Rough Sets and Near Sets in Medical Imaging: A Review
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paper_title: Image classification and retrieval algorithm based on rough set theory.

paper_content:

This paper presents an efficient algorithm to classify and retrieve images from large databases in the context of rough set theory. Color and texture are two well-known low-level perceptible features to describe an image's contents used in this paper. The features are extracted, normalized and then the rough set dependency rules are generated directly from the real valued attribute vector. Then the rough set reduction technique is applied to find all reducts of the data which contains the minimal subset of attributes that are associated with a class label for classification. We test three different popular distance measures in this work and find that quadratic distance measures provide the most accurate and perceptually relevant retrievals. The retrieval performance is measured using recall-precision measure, as is standard in all retrieval systems.
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paper_title: Tolerance near sets and image correspondence

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The principal problem considered in this paper is how to solve the image correspondence problem using a bio-inspired approach. One solution to this problem is to consider tolerance near sets that model human perception in a physical continuum. Near sets are generalisations of rough sets introduced by Zdzislaw Pawlak during the early 1980s. Tolerance near sets have been inspired by C.E. Zeeman's work on visual perception and Henri Poincare's work on the contrast between mathematical continua and the physical continua in a pragmatic philosophy of science that laid the foundations for tolerance spaces. In this paper, the basics of perceptual systems and tolerance near sets are presented as bases for the solution of the image correspondence problem. The contribution of this paper is a humanistic perception-based approach to discovering similarities between images, classifying images and an approach to quantifying the nearness of images using the Henry-Peters nearness measure.
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paper_title: Feature selection: near set approach

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The problem considered in this paper is how to select features that are useful in classifying perceptual objects that are qualitatively but not necessarily spatially near each other. The term qualitatively near is used here to mean closeness of descriptions or distinctive characteristics of objects. The solution to this problem is inspired by the work of Zdzislaw Pawlak during the early 1980s on the classification of objects. In working toward a solution of the problem of the classification of perceptual objects, this article introduces a near set approach to feature selection. Consideration of the nearness of objects has recently led to the introduction of what are known as near sets, an optimist's view of the approximation of sets of objects that are more or less near each other. Near set theory started with the introduction of collections of partitions (families of neighbourhoods) that provide a basis for a feature selection method based on the information content of the partitions of a set of sample objects. A byproduct of the proposed approach is a feature filtering method that eliminates features that are less useful in the classification of objects. This contribution of this article is the introduction of a near set approach to feature selection.
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paper_title: Biologically-Inspired Adaptive Learning: A Near Set Approach

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The problem considered in this paper is how learning by machines can be influenced beneficially by various forms of learning by biological organisms. The solution to this problem is partially solved by considering considering a model of perception that is at the level of classes in a partition defined by a particular equivalence relation in an approximation space. This form of perception provides a basis for adaptive learning that has surprising acuity. Viewing approximation spaces as the formal counterpart of perception was suggested by Ewa Ortowska in 1982. This view of perception grew out the discovery of rough sets by Zdzistaw Pawlak during the early 1980s. The particular model of perception that underlies biologically-inspired learning is based on a near set approach, which considers classes of organisms with similar behaviours. In this paper, the focus is on learning by tropical fish called glowlight tetra (Hemigarmmus erythrozonus). Ethology (study of the comparative behaviour of organisms), in particular, provides a basis for the design of an artificial ecosystem useful in simulating the behaviour of fish. The contribution of this paper is a complete framework for an ethology-based study of adaptive learning defined in the context of nearness approximation spaces.
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paper_title: Application of rough set based dynamic parameter optimization to MRI segmentation

paper_content:

We introduce a multi-spectral MRI segmentation technique based on approximate reducts derived from the data mining paradigm of the theory of rough sets. We use genetic algorithms to tune the parameterized attributes and search for the best segmentation models based on approximate reducts.
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paper_title: Affinities between Perceptual Granules: Foundations and Perspectives

paper_content:

This chapter gives a concise overview of the foundations of a perceptual near set approach to the discovery of affinities between perceptual objects and perceptual granules that provide a basis for perceptual systems useful in science and engineering. A perceptual object is something perceptible to the senses or knowable by the mind. Perceptual objects that have the same appearance are considered to be perceptually near each other, i.e., perceived objects that have perceived affinities or, at least, similar descriptions. A perceptual granule is a set of perceptual objects originating from observations of the objects in the physical world. Near set theory provides a basis for observation, comparison and classification of perceptual granules. By considering nearness relations in the context of a perceptual system, it is possible to gauge affinities (nearness) perceptual objects. Two kinds of indiscernibility relations and a tolerance relation make it possible to define various nearness relations. Examples of near images as perceptual systems are presented. The main contribution of this chapter is the introduction of a formal basis for discovering affinities between perceptual information granules.
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paper_title: Classification of objects by means of attributes

paper_content:

W: ICS PAS Reports 429/81, pages 1-20. Institute of Computer Science Polish Academy of Sciences (ICS PAS), Warsaw, Poland, 1981
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paper_title: Mining diagnostic rules from clinical databases using rough sets and medical diagnostic model

paper_content:

Since rule induction methods generate rules whose lengths are the shortest for discrimination between given classes, they tend to generate rules too short for medical experts. Thus, these rules are difficult for the experts to interpret from the viewpoint of domain knowledge. In this paper, the characteristics of experts' rules are closely examined and a new approach to generate diagnostic rules is introduced. The proposed method focuses on the hierarchical structure of differential diagnosis and consists of the following three procedures. First, the characterization of decision attributes (given classes) is extracted from databases and the classes are classified into several generalized groups with respect to the characterization. Then, two kinds of sub-rules, classification rules for each generalized group and rules for each class within each group are induced. Finally, those two parts are integrated into one rule for each decision attribute. The proposed method was evaluated on a medical database, the experimental results of which show that induced rules correctly represent experts' decision processes.
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paper_title: Rough Sets and Bayesian Methods Applied to Cancer Detection

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The paper describes an application of soft computing methods of rough sets and Bayesian inference to a breast cancer detection using electro-potentials. The statistical principal component analysis (PCA) and the rough sets methods were applied for feature extraction, reduction and selection. The quadratic discriminant was applied as a classifier for a breast cancer detection.
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paper_title: Near Sets. Special Theory about Nearness of Objects

paper_content:

The problem considered in this paper is how to approximate sets of objects that are qualitatively but not necessarily spatially near each other. The term qualitatively near is used here to mean closeness of descriptions or distinctive characteristics of objects. The solution to this problem is inspired by the work of Zdzislaw Pawlak during the early 1980s on the classification of objects by means of their attributes. This article introduces a special theory of the nearness of objects that are either static (do not change) or dynamic (change over time). The basic approach is to consider a link relation, which is defined relative to measurements associated with features shared by objects independent of their spatial relations. One of the outcomes of this work is the introduction of new forms of approximations of objects and sets of objects. The nearness of objects can be approximated using rough set methods. The proposed approach to approximation of objects is a straightforward extension of the rough set approach to approximating objects, where approximation can be considered in the context of information granules (neighborhoods). In addition, the usual rough set approach to concept approximation has been enriched by an increase in the number of granules (neighborhoods) associated with the classification of a concept as near to its approximation. A byproduct of the proposed approximation method is what we call a near set. It should also be observed that what is presented in this paper is considered a special (not a general) theory about nearness of objects. The contribution of this article is an approach to nearness as a vague concept which can be approximated from the state of objects and domain knowledge.
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paper_title: Nearness of Objects: Extension of Approximation Space Model

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The problem considered in this paper is the extension of an approximation space to include a nearness relation. Approximation spaces were introduced by Zdzis?aw Pawlak during the early 1980s as frameworks for classifying objects by means of attributes. Pawlak introduced approximations as a means of approximating one set of objects with another set of objects using an indiscernibility relation that is based on a comparison between the feature values of objects. Until now, the focus has been on the overlap between sets. It is possible to introduce a nearness relation that can be used to determine the "nearness" of sets of objects that are possibly disjoint and, yet, qualitatively near to each other. Several members of a family of nearness relations are introduced in this article. The contribution of this article is the introduction of a nearness relation that makes it possible to extend Pawlak's model for an approximation space and to consider the extension of generalized approximations spaces.
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paper_title: A Hybrid Rough Set--Particle Swarm Algorithm for Image Pixel Classification

paper_content:

This article presents a framework to hybridize the rough set theory with a famous swarm intelligence algorithm known as Particle Swarm Optimization (PSO). The hybrid rough-PSO technique has been used for grouping the pixels of an image in its intensity space. Medical and remote sensing satellite images become corrupted with noise very often. Fast and efficient segmentation of such noisy images (which is essential for their further interpretation in many cases) has remained a challenging problem for years. In this work, we treat image segmentation as a clustering problem. Each cluster is modeled with a rough set. PSO is employed to tune the threshold and relative importance of upper and lower approximations of the rough sets. Davies-Bouldin clustering validity index is used as the fitness function, which is minimized while arriving at an optimal partitioning.
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paper_title: Classification of objects by means of attributes

paper_content:

W: ICS PAS Reports 429/81, pages 1-20. Institute of Computer Science Polish Academy of Sciences (ICS PAS), Warsaw, Poland, 1981
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paper_title: Rudiments of rough sets

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Abstract Worldwide, there has been a rapid growth in interest in rough set theory and its applications in recent years. Evidence of this can be found in the increasing number of high-quality articles on rough sets and related topics that have been published in a variety of international journals, symposia, workshops, and international conferences in recent years. In addition, many international workshops and conferences have included special sessions on the theory and applications of rough sets in their programs. Rough set theory has led to many interesting applications and extensions. It seems that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences, especially in research areas such as machine learning, intelligent systems, inductive reasoning, pattern recognition, mereology, knowledge discovery, decision analysis, and expert systems. In the article, we present the basic concepts of rough set theory and point out some rough set-based research directions and applications.
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paper_title: Rough approximation of shapes in pattern recognition

paper_content:

The paper approaches the nature of a feature recognition process through the description of image features in terms of the rough sets. Since the basic condition for representing images must be satisfied by any recognition result, elementary features are defined as equivalence classes of possible occurrences of specific fragments existing in images. The names of the equivalence classes (defined through specific numbers of objects and numbers of background parts covered by a window) constitute the best lower approximation of window contents (i.e., names of recognized features). The best upper approximation is formed by the best lower approximation, its attributes, and parameters, all referenced to the object fragments situated in the window. The rough approximation of shapes is resistant to accidental changes in the width of contours and lines and to small discontinuities and, in general, to possible positions or changes in shape of the same feature. The rough sets are utilized also on the level of image processing for noiseless image quantization.
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paper_title: Segmentation of Medical Images Based on Approximations in Rough Set Theory

paper_content:

This paper presents an image segmentation method based on rough set theory. The focus of this paper is to discuss how to approximate a region of interest (ROI) when we are given multiple types of expert knowledge. The method contains three steps including preprocessing. First, we derive discretized attribute values that describe the characteristics of a ROI. Secondly, using all attributes, we build up the basic regions (namely categories) in the image so that each region contains voxels that are indiscernible on all attributes. Finally, according to the given knowledge about the ROI, we construct an ideal shape of the ROI and approximate it by the basic categories. Then the image is split into three regions: a set of voxels that are - (1) certainly included in the ROI (Positive region), (2) certainly excluded from the ROI (Negative region), (3) possibly included in the ROI (Boundary region). The ROI is consequently represented by the positive region associated with some boundary regions. In the experiments we show the result of implementing a rough image segmentation system.
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paper_title: Mining diagnostic rules from clinical databases using rough sets and medical diagnostic model

paper_content:

Since rule induction methods generate rules whose lengths are the shortest for discrimination between given classes, they tend to generate rules too short for medical experts. Thus, these rules are difficult for the experts to interpret from the viewpoint of domain knowledge. In this paper, the characteristics of experts' rules are closely examined and a new approach to generate diagnostic rules is introduced. The proposed method focuses on the hierarchical structure of differential diagnosis and consists of the following three procedures. First, the characterization of decision attributes (given classes) is extracted from databases and the classes are classified into several generalized groups with respect to the characterization. Then, two kinds of sub-rules, classification rules for each generalized group and rules for each class within each group are induced. Finally, those two parts are integrated into one rule for each decision attribute. The proposed method was evaluated on a medical database, the experimental results of which show that induced rules correctly represent experts' decision processes.
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paper_title: Motion-information-based video retrieval system using rough pre-classification

paper_content:

Motion information is the basic element for analyzing video. It represents the change of video on the time-axis and plays an important role in describing the video content. In this paper, a robust motion-based, video retrieval system is proposed. At first, shot boundary detection is achieved by analyzing luminance information, and motion information of video is abstracted and analyzed. Then rough set theory is introduced to classify the shots into two classes, global motions and local motions. Finally, shots of these two types are respectively retrieved according to the motion types of submitted shots. Experiments show that it’s effective to distinguish shots with global motions from those with local motions in various types of video, and in this situation motion-information-based video retrieval are more accurate.
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paper_title: Rough set theory based segmentation of color images

paper_content:

The theory of rough sets has gained importance and applicability in diverse areas of research, especially in data mining, knowledge discovery, artificial intelligence and information systems analysis. Rough sets have also been used in imaging, however, the application of rough sets for color image analysis has yet to be fully investigated. An interesting strategy for color image segmentation using rough set theory has been presented. A new concept of encrustation of the histogram, called histon, has been proposed for the visualization of multi-dimensional color information in on integrated fashion and its applicability in boundary region analysis has been shown. The histon correlates with the upper approximation of a set such that all elements belonging to this set are clarified as possibly belonging to the same segment or segments showing similar color value. The proposed encrustation provides a direct means of segregating pool of inhomogeneous regions into its components. Experimental results for various images have been presented.
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paper_title: A rough set-based approach to handling spatial uncertainty in binary images

paper_content:

Abstract In this paper we consider the problem of detecting binary objects using rough sets. We present a method for constructing a gray-scaled (or, fuzzy) template for use in correlation-based matching of Boolean images. We assume a cause for spatial uncertainty that is quite common in machine vision applications and present a methodology for modeling it indirectly in the construction of the template. Our technique is computationally efficient and is superior to correlation-based techniques, which can be easily fooled and automates the hand-selection of structuring elements for the hit-or-miss transform technique, both of which are usually used to solve this problem.
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paper_title: Granular computing, rough entropy and object extraction

paper_content:

The problem of image object extraction in the framework of rough sets and granular computing is addressed. A measure called ''rough entropy of image'' is defined based on the concept of image granules. Its maximization results in minimization of roughness in both object and background regions; thereby determining the threshold of partitioning. Methods of selecting the appropriate granule size and efficient computation of rough entropy are described.
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paper_title: Segmentation of Medical Images Based on Approximations in Rough Set Theory

paper_content:

This paper presents an image segmentation method based on rough set theory. The focus of this paper is to discuss how to approximate a region of interest (ROI) when we are given multiple types of expert knowledge. The method contains three steps including preprocessing. First, we derive discretized attribute values that describe the characteristics of a ROI. Secondly, using all attributes, we build up the basic regions (namely categories) in the image so that each region contains voxels that are indiscernible on all attributes. Finally, according to the given knowledge about the ROI, we construct an ideal shape of the ROI and approximate it by the basic categories. Then the image is split into three regions: a set of voxels that are - (1) certainly included in the ROI (Positive region), (2) certainly excluded from the ROI (Negative region), (3) possibly included in the ROI (Boundary region). The ROI is consequently represented by the positive region associated with some boundary regions. In the experiments we show the result of implementing a rough image segmentation system.
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paper_title: Rough representation of a region of interest in medical images

paper_content:

