Fuzzy Plane Research Articles

Multimodal Medical Image Fusion Using Two- Stage Decomposition Technique to Combine the Significant Features of Spatial Fuzzy Plane and Transformed Frequency Plane

Multimodal medical image fusion is becoming a powerful technique in various clinical applications such as disease diagnosis and treatment planning. In this work, a two-stage decomposition technique is proposed to capture the significant features from the spatial and spectral domains as well. The first stage decomposition method employs a multicluster fuzzy c-means (FCM) algorithm to produce gross- and fine-structural components. The fine-structural components containing the edge topology are again decomposed into amplitude and phase spectra in terms of the discrete cosine transformation-based discrete Fourier transform (DCT-DFT). Finally, all parts of decomposed images are integrated with three different fusion rules. A new window-based feature quality measuring (WFQM) filter is proposed for fusing the information of gross-structural components, while the singular value decomposition (SVD) method and gray-wolf optimization-based pulse-coupled neural network (GWO-PCNN) model are applied for fusing the amplitude and phase spectrum distributions of input images. As the WFQM filter and GWO-PCNN model are designed to fuse the significant information from the spatial fuzzy plane and transformed frequency plane respectively, relative contrast degradation and spectral distortion are less in the proposed fusion method. Experimental results are reported on Harvard University datasets and some qualitative as well as quantitative measures are presented for comparing the proposed method with other state-of-art-techniques. The quantitative evaluation used peak signal-to-noise ratio (PSNR), mutual information (MI), structural similarity index measurement (SSIM), visual information fidelity (VIF), and entropy (ENT) to study its superiority.

Applying Fuzzy Contrast Enhancement on Earthquake Impact Images

In this paper, fuzzy contrast enhancement technique is applied on earthquake impact images in Ranau, Sabah. The aim is to highlight the visible differences between adjacent structures in the images. The brightness differences between objects and its background is enhanced to improve the visibility. In fuzzy approach, the gray plane is mapped into fuzzy plane by using membership function. The membership values represent the degree of brightness or darkness of the pixels.

Contrast Enhancement of Scintigraphic Image Using Fuzzy Intensification.

The objective of this study was to see the effect of fuzzy intensification (INT) operator on enhancement of scintigraphic image. Nuclear medicine physician (NMP) provided 25 scintigraphic images that required enhancement. The image pixels value was converted into fuzzy plane and was subjected to contrast INT operator with parameters of INT operator i.e., cross-over = 0.5 and number of iterations = 1 and 2. The enhanced image was again brought back into spatial domain (de-fuzzification) whose intensity value was in the range 0-255. NMP compared the enhanced image with its input image and labeled it as acceptable or unacceptable. The quality of enhanced image was also accessed objectively using four different image metrics namely: Entropy, edge content, absolute mean brightness error and saturation metrics. Most of the enhanced images (18 out of 25 images) obtained at cross-over = 0.5 and number of iterations = 1 are acceptable and found to have overall better contrast compared to the corresponding input image. Four images (two brain positron emission tomography scan and two I-131 scan) obtained at cross-over = 0.5 and with iteration = 2 are acceptable. Three input images (one dimercaptosuccinic acid (DMSA), one I-131 and one I-131- metaiodo-benzyl-guanidine (MIBG) scan) were better than their enhanced images. The enhancement produced by fuzzy INT operator was encouraging. Majority of enhanced images were acceptable at cross-over = 0.5 and number iterations = 1.

