Local Membership Function Research Articles

Uncertainty parameter weighted entropy-based fuzzy c-means algorithm using complemented membership functions for noisy volumetric brain MR image segmentation

In this paper, we propose an uncertainty parameter weighted entropy-based fuzzy c-means clustering algorithm for noisy volumetric (3D) brain MR image segmentation using complemented global and spatially constraint local membership functions. Due to inherent noise and intensity inhomogeneity (IIH), the acquired MR images have blurry tissue boundaries. This leads to a situation where uncertainty arises while labeling a pixel/voxel into its proper tissue region. Further, it magnifies in the regions of different tissue boundaries. The proposed algorithm addresses this issue by introducing a class-level uncertainty parameter for each voxel and weightedly incorporating in the fuzzy objective function using complemented global and spatially constraint local fuzzy membership functions. It also incorporates total uncertainties in the 3D image domain by means of Shannon entropy. The complemented local fuzzy membership function estimates the degree of non-association, constraint by the local region-level intensity distribution. This framework allows the algorithm to utilize the spatial intensity distribution both in locally and globally within the image domain and produce more accurate cluster prototypes. We validate the proposed algorithm qualitatively and quantitatively with 10 3D simulated brain MR images, contaminated by noise and intensity inhomogeneity, 4 volumes of clinical real patient 3D brain MR images and a synthetic 3D image with added Rician noise. The simulation results in several evaluation indices indicate its superiority over state-of-the-art algorithms developed in recent past.

An Adaptive Smoothness Parameter Strategy for Variational Optical Flow Model

The smoothness parameter is used to balance the weight of the data term and the smoothness term in variational optical flow model, which plays very significant role for the optical flow estimation, but existing methods fail to obtain the optimal smoothness parameters (OSP). In order to solve this problem, an adaptive smoothness parameter strategy is proposed. First, an amalgamated simple linear iterative cluster (SLIC) and local membership function (LMF) algorithm is used to segment the entire image into several superpixel regions. Then, image quality parameters (IQP) are calculated, respectively, for each superpixel region. Finally, a neural network model is applied to compute the smoothness parameter by these image quality parameters of each superpixel region. Experiments were done in three public datasets (Middlebury, MPI_Sintel, and KITTI) and our self-constructed outdoor dataset with the proposed method and other existing classical methods; the results show that our OSP method achieves higher accuracy than other smoothness parameter selection methods in all these four datasets. Combined with the dual fractional order variational optical flow model (DFOVOFM), the proposed model shows better performance than other models in scenes with illumination inhomogeneity and abnormity. The OSP method fills the blank of the research of adaptive smoothness parameter, pushing the development of the variational optical flow models.

A novel fuzzy clustering algorithm by minimizing global and spatially constrained likelihood-based local entropies for noisy 3D brain MR image segmentation

In this paper, we propose a novel fuzzy clustering algorithm by minimizing global and spatially constrained likelihood-based local entropies (FCMGsLE) for segmenting noisy 3D brain magnetic resonance (MR) image volumes. For each voxel, in order to measure uncertainties that arise while identifying its class, two different entropies are defined. In particular, they measure the amount of uncertainties in terms of global entropy using fuzzifier weighted global membership function and spatially constrained likelihood-based local entropy using fuzzifier weighted local membership function. To mitigate the effect of noise and intensity inhomogeneity (IIH) or radio frequency (RF) inhomogeneity, the local membership function is induced by spatially constrained likelihood measure. These entropies are minimized through a fuzzy objective function to obtain the cluster prototypes and membership functions. The final membership function is obtained by integrating these global and local membership functions using weighted parameters. The algorithm is assessed both qualitatively and quantitatively on ten 3D volumes of simulated and clinical brain MR image data having high levels of noise and intensity inhomogeneity and a synthetic 3D image volume with Rician noise. The simulation results reveal that the proposed algorithm outperforms several state-of-the-art algorithms devised in recent past when evaluated in terms of segmentation accuracy, Dice similarity coefficient, partition coefficient, and partition entropy

3D unsupervised modified spatial fuzzy c-means method for segmentation of 3D brain MR image