This paper introduces the rough representation of a region of interest (ROI) in medical images. The main advantage of this method is its ability to represent inconsistency between the knowledge-driven shape and image-driven shape of a ROI using rough approximations. The method consists of three steps including preprocessing. First, we derive discretized attribute values that describe the characteristics of a ROI. Next, using all attributes, we build up the basic regions in the image so that each region includes voxels that are indiscernible on all attributes. Finally, according to the given knowledge about the ROI, we construct an ideal shape of the ROI and approximate it by the basic categories. Then the image is split into three regions: a set of voxels that are (1) certainly included in the ROI (Positive region), (2) certainly excluded from the ROI (Negative region), (3) possibly included in the ROI (Boundary region). The ROI is consequently represented by the positive region associated with some boundary regions. In the experiments we show the result of implementing a rough image segmentation system.
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paper_title: Granular computing, rough entropy and object extraction

paper_content:

The problem of image object extraction in the framework of rough sets and granular computing is addressed. A measure called ''rough entropy of image'' is defined based on the concept of image granules. Its maximization results in minimization of roughness in both object and background regions; thereby determining the threshold of partitioning. Methods of selecting the appropriate granule size and efficient computation of rough entropy are described.
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paper_title: THE INFORMATION ENTROPY, ROUGH ENTROPY AND KNOWLEDGE GRANULATION IN ROUGH SET THEORY

paper_content:

Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty. In this paper, we introduce the concepts of information entropy, rough entropy and knowledge granulation in rough set theory, and establish the relationships among those concepts. These results will be very helpful for understanding the essence of concept approximation and establishing granular computing in rough set theory.
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paper_title: Granular computing, rough entropy and object extraction

paper_content:

The problem of image object extraction in the framework of rough sets and granular computing is addressed. A measure called ''rough entropy of image'' is defined based on the concept of image granules. Its maximization results in minimization of roughness in both object and background regions; thereby determining the threshold of partitioning. Methods of selecting the appropriate granule size and efficient computation of rough entropy are described.
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paper_title: Rough set theory based segmentation of color images

paper_content:

The theory of rough sets has gained importance and applicability in diverse areas of research, especially in data mining, knowledge discovery, artificial intelligence and information systems analysis. Rough sets have also been used in imaging, however, the application of rough sets for color image analysis has yet to be fully investigated. An interesting strategy for color image segmentation using rough set theory has been presented. A new concept of encrustation of the histogram, called histon, has been proposed for the visualization of multi-dimensional color information in on integrated fashion and its applicability in boundary region analysis has been shown. The histon correlates with the upper approximation of a set such that all elements belonging to this set are clarified as possibly belonging to the same segment or segments showing similar color value. The proposed encrustation provides a direct means of segregating pool of inhomogeneous regions into its components. Experimental results for various images have been presented.
---
paper_title: Application of rough set based dynamic parameter optimization to MRI segmentation

paper_content:

We introduce a multi-spectral MRI segmentation technique based on approximate reducts derived from the data mining paradigm of the theory of rough sets. We use genetic algorithms to tune the parameterized attributes and search for the best segmentation models based on approximate reducts.
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paper_title: Rough Set-Based Clustering with Refinement Using Shannon's Entropy Theory

paper_content:

Lots of clustering algorithms have been developed, while most of them cannot process objects in hybrid numerical/nominal attribute space or with missing values. In most of them, the number of clusters should be manually determined and the clustering results are sensitive to the input order of the objects to be clustered. These limit applicability of the clustering and reduce the quality of clustering. To solve this problem, an improved clustering algorithm based on rough set (RS) and entropy theory was presented. It aims at avoiding the need to prespecify the number of clusters, and clustering in both numerical and nominal attribute space with the similarity introduced to replace the distance index. At the same time, the RS theory endows the algorithm with the function to deal with vagueness and uncertainty in data analysis. Shannon's entropy was used to refine the clustering results by assigning relative weights to the set of attributes according to the mutual entropy values. A novel measure of clustering quality was also presented to evaluate the clusters. This algorithm was analyzed and applied later to cluster the data set of one industrial product. The experimental results confirm that performances of efficiency and clustering quality of this algorithm are improved.
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paper_title: Applications of rough set based K-means, Kohonen SOM, GA clustering

paper_content:

Rough set theory provides an alternative way of representing sets whose exact boundary cannot be described due to incomplete information. Rough sets have been widely used for classification and can be equally beneficial in clustering. The clusters in practical data mining do not necessarily have crisp boundaries. An object may belong to more than one cluster. This paper describes modifications of clustering based on Genetic Algorithms, K-means algorithm, and Kohonen Self-Organizing Maps (SOM). These modifications make it possible to represent clusters as rough sets. Rough clusters are shown to be useful for representing groups of highway sections, Web users, and supermarket customers. The rough clusters are also compared with conventional and fuzzy clusters.
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paper_title: Image segmentation via adaptive K-mean clustering and knowledge-based morphological operations with biomedical applications

paper_content:

Image segmentation remains one of the major challenges in image analysis. In medical applications, skilled operators are usually employed to extract the desired regions that may be anatomically separate but statistically indistinguishable. Such manual processing is subject to operator errors and biases, is extremely time consuming, and has poor reproducibility. We propose a robust algorithm for the segmentation of three-dimensional (3-D) image data based on a novel combination of adaptive K-mean clustering and knowledge-based morphological operations. The proposed adaptive K-mean clustering algorithm is capable of segmenting the regions of smoothly varying intensity distributions. Spatial constraints are incorporated in the clustering algorithm through the modeling of the regions by Gibbs random fields. Knowledge-based morphological operations are then applied to the segmented regions to identify the desired regions according to the a priori anatomical knowledge of the region-of-interest. This proposed technique has been successfully applied to a sequence of cardiac CT volumetric images to generate the volumes of left ventricle chambers at 16 consecutive temporal frames. Our final segmentation results compare favorably with the results obtained using manual outlining. Extensions of this approach to other applications can be readily made when a priori knowledge of a given object is available.
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paper_title: Medical Image Segmentation Using K-Means Clustering and Improved Watershed Algorithm

paper_content:

We propose a methodology that incorporates k-means and improved watershed segmentation algorithm for medical image segmentation. The use of the conventional watershed algorithm for medical image analysis is widespread because of its advantages, such as always being able to produce a complete division of the image. However, its drawbacks include over-segmentation and sensitivity to false edges. We address the drawbacks of the conventional watershed algorithm when it is applied to medical images by using k-means clustering to produce a primary segmentation of the image before we apply our improved watershed segmentation algorithm to it. The k-means clustering is an unsupervised learning algorithm, while the improved watershed segmentation algorithm makes use of automated thresholding on the gradient magnitude map and post-segmentation merging on the initial partitions to reduce the number of false edges and over-segmentation. By comparing the number of partitions in the segmentation maps of 50 images, we showed that our proposed methodology produced segmentation maps which have 92% fewer partitions than the segmentation maps produced by the conventional watershed algorithm
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paper_title: Segmentation of 3D brain MR using an adaptive K-means clustering algorithm

paper_content:

An algorithm is described for segmenting 3D MR brain image into K different tissue types, which include gray, white matter and CSF, and maybe other abnormal tissues. MR images considered can be either scale- or multi-valued. Each scale-valued image is modeled as a collection of regions with slowly varying intensity plus a white Gaussian noise. Each tissue type is modeled by a Markov random field with the second order neighborhood in a 3D lattice. The proposed algorithm is an adaptive K-means clustering algorithm for 3-dimensional and multi-valued images. Each iteration consists of two steps: estimate mean intensity at each location for each type, and estimate tissue types by maximizing the a posteriori probability. The algorithm slowly adapts to the local intensity variation of each region, so it is robust to the "shading" effect. It has the potential to routinely process clinical MR images with minimal user involvement. Its performance is tested using patient data. >
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paper_title: Rough approximation of shapes in pattern recognition

paper_content:

The paper approaches the nature of a feature recognition process through the description of image features in terms of the rough sets. Since the basic condition for representing images must be satisfied by any recognition result, elementary features are defined as equivalence classes of possible occurrences of specific fragments existing in images. The names of the equivalence classes (defined through specific numbers of objects and numbers of background parts covered by a window) constitute the best lower approximation of window contents (i.e., names of recognized features). The best upper approximation is formed by the best lower approximation, its attributes, and parameters, all referenced to the object fragments situated in the window. The rough approximation of shapes is resistant to accidental changes in the width of contours and lines and to small discontinuities and, in general, to possible positions or changes in shape of the same feature. The rough sets are utilized also on the level of image processing for noiseless image quantization.
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paper_title: Information-preserving hybrid data reduction based on fuzzy-rough techniques

paper_content:

Data reduction plays an important role in machine learning and pattern recognition with a high-dimensional data. In real-world applications data usually exists with hybrid formats, and a unified data reducing technique for hybrid data is desirable. In this paper, an information measure is proposed to computing discernibility power of a crisp equivalence relation or a fuzzy one, which is the key concept in classical rough set model and fuzzy-rough set model. Based on the information measure, a general definition of significance of nominal, numeric and fuzzy attributes is presented. We redefine the independence of hybrid attribute subset, reduct, and relative reduct. Then two greedy reduction algorithms for unsupervised and supervised data dimensionality reduction based on the proposed information measure are constructed. Experiments show the reducts found by the proposed algorithms get a better performance compared with classical rough set approaches.
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paper_title: Joining associative classifier for medical images

paper_content:

One of the best prevention measures against breast cancer is the early tumor detection in digital mammography. Detecting tumor in mammography is a difficult task because of their size and the high content of similar patterns in the image. This brings the necessity of creating automatic tools to find whether a mammography present tumor or not. In this paper we join association rule classifier with rough set theory which we call the joining associative classifier (JAC) to mining digital mammography. The experimental results shows that this joining associative classifier performance at 77.48% of classifying accuracy which is higher than 69.11% using associative classifier only. At the same time, the number of rules decreased distinctively. Moreover, the experiments we conducted demonstrate the use and effectiveness of association rule mining in image categorization.
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paper_title: ROUGH FEATURE SELECTION FOR NEURAL NETWORK BASED IMAGE CLASSIFICATION

paper_content:

Effective feature selection is essential to the development of any intelligent classifier which is intended for use in high-dimension domains. This paper presents an approach that incorporates a rough set-assisted feature reduction method and a neural network-based classifier for image classification. The approach minimises the need for feature extraction without altering the underlying semantics of the features chosen. Through the proposed integration the size of the neural network classifier, which is sensitive to the dimensionality of the dataset, becomes manageable and the network is able to classify images that would otherwise require many more features to represent. Comparative study results from realistic applications demonstrate the success of this work.
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paper_title: Symbol-Based Machine Learning Approach for Supervised Segmentation of Follicular Lymphoma Images

paper_content:

Lymphoma is a broad term encompassing a variety of cancers of the lymphatic system. Lymphoma is differentiated by the type of cell that multiplies and how the cancer presents itself. It is very important to get an exact diagnosis regarding lymphoma and to determine the treatments that will be most effective for the patient's condition. Our work was focused on the identification of lymphomas by finding follicles in microscopy images provided by the Laboratory of Pathology in the University Hospital of Tenerife, Spain. Roughly we can divide our work in two stages: in the first stage we did image pre-processing and feature extraction, and in the second stage we used different rough set approaches for pixel classification. These results were compared to decision tree results we obtained earlier. Symbolic machine learning approaches are often neglected when looking for image analysis tools. The results we got are very promising and show that symbolic approaches can be successful in image analysis applications.
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paper_title: Rough sets as a front end of neural-networks texture classifiers

paper_content:

Abstract The paper describes an application of rough sets method to feature selection and reduction as a front end of neural-network-based texture images recognition. The methods applied include singular-value decomposition (SVD) for feature extraction, principal components analysis (PCA) for feature projection and reduction, and rough sets methods for feature selection and reduction. For texture classification the feedforward backpropagation neural networks were applied. The numerical experiments show the ability of rough sets to select reduced set of pattern's features (minimizing the pattern size), while providing better generalization of neural-network texture classifiers.
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paper_title: Image enhancement using smoothing with fuzzy sets

paper_content:

A model for grey-tone image enhancement using the concept of fuzzy sets is suggested. It involves primary enhancement, smoothing, and then final enhancement. The algorithm for both the primary and final enhancements includes the extraction of fuzzy properties corresponding to pixels and then successive applications of the fuzzy operator "contrast intensifier" on the property plane. The three different smoothing techniques considered in the experiment are defocussing, averaging, and maxmin rule over the neighbors of a pixel. The reduction of the "index of fuzziness" and "entropy" for different enhanced outputs (corresponding to different values of fuzzifiers) is demonstrated for an English script input. Enhanced output as obtained by histogram modification technique is also presented for comparison.
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paper_title: Rough neural intelligent approach for image classification: A case of patients with suspected breast cancer

paper_content:

The objective of this paper is to introduce a rough neural intelligent approach for rule generation and image classification. Hybridization of intelligent computing techniques has been applied to see their ability and accuracy to classify breast cancer images into two outcomes: malignant cancer or benign cancer. Algorithms based on fuzzy image processing are first applied to enhance the contrast of the whole original image; to extract the region of interest and to enhance the edges surrounding that region. Then, we extract features characterizing the underlying texture of the regions of interest by using the gray-level co-occurrence matrix. Then, the rough set approach to attribute reduction and rule generation is presented. Finally, rough neural network is designed for discrimination of different regions of interest to test whether they represent malignant cancer or benign cancer. Rough neural network is built from rough neurons, each of which can be viewed as a pair of sub-neurons, corresponding to the lower and upper bounds. ::: ::: To evaluate performance of the presented rough neural approach, we run tests over different mammogram images. The experimental results show that the overall classification accuracy offered by rough neural approach is high compared with other intelligent techniques.
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paper_title: Rough set feature selection and rule induction for prediction of malignancy degree in brain glioma

paper_content:

The degree of malignancy in brain glioma is assessed based on magnetic resonance imaging (MRI) findings and clinical data before operation. These data contain irrelevant features, while uncertainties and missing values also exist. Rough set theory can deal with vagueness and uncertainty in data analysis, and can efficiently remove redundant information. In this paper, a rough set method is applied to predict the degree of malignancy. As feature selection can improve the classification accuracy effectively, rough set feature selection algorithms are employed to select features. The selected feature subsets are used to generate decision rules for the classification task. A rough set attribute reduction algorithm that employs a search method based on particle swarm optimization (PSO) is proposed in this paper and compared with other rough set reduction algorithms. Experimental results show that reducts found by the proposed algorithm are more efficient and can generate decision rules with better classification performance. The rough set rule-based method can achieve higher classification accuracy than other intelligent analysis methods such as neural networks, decision trees and a fuzzy rule extraction algorithm based on Fuzzy Min–Max Neural Networks (FRE-FMMNN). Moreover, the decision rules induced by rough set rule induction algorithm can reveal regular and interpretable patterns of the relations between glioma MRI features and the degree of malignancy, which are helpful for medical experts.
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paper_title: Rough Set Approach for Classification of Breast Cancer Mammogram Images

paper_content:

This paper presents a study on classification of breast cancers in digital mammography images, using rough set theory in conjunction with statistical feature extraction techniques. First, we improve the contrast of the digitized mammograms by applying computer image processing techniques to enhance x-ray images and then subsequently extract features from suspicious regions characterizing the underlying texture of the breast regions. Feature extractions are derived from the gray-level co-occurrence matrix, then the features were normalized and the rough set dependency rules are generated directly from the real value attribute vector. These rules can then be passed to a classifier for discrimination for different regions of interest to test whether they are normal or abnormal. The experimental results show that the proposed algorithm performs well reaching over 98 % in accuracy....
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paper_title: Histogram equalisation with S and π functions in detecting X-ray edges

paper_content:

An algorithm consisting of a histogram equalisation technique followed by further enhancement using S and π membership functions is described to detect the small variation in grey levels of X-ray images. The effectiveness of the algorithm in identifying the different regional contours related to growth of normal bones is demonstrated.
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paper_title: A rough-fuzzy approach for generating classification rules

paper_content:

The generation of effective feature pattern-based classification rules is essential to the development of any intelligent classifier which is readily comprehensible to the user. This paper presents an approach that integrates a potentially powerful fuzzy rule induction algorithm with a rough set-assisted feature reduction method. The integrated rule generation mechanism maintains the underlying semantics of the feature set. Through the proposed integration, the original rule induction algorithm (or any other similar technique that generates descriptive fuzzy rules), which is sensitive to the dimensionality of the dataset, becomes usable on classifying patterns composed of a moderately large number of features. The resulting learned ruleset becomes manageable and may outperform rules learned using more features. This, as demonstrated with successful realistic applications, makes the present approach effective in handling real world problems.
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paper_title: Rough neural intelligent approach for image classification: A case of patients with suspected breast cancer

paper_content:

The objective of this paper is to introduce a rough neural intelligent approach for rule generation and image classification. Hybridization of intelligent computing techniques has been applied to see their ability and accuracy to classify breast cancer images into two outcomes: malignant cancer or benign cancer. Algorithms based on fuzzy image processing are first applied to enhance the contrast of the whole original image; to extract the region of interest and to enhance the edges surrounding that region. Then, we extract features characterizing the underlying texture of the regions of interest by using the gray-level co-occurrence matrix. Then, the rough set approach to attribute reduction and rule generation is presented. Finally, rough neural network is designed for discrimination of different regions of interest to test whether they represent malignant cancer or benign cancer. Rough neural network is built from rough neurons, each of which can be viewed as a pair of sub-neurons, corresponding to the lower and upper bounds. ::: ::: To evaluate performance of the presented rough neural approach, we run tests over different mammogram images. The experimental results show that the overall classification accuracy offered by rough neural approach is high compared with other intelligent techniques.
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paper_title: A Better Classifier Based on Rough Set and Neural Network for Medical Images

paper_content:

Detecting tumor in mammography is a difficult task because of complexity in the image. This brings the necessity of creating automatic tools to find whether a mammography present tumor or not. In this paper we integrate neural network with reduction of rough set theory which we call the rough neural network (RNN) to classify digital mammography. The experimental results show that the RNN performs better than purely using neural network in terms of time, and it can get 92.37% classifying accuracy which is higher than 81.25% using neural network only.
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paper_title: Rough Neural Computing in Signal Analysis

paper_content:

This paper introduces an application of a particular form of rough neural computing in signal analysis. The form of rough neural network used in this study is based on rough sets, rough membership functions, and decision rules. Two forms of neurons are found in such a network: rough membership function neurons and decider neurons. Each rough membership function neuron constructs upper and lower approximation equivalence classes in response to input signals as an aid to classifying inputs. In this paper, the output of a rough membership function neuron results from the computation performed by a rough membership function in determining degree of overlap between an upper approximation set representing approximate knowledge about inputs and a set of measurements representing certain knowledge about a particular class of objects. Decider neurons implement granules derived from decision rules extracted from data sets using rough set theory. A decider neuron instantiates approximate reasoning in assessing rough membership function values gleaned from input data. An introduction to the basic concepts underlying rough membership neural networks is briefly given. An application of rough neural computing in classifying the power system faults is considered.
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paper_title: ROUGH FEATURE SELECTION FOR NEURAL NETWORK BASED IMAGE CLASSIFICATION

paper_content:

Effective feature selection is essential to the development of any intelligent classifier which is intended for use in high-dimension domains. This paper presents an approach that incorporates a rough set-assisted feature reduction method and a neural network-based classifier for image classification. The approach minimises the need for feature extraction without altering the underlying semantics of the features chosen. Through the proposed integration the size of the neural network classifier, which is sensitive to the dimensionality of the dataset, becomes manageable and the network is able to classify images that would otherwise require many more features to represent. Comparative study results from realistic applications demonstrate the success of this work.
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paper_title: Rough sets as a front end of neural-networks texture classifiers

paper_content:

Abstract The paper describes an application of rough sets method to feature selection and reduction as a front end of neural-network-based texture images recognition. The methods applied include singular-value decomposition (SVD) for feature extraction, principal components analysis (PCA) for feature projection and reduction, and rough sets methods for feature selection and reduction. For texture classification the feedforward backpropagation neural networks were applied. The numerical experiments show the ability of rough sets to select reduced set of pattern's features (minimizing the pattern size), while providing better generalization of neural-network texture classifiers.
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paper_title: Towards Rough Neural Computing Based on Rough Membership Functions: Theory and Application

paper_content:

This paper introduces a neural network architecture based on rough sets and rough membership functions. The neurons of such networks instantiate approximate reasoning in assessing knowledge gleaned from input data. Each neuron constructs upper and lower approximations as an aid to classifying inputs. Rough neuron output has various forms. I n this paper, rough neuron output results from the application of a rough membership function. A brief introduction to the basic concepts underlying rough membership neural networks i s g iven. A n application of rough neural computing is briefly considered in classifying the waveforms of power system faults. Experimental results with rough neural classification of waveforms are also given.
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paper_title: Vocabulary Mining for Information Retrieval: Rough Sets and Fuzzy Sets

paper_content:

Abstract Vocabulary mining in information retrieval refers to the utilization of the domain vocabulary towards improving the user’s query. Most often queries posed to information retrieval systems are not optimal for retrieval purposes. Vocabulary mining allows one to generalize, specialize or perform other kinds of vocabulary-based transformations on the query in order to improve retrieval performance. This paper investigates a new framework for vocabulary mining that derives from the combination of rough sets and fuzzy sets. The framework allows one to use rough set-based approximations even when the documents and queries are described using weighted, i.e., fuzzy representations. The paper also explores the application of generalized rough sets and the variable precision models. The problem of coordination between multiple vocabulary views is also examined. Finally, a preliminary analysis of issues that arise when applying the proposed vocabulary mining framework to the Unified Medical Language System (a state-of-the-art vocabulary system) is presented. The proposed framework supports the systematic study and application of different vocabulary views in information retrieval.
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paper_title: Rough fuzzy set based scale space transforms and their use in image analysis

paper_content:

In this paper we present a multi-scale method based on the hybrid notion of rough fuzzy sets, coming from the combination of two models of uncertainty like vagueness by handling rough sets and coarseness by handling fuzzy sets. Marrying both notions lead to consider, as instance, approximation of sets by means of similarity relations or fuzzy partitions. The most important features are extracted from the scale spaces by unsupervised cluster analysis, to successfully tackle image processing tasks. Here, we report some results achieved by applying the method to multi-class image segmentation and edge detection, but it can be shown to be successfully applied to texture discrimination problem too.
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paper_title: Classification of multispectral images through a rough-fuzzy neural network

paper_content:

A new fuzzy Hopfield-model net based on rough-set reason- ing is proposed for the classification of multispectral images. The main purpose is to embed a rough-set learning scheme into the fuzzy Hopfield network to construct a classification system called a rough-fuzzy Hopfield net (RFHN). The classification system is a paradigm for the implementation of fuzzy logic and rough systems in neural network ar- chitecture. Instead of all the information in the image being fed into the neural network, the upper- and lower-bound gray levels, captured from a training vector in a multispectal image, are fed into a rough-fuzzy neuron in the RFHN. Therefore, only 2/N pixels are selected as the training samples if an N-dimensional multispectral image was used. In the simu- lation results, the proposed network not only reduces the consuming time but also reserves the classification performance. © 2004 Society of
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paper_title: Fuzzy-Rough set based nearest neighbor clustering classification algorithm

paper_content:

We propose a new nearest neighbor clustering classification algorithm based on fuzzy-rough set theory (FRNNC). First, we make every training sample fuzzy-roughness and use edit nearest neighbor algorithm to remove training sample points in class boundary or overlapping regions, and then use Mountain Clustering method to select representative cluster center points, then Fuzzy-Rough Nearest neighbor algorithm (FRNN) is applied to classify the test data. The new algorithm is applied to hand gesture image recognition, the results show that it is more effective and performs better than other nearest neighbor methods.
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paper_title: Evolutionary Modular MLP with Rough Sets and ID3 Algorithm for Staging of Cervical Cancer

paper_content:

This paper describes a way of designing a hybrid system for detecting the different stages of cervical cancer. Hybridisation includes the evolution of knowledge-based subnetwork modules with GAs using rough set theory and the ID3 algorithm. Crude subnetworks for each module are initially obtained via rough set theory and the ID3 algorithm. These subnetworks are then combined, and the final network is evolved using genetic algorithms. The evol-ution uses a restricted mutation operator which utilises the knowledge of the modular structure, already generated, for faster convergence. The GA tunes the network weights and structure simultaneously. The aforesaid integration enhances the performance in terms of classification score, network size and training time, as compared to the conven-tional MLP. This methodology also helps in imposing a structure on the weights, which results in a network more suitable for rule extraction.
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paper_title: Unsupervised Rough Set Classification Using GAs

paper_content:

The rough set is a useful notion for the classification of objects when the available information is not adequate to represent classes using precise sets. Rough sets have been successfully used in information systems for learning rules from an expert. This paper describes how genetic algorithms can be used to develop rough sets. The proposed rough set theoretic genetic encoding will be especially useful in unsupervised learning. A rough set genome consists of upper and lower bounds for sets in a partition. The partition may be as simple as the conventional expert class and its complement or a more general classification scheme. The paper provides a complete description of design and implementation of rough set genomes. The proposed design and implementation is used to provide an unsupervised rough set classification of highway sections.
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paper_title: Rough set feature selection and rule induction for prediction of malignancy degree in brain glioma

paper_content:

The degree of malignancy in brain glioma is assessed based on magnetic resonance imaging (MRI) findings and clinical data before operation. These data contain irrelevant features, while uncertainties and missing values also exist. Rough set theory can deal with vagueness and uncertainty in data analysis, and can efficiently remove redundant information. In this paper, a rough set method is applied to predict the degree of malignancy. As feature selection can improve the classification accuracy effectively, rough set feature selection algorithms are employed to select features. The selected feature subsets are used to generate decision rules for the classification task. A rough set attribute reduction algorithm that employs a search method based on particle swarm optimization (PSO) is proposed in this paper and compared with other rough set reduction algorithms. Experimental results show that reducts found by the proposed algorithm are more efficient and can generate decision rules with better classification performance. The rough set rule-based method can achieve higher classification accuracy than other intelligent analysis methods such as neural networks, decision trees and a fuzzy rule extraction algorithm based on Fuzzy Min–Max Neural Networks (FRE-FMMNN). Moreover, the decision rules induced by rough set rule induction algorithm can reveal regular and interpretable patterns of the relations between glioma MRI features and the degree of malignancy, which are helpful for medical experts.
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paper_title: A Hybrid Rough Set--Particle Swarm Algorithm for Image Pixel Classification

paper_content:

This article presents a framework to hybridize the rough set theory with a famous swarm intelligence algorithm known as Particle Swarm Optimization (PSO). The hybrid rough-PSO technique has been used for grouping the pixels of an image in its intensity space. Medical and remote sensing satellite images become corrupted with noise very often. Fast and efficient segmentation of such noisy images (which is essential for their further interpretation in many cases) has remained a challenging problem for years. In this work, we treat image segmentation as a clustering problem. Each cluster is modeled with a rough set. PSO is employed to tune the threshold and relative importance of upper and lower approximations of the rough sets. Davies-Bouldin clustering validity index is used as the fitness function, which is minimized while arriving at an optimal partitioning.
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paper_title: Rough set based 1-v-1 and 1-v-r approaches to support vector machine multi-classification

paper_content:

Support vector machines (SVMs) are essentially binary classifiers. To improve their applicability, several methods have been suggested for extending SVMs for multi-classification, including one-versus-one (1-v-1), one-versus-rest (1-v-r) and DAGSVM. In this paper, we first describe how binary classification with SVMs can be interpreted using rough sets. A rough set approach to SVM classification removes the necessity of exact classification and is especially useful when dealing with noisy data. Next, by utilizing the boundary region in rough sets, we suggest two new approaches, extensions of 1-v-r and 1-v-1, to SVM multi-classification that allow for an error rate. We explicitly demonstrate how our extended 1-v-r may shorten the training time of the conventional 1-v-r approach. In addition, we show that our 1-v-1 approach may have reduced storage requirements compared to the conventional 1-v-1 and DAGSVM techniques. Our techniques also provide better semantic interpretations of the classification process. The theoretical conclusions are supported by experimental findings involving a synthetic dataset.
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paper_title: An Automatic Classification System Applied in Medical Images

paper_content:

In this paper, a multi-class classification system is developed for medical images. We have mainly explored ways to use different image features, and compared two classifiers: Principle Component Analysis (PCA) and Supporting Vector Machines (SVM) with RBF (radial basis functions) kernels. Experimental results showed that SVM with a combination of the middle-level blob feature and low-level features (down-scaled images and their texture maps) achieved the highest recognition accuracy. Using the 9000 given training images from ImageCLEF05, our proposed method has achieved a recognition rate of 88.9% in a simulation experiment. And according to the evaluation result from the ImageCLEF05 organizer, our method has achieved a recognition rate of 82% over its 1000 testing images.
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paper_title: An Improved SVM Classifier for Medical Image Classification

paper_content:

Support Vector Machine (SVM) has high classifying accuracy and good capabilities of fault-tolerance and generalization. The Rough Set Theory (RST) approach has the advantages on dealing with a large amount of data and eliminating redundant information. In this paper, we join SVM classifier with RST which we call the Improved Support Vector Machine (ISVM) to classify digital mammography. The experimental results show that this ISVM classifier can get 96.56% accuracy which is higher about 3.42% than 92.94% using SVM, and the error recognition rates are close to 100% averagely.
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paper_title: A hybrid classifier based on rough set theory and support vector machines

paper_content:

Rough set theory (RST) can mine useful information from a large number of data and generate decision rules without prior knowledge. Support vector machines (SVMs) have good classification performances and good capabilities of fault-tolerance and generalization. To inherit the merits of both RST and SVMs, a hybrid classifier called rough set support vector machines (RS-SVMs) is proposed to recognize radar emitter signals in this paper. RST is used as preprocessing step to improve the performances of SVMs. A large number of experimental results show that RS-SVMs achieve lower recognition error rates than SVMs and RS-SVMs have stronger capabilities of classification and generalization than SVMs, especially when the number of training samples is small. RS-SVMs are superior to SVMs greatly.
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paper_title: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics

paper_content:

This paper presents a database containing 'ground truth' segmentations produced by humans for images of a wide variety of natural scenes. We define an error measure which quantifies the consistency between segmentations of differing granularities and find that different human segmentations of the same image are highly consistent. Use of this dataset is demonstrated in two applications: (1) evaluating the performance of segmentation algorithms and (2) measuring probability distributions associated with Gestalt grouping factors as well as statistics of image region properties.
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paper_title: Shadowed sets: representing and processing fuzzy sets

paper_content:

This study introduces a new concept of shadowed sets that can be regarded as a certain operational framework simplifying processing carried out with the aid of fuzzy sets and enhancing interpretation of results obtained therein. Some conceptual links between this idea and some others known in the literature are established. In particular, it is demonstrated how fuzzy sets can induce shadowed sets. Subsequently, shadowed sets reveal interesting conceptual and algorithmic relationships existing between rough sets and fuzzy sets. Detailed computational aspects of shadowed sets are discussed. Several illustrative examples are provided.
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paper_title: Rough sets, neighborhood systems and granular computing

paper_content:

Granulation of a universe involves grouping of similar elements into granules. With granulated views, we deal with approximations of concepts, represented by subsets of the universe, in terms of granules. This paper examines the problem of approximations with respect to various granulations of the universe. The granulation structures used by both rough set theory and neighborhood systems, and the corresponding approximation structures, are studied.
---
paper_title: Shadowed sets: bridging fuzzy and rough sets

paper_content:

In an apparatus of the type wherein ink under pressure is applied to a nozzle which is vibrated, and the ink emitted by the nozzle thereafter breaks down into ink drops which are charged in a charging tunnel in response to video signals, an arrangement for establishing the nozzle vibration frequency to be a function of the video signals' frequency and the shape of the video signals.
---
paper_title: Affinities between Perceptual Granules: Foundations and Perspectives

paper_content:

This chapter gives a concise overview of the foundations of a perceptual near set approach to the discovery of affinities between perceptual objects and perceptual granules that provide a basis for perceptual systems useful in science and engineering. A perceptual object is something perceptible to the senses or knowable by the mind. Perceptual objects that have the same appearance are considered to be perceptually near each other, i.e., perceived objects that have perceived affinities or, at least, similar descriptions. A perceptual granule is a set of perceptual objects originating from observations of the objects in the physical world. Near set theory provides a basis for observation, comparison and classification of perceptual granules. By considering nearness relations in the context of a perceptual system, it is possible to gauge affinities (nearness) perceptual objects. Two kinds of indiscernibility relations and a tolerance relation make it possible to define various nearness relations. Examples of near images as perceptual systems are presented. The main contribution of this chapter is the introduction of a formal basis for discovering affinities between perceptual information granules.
---
paper_title: Shadowed Clustering for Speech Data and Medical Image Segmentation

paper_content:

The paper presents a novel application of the shadowed clustering algorithm for uncertainty modeling and CT scan image segmentation. The core, shadowed and the exclusion regions, generated via shadowed c-means (SCM), quantize the ambiguity into three zones. This leads to faster convergence and reduced computational complexity. It is observed that SCM generates the best prototypes even in the presence of noise, thereby producing the best approximation of a structure in the unsupervised mode. A comparison with rough-fuzzy clustering algorithm reveals the automatic determination of the threshold and absence of externally tuned parameters in SCM. Experiments suggest that SCM is better suited for extraction of regions under vascular insult in the brain via pixel clustering. The relative efficacy of SCM in brain infarction diagnosis is validated by expert radiologists.
---
paper_title: Tolerance Approximation Spaces

paper_content:

We generalize the notion of an approximation space introduced in [8]. In tolerance approximation spaces we define the lower and upper set approximations. We investigate some attribute reduction problems for tolerance approximation spaces determined by tolerance information systems. The tolerance relation defined by the so called uncertainty function or the positive region of a given partition of objects have been chosen as invariants in the attribute reduction process. We obtain the solutions of the reduction problems by applying boolean reasoning [1]. The solutions are represented by tolerance reducts and relative tolerance reducts.
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paper_title: Tolerance space theory and some applications

paper_content:

The paper deals with the notion of tolerance space (introduced by E. C. Zeeman, but discerned earlier by H. Poincare), which formalizes the idea of resemblance. The category of tolerance spaces is described, their homology and homotopy theories developed. Applications include almost-fixed point theorems, almost-solution existence theorems for difference schemes and the three-channel principle (a general theorem on multichannel data transmission).
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paper_title: Tolerance near sets and image correspondence

paper_content:

The principal problem considered in this paper is how to solve the image correspondence problem using a bio-inspired approach. One solution to this problem is to consider tolerance near sets that model human perception in a physical continuum. Near sets are generalisations of rough sets introduced by Zdzislaw Pawlak during the early 1980s. Tolerance near sets have been inspired by C.E. Zeeman's work on visual perception and Henri Poincare's work on the contrast between mathematical continua and the physical continua in a pragmatic philosophy of science that laid the foundations for tolerance spaces. In this paper, the basics of perceptual systems and tolerance near sets are presented as bases for the solution of the image correspondence problem. The contribution of this paper is a humanistic perception-based approach to discovering similarities between images, classifying images and an approach to quantifying the nearness of images using the Henry-Peters nearness measure.
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paper_title: Handbook of biomedical image analysis

paper_content:

A Basic Model for IVUS Image Simulation.- Quantitative Functional Imaging with Positron Emission Tomography.- Advances in Magnetic Resonance Angiography and Physical Principles.- Recent Advances in the Level Set Method - Shape from Shading Models.- Wavelets in Medical Image Processing - Improving the Initialization, Convergence, and Memory Utilization for Defomable Models.- Level Set Segmentation of Biological Volume Database.- Advanced Segmentation (Level Set) Techniques.- A Regional-aided Color Geometric Snake.- Co-Volume Level Set Method in Subjective Surface Based Medical Image Segmentation.- Model-Based Brain Tissue Classification.- Supervised Texture Classification for Intravascular Tissue Characterization.- Medical Image Segmentation: Methods and Applications in Functional Imaging.- Automatic Segmentation of Pancreatic Tumors in Computed Tomography.- Computerized Analysis and Vasodilation Parameterization in Flow-Mediated Dilation Tests from Ultrasonic Image Sequences.- Statistical and Adaptive Approaches for Optimal Segmentation in Medical Images.- Automatic Analysis of Color Fundus Photographs and its Application to the Diagnosis of Diabetic Retinopathy.- Segmentation Issues in Carotid Artery Atherosclerotic Plague Analysis with MRI.- Accurate Lumen Identification, Detection, and Quantification in MR Plague Volumes.- Hessian-based Multiscale Enhancement, Description, and Quantification of Second-Order 3D Local Structures from Medical Volume Data.- A Knowledge-Based Scheme for Digital Mammography - Simultaneous Fuzzy Segmentation of Medical Images.- Computer Aided Diagnosis of Mammographic Calcification Clusters: Impact of Segmentation.- Computer Supported Segmentation of Radiological Data.- Medical Image Registration: Theory Algorithms, and Case Studies.- State of the Art of Level Set Methods in Segmentation and Registration of Medical Imaging Modalities.- Three-Dimensional Rigid and Non-Rigid Image Restriction for the Pelvis and Prostate.- Stereo and Temporal Retinal Image Registration by Mutual Information Maximization.- Quantification of Brain Aneurysm Dimensions from CTA for Surgical Planning of Coiling Intervention.- Inverse Consistent Image Registration.- A Computer-Aided Design System for Segmentation of Volumetric Images.- Inter-subject Non-Rigid Registration: an Overview with Classification and the Romeo Algorithm.- Elastic Registration for Biomedical Applications.- Cross-entropy, reversed cross-entropy, and symmetric divergence similarity measures for 3D image registration: a comparative study.- Quo Vadis, Atlas-Based Segmentation?.- Index.
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paper_title: An image model for quantitative image analysis

paper_content:

A basic assumption of most quantitative analysis techniques based on images is that each pixel within images represents a pure single class type, or object. In most cases, however, this assumption is not quite true due to finite resolutions of imaging systems. That is, pixels mapped to object boundaries may represent measurements of multiple objects. This paper presents a statistical image model which allows multiple classes within each pixel. The model assumes multichannel measurements, such as 3-channel color images, multi-spectral scanner, and thematic mapper images. Utilizing our model, we observed significant reduction in classification error and variations of quantitative measurement data.
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paper_title: CONSIDERING NEIGHBORHOOD INFORMATION IN IMAGE FUZZY CLUSTERING

paper_content:

Fuzzy C-means clustering algorithm is a classical non-supervised classification method.For image classification, fuzzy C-means clustering algorithm makes decisions on a pixel-by-pixel basis and does not take advantage of spatial information, regardless of the pixels' correlation. In this letter, a novel fuzzy C-means clustering algorithm is introduced, which is based on image's neighborhood system. During classification procedure, the novel algorithm regards all pixels'fuzzy membership as a random field. The neighboring pixels' fuzzy membership information is used for the algorithm's iteration procedure. As a result, the algorithm gives a more smooth classification result and cuts down the computation time.
---
paper_title: Rough sets, neighborhood systems and granular computing

paper_content:

Granulation of a universe involves grouping of similar elements into granules. With granulated views, we deal with approximations of concepts, represented by subsets of the universe, in terms of granules. This paper examines the problem of approximations with respect to various granulations of the universe. The granulation structures used by both rough set theory and neighborhood systems, and the corresponding approximation structures, are studied.
---
paper_title: Affinities between Perceptual Granules: Foundations and Perspectives

paper_content:

This chapter gives a concise overview of the foundations of a perceptual near set approach to the discovery of affinities between perceptual objects and perceptual granules that provide a basis for perceptual systems useful in science and engineering. A perceptual object is something perceptible to the senses or knowable by the mind. Perceptual objects that have the same appearance are considered to be perceptually near each other, i.e., perceived objects that have perceived affinities or, at least, similar descriptions. A perceptual granule is a set of perceptual objects originating from observations of the objects in the physical world. Near set theory provides a basis for observation, comparison and classification of perceptual granules. By considering nearness relations in the context of a perceptual system, it is possible to gauge affinities (nearness) perceptual objects. Two kinds of indiscernibility relations and a tolerance relation make it possible to define various nearness relations. Examples of near images as perceptual systems are presented. The main contribution of this chapter is the introduction of a formal basis for discovering affinities between perceptual information granules.
---
paper_title: Topological Concepts applied to Digital Image Processing

paper_content:

This article describes an automatic method applicable to the segmentation of mediastinum Computerized Axial Tomography (CAT) images with tumors, by means of Alternating Sequential Filters (ASFs) of Mathematical Morphology, and connected components extraction based on continuous topology concepts. Digital images can be related to topological space structures, and then general topology principles can be straightforwardly implemented. This method allows not only to accurately determine the area and external boundary of the segmented structures but also to obtain their precise location. Throughout these last years, technological development has significantly improved diagnostic imaging, enabling renal tumor and incidental hepatic tumor detection -usually small in size- in younger people and with an eventually lower malignant potential. This has led to a remarkable advance in interventionist techniques such as cryosurgery and radiofrequency ablation, preventing, in some cases, major surgeries, decreasing morbid-mortality rate, hospital stay and total treatment costs. Notwithstanding this, both cryosurgery and radiofrequency ablation, through extremely low and high temperatures, respectively, kill tumor as well as healthy cells, rendering crucial the identification of tumors with an extraordinary spatial accuracy.
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paper_title: Neighborhood systems and approximation in relational databases and knowledge bases

paper_content:

In solving mathematical equations, it is often sufficient to find approximate solutions; in answering database queries, very often the situation is similar. To formulate the notion of approximation, the neighborhood system or topology is introduced into the relational model - called topological data model. Moreover, when a knowledge base is derived from a database, a neighborhood system can also be introduced. The notion of topology in database and knowledge base supports the approximate retrieval and reasoning in the similar fashion the topology supports the approximate solutions in numerical analysis and functional analysis. The approximate reasoning here is different from the usual approximate reasoning that uses certainty factors. This paper is a step toward a formalization of what Dr. Hao Wang called "approximate proof" in his celebrated paper "Toward mechanical mathematics" and his subsequent papers for which he received, among other honors, the first Milestone Award in automated theorem-proving.
---
paper_title: Tolerance space theory and some applications

paper_content:

The paper deals with the notion of tolerance space (introduced by E. C. Zeeman, but discerned earlier by H. Poincare), which formalizes the idea of resemblance. The category of tolerance spaces is described, their homology and homotopy theories developed. Applications include almost-fixed point theorems, almost-solution existence theorems for difference schemes and the three-channel principle (a general theorem on multichannel data transmission).
---
paper_title: Shadowed sets: representing and processing fuzzy sets

paper_content:

This study introduces a new concept of shadowed sets that can be regarded as a certain operational framework simplifying processing carried out with the aid of fuzzy sets and enhancing interpretation of results obtained therein. Some conceptual links between this idea and some others known in the literature are established. In particular, it is demonstrated how fuzzy sets can induce shadowed sets. Subsequently, shadowed sets reveal interesting conceptual and algorithmic relationships existing between rough sets and fuzzy sets. Detailed computational aspects of shadowed sets are discussed. Several illustrative examples are provided.
---
paper_title: Shadowed sets: bridging fuzzy and rough sets

paper_content:

In an apparatus of the type wherein ink under pressure is applied to a nozzle which is vibrated, and the ink emitted by the nozzle thereafter breaks down into ink drops which are charged in a charging tunnel in response to video signals, an arrangement for establishing the nozzle vibration frequency to be a function of the video signals' frequency and the shape of the video signals.
---
paper_title: Shadowed Sets and Related Algebraic Structures

paper_content:

BZMV^{dM} algebras are introduced as an abstract environment to describe both shadowed and fuzzy sets. This structure is endowed with two unusual complementations: a fuzzy one ¬ and an intuitionistic one ∼. Further, we show how to define in any BZMV^{dM} algebra the Boolean sub-algebra of exact elements and to give a rough approximation of fuzzy elements through a pair of exact elements using an interior and an exterior mapping. Then, we introduce the weaker notion of pre-BZMV^{dM} algebra. This structure still have as models fuzzy and shadowed sets but with respect to a weaker notion of intuitionistic negation ∼_α with α ∈ [0, h). In pre-BZMV^{dM} algebras it is still possible to define an interior and an exterior mapping but, in this case, we have to distinguish between open and closed exact elements. Finally, we see how it is possible to define α-cuts and level fuzzy sets in the pre-BZMV^{dM} algebraic context of fuzzy sets.
---
paper_title: Shadowed Clustering for Speech Data and Medical Image Segmentation

paper_content:

The paper presents a novel application of the shadowed clustering algorithm for uncertainty modeling and CT scan image segmentation. The core, shadowed and the exclusion regions, generated via shadowed c-means (SCM), quantize the ambiguity into three zones. This leads to faster convergence and reduced computational complexity. It is observed that SCM generates the best prototypes even in the presence of noise, thereby producing the best approximation of a structure in the unsupervised mode. A comparison with rough-fuzzy clustering algorithm reveals the automatic determination of the threshold and absence of externally tuned parameters in SCM. Experiments suggest that SCM is better suited for extraction of regions under vascular insult in the brain via pixel clustering. The relative efficacy of SCM in brain infarction diagnosis is validated by expert radiologists.
---

Title: Rough Sets and Near Sets in Medical Imaging: A Review

Section 1: ROUGH SETS: FOUNDATIONS
Description 1: This section provides a brief explanation of the basic framework of rough set theory, along with some of the key definitions.

Section 2: ROUGH IMAGE PROCESSING
Description 2: This section introduces various rough image processing methodologies to handle the different challenges posed by medical imaging.

Section 3: QUANTITATIVE EVALUATION
Description 3: This section presents some quantitative measures that are capable of quantifying the relative utility of enhancement techniques in digital imaging, generated rules, and quality of classification measures.

Section 4: HYBRID INTELLIGENT APPROACHES
Description 4: This section reviews various approaches that combine rough sets with other computational intelligence techniques, such as neural networks, fuzzy sets, genetic algorithms, particle swarm optimization, and support vector machines.

Section 5: CLASSIFYING IMAGES: NEAR SET APPROACH
Description 5: This section gives a brief introduction to a near set approach to classifying images, separating medical images into nonoverlapping sets similar to each other.

Section 6: PROMISING GENERALIZATIONS OF ROUGH SETS IN MEDICAL IMAGING
Description 6: This section presents other generalizations of rough sets that show promise in medical image analysis, including tolerance spaces, neighborhood systems, and shadowed sets.

Section 7: CHALLENGES AND FUTURE DIRECTIONS
Description 7: This section discusses the challenges and future trends for rough set and near set methods in medical imaging, emphasizing the potential of hybrid approaches.