Analytical fuzzy space geometry II

In the present paper, we attempt to construct space fuzzy lines as well as fuzzy planes in R3. We construct a space fuzzy line as a bi-infinite extension of a space fuzzy line segment. A particular case of space fuzzy lines, namely, symmetric fuzzy lines, is also investigated. Importantly, the concept of skew fuzzy lines and the shortest distance between skew fuzzy lines are discussed in R3. In addition, the fuzzy planes are proposed in three different forms: a three-point form, an intercept form, and a fuzzy plane passing through an S-type space fuzzy point and perpendicular to a given crisp direction. The construction of all the different forms of fuzzy planes depends on the known details about the fuzzy planes, such as three S-type space fuzzy points, or its three intercepts, or an S-type space fuzzy point and a crisp direction. In the sequel, a symmetric fuzzy plane is investigated. The study and construction of all the proposed ideas are done with the help of the same and inverse points of S-type space fuzzy points. Geometric properties of the proposed space fuzzy lines and all the proposed forms of fuzzy planes are also explored. Numerical examples support all the formulations and studies. Notably, we also provide the algorithms to find the membership grade of a point in(i)the space fuzzy line passing through two continuous space fuzzy points,(ii)the shortest distance between symmetric skew fuzzy lines,(iii)the three-point form of the fuzzy plane,(iv)the intercept form of the fuzzy plane, and(v)the fuzzy plane passing through an S-type space fuzzy point and perpendicular to a given crisp direction.

Pre-processing of the x-ray to increase the sensitivity of visual analysis

In the field of medical imaging, it is fundamental to improve medical images of different physical nature to increase the likelihood of diagnosis based on them. X-rays are one of the oldest techniques used to analyze dense tissue abnormalities. Insufficient quality of X-rays is due to both the physical characteristics of the equipment used and the process of their for-mation. There are two main approaches to digital image processing - spatial methods, which are based on direct manipulation of the pixels of the original image and frequency conversion methods. These image processing methods consider pixel values as exact constants, while there are objective reasons for the presence of digital uncertainties, which are due to loss of information when displaying objects from three-dimensional (3-D) space, to 2-D projections, uncertainty of the gray level, statistical randomness, etc. To account for these factors, new methods are currently being developed that are based on the ideas of ambiguity. This approach is a kind of nonlinear transformation that allows you to take into account factors that are ambiguous. Fuzzy methods are based on mapping gray brightness levels to a fuzzy plane using membership transformations. The image is represented as a mass of fuzzy sets relative to the analyzed property with the value of the membership function that varies in the range [0-1]. The aim of this article is to assess the impact on the quality of the bright characteristics of the X-ray image of the results of using a combination of spatial methods of histogram equalization, fuzzy intensification and improvement in the frequency domain. The proposed algorithm provides a redistribution of the brightness of the histogram in the middle range of gray levels, which corresponds to the best visual (according to Weber - Fechner's law) per-ception, allows to increase the contrast and resolution of the image. There is a significant effect on the result of improving the image of the parameters of fuzzy intensifications. Experimental results are given on the example of real images.

Constructing the Fuzzy Hyperbola and Its Applications in Analytical Fuzzy Plane Geometry

In this paper, we studied about a detailed analysis of fuzzy hyperbola. In the previous studies, some methods for fuzzy parabola are discussed (Ghosh and Chakraborty, 2019). To define the fuzzy hyperbola, it is necessary to modify the method applied for the fuzzy parabola. To obtain a conic, it is necessary to know at least five points on this curve. First of all, in this study, we examined how to detect these five fuzzy points. We have discussed in detail the impact of points in this examination on finding fuzzy membership degrees and determining the curve. We show the use of the algorithm for calculating the coefficients in the conic equation on the examples. We make detailed drawings of all the fuzzy hyperbolas found and depicted the geometric location of fuzzy points with different membership degrees on the graph. As can be seen from the figures in our study, the importance of membership degrees in fuzzy space is that it causes us to find different numbers of hyperbola curves for the five points we study with. In addition, finding the membership of a given point to the fuzzy hyperbola is possible by solving nonlinear equations under different angular approaches. This examination is shown in detail in this study, and the results in the examples are evaluated by geometric comments. The systems formed by the fuzzy hyperbola curves are found to have different areas of use, as presented in the Conclusion. Some of usage areas of fuzzy hyperbola are radar systems, scanning devices, photosynthesis, heat, and CO2 distribution of plants.