This paper proposed a novel 3D unsupervised spatial fuzzy-based brain MRI volume segmentation technique in the presence of intensity inhomogeneity and noise. Instead of static masking, dynamic 3D masking has been proposed to measure the correlation among neighbors. The local membership function is defined based on the weighted correlation among neighbors. The local and global membership functions are combined to suppress the inhomogeneity and noise at the time of clustering. A weighted function is defined based on the 3D dynamic neighborhood to optimize the objective function in 3D space. In 2D slice-based MRI image segmentation techniques, the selection of the slice of interest is very important and it depends on the experience and skills of the expertise. As the proposed unsupervised method segments the 3D brain MRI volume as a whole, there is no need of such expertise. The detailed analysis of the results shows that the proposed unsupervised spatial fuzzy-based 3D brain MRI image segmentation technique is superior over the considered state-of-the-art methods in terms of cluster validation functions.

Local contextual information and Gaussian function induced fuzzy clustering algorithm for brain MR image segmentation and intensity inhomogeneity estimation

This paper presents a fuzzy clustering algorithm, where local contextual information and a Gaussian function are incorporated into the objective function, for simultaneous brain MR image segmentation and intensity inhomogeneity estimation. In doing so, for each pixel, we define a local contextual information, which actually defines its association among the other neighboring pixels based on intensity distribution. In particular, this information defines the possibility of the pixel to belong into a specific tissue type. Whereas, for each tissue region, a Gaussian surface is defined to estimate the intensity inhomogeneity (IIH) using the local image gradients, which are believed to be caused by the IIH. We use this Gaussian surface to compensate the effect of IIH. In addition, for each pixel, we have introduced global and local membership functions, which in combined in association with the other parameters are responsible for generation of cluster prototypes. The IIH of the entire image region is iteratively removed from the image and the final segmentation result is obtained based on the global membership values. The simulation results on two benchmarks brain MR image databases and four volumes of real-patient brain MR image data show its efficiency and superiority over other fuzzy-based clustering algorithms.

A two-stage fuzzy multi-objective framework for segmentation of 3D MRI brain image data

Segmentation of Magnetic Resonance Imaging (MRI) brain image data has a significant impact on the computer guided medical image diagnosis and analysis. However, due to limitation of image acquisition devices and other related factors, MRI images are severely affected by the noise and inhomogeneity artefacts which lead to blurry edges in the intersection of the intra-organ soft tissue regions, making the segmentation process more difficult and challenging. This paper presents a novel two-stage fuzzy multi-objective framework (2sFMoF) for segmenting 3D MRI brain image data. In the first stage, a 3D spatial fuzzy c-means (3DSpFCM) algorithm is introduced by incorporating the 3D spatial neighbourhood information of the volume data to define a new local membership function along with the global membership function for each voxel. In particular, the membership functions actually define the underlying relationship between the voxels of a close cubic neighbourhood and image data in 3D image space. The cluster prototypes thus obtained are fed into a 3D modified fuzzy c-means (3DMFCM) algorithm, which further incorporates local voxel information to generate the final prototypes. The proposed framework addresses the shortcomings of the traditional FCM algorithm, which is highly sensitive to noise and may stuck into a local minima. The method is validated on a synthetic image volume and several simulated and in-vivo 3D MRI brain image volumes and found to be effective even in noisy data. The empirical results show the supremacy of the proposed method over the other FCM based algorithms and other related methods devised in the recent past.

A modified fuzzy C‐means algorithm using scale control spatial information for MRI image segmentation in the presence of noise

