problems of the type mentioned above cannot be accomplished without some form of parallel action. A stored program computer is described which can handle spatial problems by operating directly on information in planar form without scanning or using other techniques for transforming the problem into some other domain. The order structure of this machine is explained and illustrated by a few simple programs. An estimate of the size of the computer (based on one possible design) is given. Programs have been written that enable the machine to recognize alphabetic characters independent of position, proportion, and size.
Article
The ability of human beings to retrieve information on the basis of associated cues continues to elicit great interest among researchers. Investigations of how the brain is capable to make such associations from partial information have led to a variety of theoretical neural network models that act as associative memories. Several researchers have had significant success in retrieving complete stored patterns from noisy or incomplete input pattern keys by using morphological associative memories. Thus far morphological associative memories have been employed in two different ways: a direct approach which is suitable for input patterns containing either dilative or erosive noise and an indirect one for arbitrarily corrupted input patterns which is based on kernel vectors. In a recent paper [22], we suggested how to select these kernel vectors and we deduced exact statements on the amount of noise which is permissible for perfect recall. In this paper, we establish the proofs for all our...
On defining equations for the elements of associative and commutative algebras
  • V M Chernov
V. M. Chernov, On defining equations for the elements of associative and commutative algebras, in Space-Time Structure. Algebra and Geometry, Ed. By D. Pavlov, Gh. Atanasiu, and V. Balan (Lilia Print, 2007), pp. 182-188.
A homogeneous unification of image algebra. Part I: The homogenous algebra, Part II: Unification of image algebra
  • E R Dougherty
E. R. Dougherty, A homogeneous unification of image algebra. Part I: The homogenous algebra, Part II: Unification of image algebra, Imaging Sci. 33 (4) (1989) 136-149.