Multi-class fuzzy support matrix machine for classification in roller bearing fault diagnosis

As a new classification method with the matrix as the input, support matrix machine (SMM) makes full use of the structured information between rows and columns of the input matrix to establish an accurate prediction model, which has been widely used in the field of fault diagnosis. However, the principle of SMM is to construct two parallel hyperplanes to complete the segmentation between different types of samples. When there are noise and outliers in the sample data, it is difficult for SMM to construct an ideal parallel hyperplane. In view of this, this paper proposes a multi-class fuzzy support matrix machine (MFSMM) by establishing nonparallel hyperplane objective function and integrating fuzzy attributes. In MFSMM, MFSMM establishes two nonparallel fuzzy hyperplanes by objective function, which maximizes the interval between any two fuzzy hyperplanes while considering the sample structure information. Meanwhile, fuzzy plane assigns different membership degrees to different training samples, which greatly reduces the influence of noise on the construction of optimal classification hyperplane. By analyzing two kinds of roller bearing experimental data, the results show that MFSMM has higher classification accuracy and stronger fault tolerance for samples with uncertain information.

A novel intuitionistic fuzzy soft set based colonogram enhancement for polyps localization

AbstractThis article represents a colonogram enhancement approach using intuitionistic fuzzy set (IFS) and fuzzy soft set (FSS) to improve the visual quality and highlight the local details in enhanced images without artifacts. The proposed method has the advantages of IFSs and fuzzy soft sets (FSSs) which can deal with gray‐level ambiguity in colonoscopy images. The combination of IFS and FSS works on intricate color variations with an adaptive parametric maps. First, the S‐membership function has been applied on the images to map into intuitionistic fuzzy space. We obtain intuitionistic fuzzy image from source image followed by decomposition of several blocks. Thereafter, the FSS is employed to get subsequent intuitionistic fuzzy soft matrix from individual image block. The FSS utilizes a class of parametric coefficients to obtain the hesitant score of individual pixels in each block through the soft‐score measure (SSM). Finally, the proposed method intensifies each membership degree in all blocks in the fuzzy plane using SSM and achieves an enhanced colonogram via defuzzification. Extensive experiment involving large data sets shows that the designed method exhibits better performance in contrast enhancement and visual quality improvement of colonograms for malformation detection (such as a polyps, malignant precancerous cells) in comparison with the state‐of‐art methods.

Development of intuitionistic fuzzy special embedded convolutional neural network for mammography enhancement

SummaryThis article proposes a novel mammogram enhancement approach using adaptive intuitionistic fuzzy special set (IFSS) with deep convolutional neural network (called MECNNIFS) for visual interpretation of mammography lesions, lumps, and abnormal cells in low‐dose X‐ray images. The proposed MECNNIFS scheme utilizes the membership grade modification by IFSS on low‐dose X‐ray images (mammography). The suggested model attempts to increase the underexposed and abnormal structural regions such as breast lesions, lumps, and nodules on the mammogram. The proposed algorithm initially separates mammograms using convolutional neural networks (CNNs) into foreground and background areas and then fuzzifies the image by intuitionistic fuzzy set theory. Low‐level features of a mammogram of the adjacent part are integrated with CNN in pixel classification during the separation task stage to improve the performance. Hyperbolic regularization and hesitant score have been applied on fuzzy plane to quantify the uncertainty and fuzziness in spatial domain for the proposed contrast enhancement. Finally, an enhanced mammogram is acquired through the process of defuzzification. The results show better quality and performance for improvement of contrast and visual quality in mammograms compared with other state‐of‐the‐art methods.

Enhancement of dronogram aid to visual interpretation of target objects via intuitionistic fuzzy hesitant sets

In this paper, we address the hesitant information in enhancement task often caused by differences in image contrast. Enhancement approaches generally use certain filters which generate artifacts or are unable to recover all the objects details in images. Typically, the contrast of an image quantifies a unique ratio between the amounts of black and white through a single pixel. However, contrast is better represented by a group of pixels. We have proposed a novel image enhancement scheme based on intuitionistic hesitant fuzzy sets (IHFSs) for drone images (dronogram) to facilitate better interpretations of target objects. First, a given dronogram is divided into foreground and background areas based on an estimated threshold from which the proposed model measures the amount of black/white intensity levels. Next, we fuzzify both of them and determine the hesitant score indicated by the distance between the two areas for each point in the fuzzy plane. Finally, a hyperbolic operator is adopted for each membership grade to improve the photographic quality leading to enhanced results via defuzzification. The proposed method is tested on a large drone image database. Results demonstrate better contrast enhancement, improved visual quality, and better recognition compared to the state-of-the-art methods.

Fuzzy weighted histogram equalisation for contrast enhancement of mammogram images

The early detection of breast cancer in the mammograms is very important in the field of medicine. Histogram equalisation is mainly used for contrast enhancement. The histogram equalisation (HE) usually results in excessive contrast enhancement because of lack of control on the level of enhancement. A novel technique, Fuzzy Weighted Histogram Equalisation (FWHE) for Contrast Enhancement of Mammogram Images is presented in this paper. The proposed method consists of three stages. First, the grey level intensities of the original mammogram image are transformed to fuzzy plane and the amount of fuzziness is adjusted by using contrast intensification operator. In the second stage, the Probability Distribution Function (PDF) of the fuzzy matrix is modified by applying weighting and thresholding and then, the HE procedure is applied to the fuzzy plane of the mammogram image. Finally, the fuzzy plane is de-fuzzified to get contrast enhanced mammogram image. From the qualitative and quantitative measures, it is interesting to see that the proposed method provides optimum results by giving better contrast enhancement and preserving the local information of the original mammogram image.

Fuzzy weighted histogram equalisation for contrast enhancement of mammogram images

The early detection of breast cancer in the mammograms is very important in the field of medicine. Histogram equalisation is mainly used for contrast enhancement. The histogram equalisation (HE) usually results in excessive contrast enhancement because of lack of control on the level of enhancement. A novel technique, Fuzzy Weighted Histogram Equalisation (FWHE) for Contrast Enhancement of Mammogram Images is presented in this paper. The proposed method consists of three stages. First, the grey level intensities of the original mammogram image are transformed to fuzzy plane and the amount of fuzziness is adjusted by using contrast intensification operator. In the second stage, the Probability Distribution Function (PDF) of the fuzzy matrix is modified by applying weighting and thresholding and then, the HE procedure is applied to the fuzzy plane of the mammogram image. Finally, the fuzzy plane is de-fuzzified to get contrast enhanced mammogram image. From the qualitative and quantitative measures, it is interesting to see that the proposed method provides optimum results by giving better contrast enhancement and preserving the local information of the original mammogram image.

Mammogram Enhancement Using Intuitionistic Fuzzy Sets.

Conventional mammogram enhancement methods use transform-domain filtering, which possibly produce some artifacts or not well highlight all local details in images. This paper presents a new enhancement method based on intuitionistic fuzzy sets. The presented algorithm initially separates a mammogram via a global threshold and then fuzzifies the image utilizing the intuitionistic fuzzy membership function that adopts restricted equivalence functions. After that, the presented scheme hyperbolizes membership degrees of foreground and background areas, defuzzifies the fuzzy plane, and achieves a filtered image via normalization. Finally, an enhanced mammogram is obtained by fusing the original image with filtered one. These implementations can be processed in parallel. This algorithm can improve the contrast and visual quality of regions of interest. Real data experiments demonstrate that our method has better performance regarding the improvement of contrast and visual quality of abnormalities in mammograms (such as masses and/or microcalcifications), compared with classical baseline methods. This algorithm has potential for understanding and determining abnormalities.

Analytical fuzzy plane geometry III

In this study, we attempt to construct fuzzy circles in a fuzzy geometrical plane. We provide a comprehensive study where we find a fuzzy number with a predetermined fuzzy distance from a given fuzzy number. We formulate fuzzy circles using the conventional basic definitions of crisp circles. Two different formulations of fuzzy circles are proposed, which depend on the information known about a fuzzy circle. The interrelations between the evaluated fuzzy circles are investigated. We show that the center of a fuzzy circle may not be a fuzzy point. However, the radius of a fuzzy circle that passes through three given fuzzy points is always a fuzzy number. The concepts of same and inverse points and a fuzzy number along a line are used to define and analyze the proposed ideas. Our discussions and studies are supported by suitable numerical and pictorial examples.

Particle Swarm Optimization for Position Control of Induction Motor

This paper proposes a position control of induction motor using particle swarm optimization (PSO) and fuzzy phase plane controller. Fuzzy membership functions, phase plane theory and the PSO are employed to design the proposed controller (FPPC) for controlling the position of an induction motor, based on the desired specifications. The proposed FPPC has merits of rapid response, simply designed fuzzy logic control and an explicitly designed phase plane theory. Simulations and experimental results reveal that the proposed FPPC is superior in optimal position control to conventional PI controller.

Analytical fuzzy plane geometry II

This paper formulates fuzzy lines in a fuzzy geometric plane. We construct a fuzzy line passing through several fuzzy points whose cores are collinear. Consecutively four different forms for fuzzy lines: a two-point form, a point-slope form, a slope-intercept form, and an intercept form are proposed. Their properties and interrelations are also investigated. We demonstrate the construction of the membership function of all four forms and illustrate this with suitable examples. It is shown that the two-point form and intercept form are equivalent. However, the two-point form or intercept form cannot, in general, be equivalent to the point-slope form or the slope-intercept form. To define and analyze all the proposed ideas, the concepts of same and inverse points in fuzzy geometry are used. All our discussions are supported by suitable examples.

Analytical fuzzy plane geometry I

This paper provides a detailed analysis of fuzzy point, fuzzy line segment, fuzzy distance and the angle between two fuzzy line segments. Two new concepts, same points and inverse points, are defined for this analysis. The basic properties of fuzzy distance, ideas about the containment of a fuzzy point on a fuzzy line segment and the coincidence of two fuzzy points are also described. A linear combination of two fuzzy points is introduced to define a fuzzy line segment. The fuzzy point dividing a fuzzy line segment in a given ratio is also investigated. All the discussion points are supported by suitable examples.

On fuzzify the notion of Grassmannianin fuzzy n-dimensional projective space

In this paper the partitions of fuzzy points of fuzzy -dimensional vector space into fuzzy 3-dimensional vector spaces and fuzzy n-dimensional projective space λ′ from fuzzy-dimensional vector space λ on V for n > 2, into fuzzy projective planes are given. Here, we restrict ourselves to the case, that a subspace should necessarily have the same values in its points as the whole space and an i-dimensional subspace of V, containing all for j>i, and are reals in [0,1]. Key words: Fuzzy point, fuzzy vector line, fuzzy vector plane, fuzzy vector space, fuzzy projective plane, fuzzy projective space.

Fuzzy ellipsoidal projective plane model

A definition of fuzzy plane projective geometry (FPPG) and fuzzy Desargues' proposition are given in Gupta and Ray (1993). In this work, we give fuzzy ellipsoidal projective plane model (FEPP) and then show that fuzzy Pappus theorem is satisfied in this fuzzy ellipsoidal projective plane model. Key words: Fuzzy sets (fuzzy) projective planes, fuzzy point, fuzzy line, vertical class, (Fuzzy) Pappus theorem.

Time-frequency spectral analysis of gas-liquid two-phase flow’s fluctuations

In order to study different flow patterns’ dynamic characteristics of gas-liquid two-phase flow, three time-frequency analysis methods are introduced to process the dynamic differential pressure signal of gas-liquid two-phase flow, such as the wavelet transform, Hilbert-Huang transform and adaptive optimal-kernel method. The results show that the main part of energy is transferred from frequency band 15—35 Hz to 0—8 Hz when the flow pattern changes from bubbly flow to slug flow and plug flow, and two spectrum peaks are observed at slug flow. The experimental results show that the time-frequency resolution of Hilbert-Huang transform and adaptive optimal-kernel is higher than that of wavelet transform. The extractions of ridge information based on adaptive optimal-kernel overcome the influence of fuzzy plane windowing effect, and enhance the readability of time-frequency plane information. The time-frequency analysis clearly shows the dynamic characteristics of different flow patterns, and describes the variation rules with time. It is helpful to further study the mechanism of gas-liquid two-phase flow.