AbstractThe fuzzy C‐means (FCM) algorithm does not fully utilize the spatial information for image segmentation and is sensitive to the presence of noise and intensity inhomogeneity in magnetic resonance imaging (MRI) images. The underlying reason is that using a single fuzzy membership function the FCM algorithm cannot properly represent pattern associations to all clusters. In this paper, we present a modified FCM (mFCM) algorithm by incorporating scale control spatial information for segmentation of MRI images in the presence of high levels of noise and intensity inhomogeneity. The algorithm utilizes scale controlled spatial information from the neighbourhood of each pixel under consideration in the form of a probability function. Using this probability function, a local membership function is introduced for each pixel. Finally, new clustering centre and weighted joint membership functions are introduced based on the local membership and global membership functions. The resulting mFCM algorithm is robust to the noise and intensity inhomogeneity in MRI image data and thereby improves the segmentation results. The experimental results on a synthetic image, four volumes of simulated and one volume of real‐patient MRI brain images show that the mFCM algorithm outperforms k‐means, FCM and some other recently proposed FCM‐based algorithms for image segmentation in terms of qualitative and quantitative studies such as cluster validity functions, segmentation accuracy and tissue segmentation accuracy. Copyright © 2015 John Wiley & Sons, Ltd.

A soft image representation approach by exploiting local neighborhood structure of self-organizing map (SOM)

When images are described with visual words based on vector quantization of low-level color, texture, and edge-related visual features of image regions, it is usually referred as "bag-of-visual words (BoVW)"-based presentation. Although it has proved to be effective for image representation similar to document representation in text retrieval, the hard image encoding approach based on one-to-one mapping of regions to visual words is not expressive enough to characterize the image contents with higher level semantics and prone to quantization error. Each word is considered independent of all the words in this model. However, it is found that the words are related and their similarity of occurrence in documents can reflect the underlying semantic relations between them. To consider this, a soft image representation scheme is proposed by spreading each region's membership values through a local fuzzy membership function in a neighborhood to all the words in a codebook generated by self-organizing map (SOM). The topology preserving property of the SOM map is exploited to generate a local membership function. A systematic evaluation of retrieval results of the proposed soft representation on two different image (natural photographic and medical) collections has shown significant improvement in precision at different recall levels when compared to different low-level and "BoVW"-based feature that consider only probability of occurrence (or presence/absence) of a word.

Zoning methods for handwritten character recognition: A survey

This paper presents a survey on zoning methods for handwritten character recognition. Through the analysis of the relevant literature in the field, the most valuable zoning methods are presented in terms of both topologies and membership functions. Throughout the paper, diverse zoning topologies are presented based on both static and adaptive approaches. Concerning static approaches, uniform and non-uniform zoning strategies are discussed. When adaptive zonings are considered, manual and automatic strategies for optimal zoning design are illustrated as well as the most appropriate zoning representation techniques. In addition, the role of membership functions for zoning-based classification is highlighted and the diverse approaches to membership function selection are presented. Concerning global membership functions, the paper introduces order-based approaches as well as fuzzy approaches using border-based and ranked-based fuzzy membership values. Concerning local membership functions, the recent parameter-based approaches are described, in which the optimal membership-function is selected for each zone of the zoning method. Finally, a comparative analysis on the performance of zoning methods is presented and the most interesting approaches are focused on in terms of topology design and membership function selection. A list of selected references is provided as a useful tool for interested researchers working in the field.

Visual query processing for efficient image retrieval using a SOM-based filter-refinement scheme

Visual query processing is one of the new issues for content-based image retrieval. In this paper, we propose (i) a filter-refinement scheme based on a modified form of the self-organizing map and (ii) a new interactive approach for similarity matching in image retrieval based on visual query processing. Specifically, we first propose a new local membership function, which preserves the relationships between the input feature vectors of the images and their neighboring weight vectors, to project the high dimensional input feature vectors to a low dimensional grid. Then, all the input feature vectors are mapped and visualized in the 2D grid. The feature vector of the query image is mapped and visualized in the 2D grid as well. The users not only can visualize the locations of the query image and the image data in the database, but also visualize the locations of the relevant and irrelevant images. Next, the users retrieve the candidates from the 2D grid interactively through visual query processing in the filter phase. Finally, the query results are obtained from the candidates by performing similarity ranking in the original feature space during the refinement phase. In order to accelerate the query process, we use a hierarchical tree to index the weight vectors of the self-organizing map (SOM) units to reduce the computation cost for finding the best matching unit. Our experiments show that (i) the proposed approach works well on both synthetic datasets and image data, (ii) the proposed visual query processing approach is more efficient than conventional approaches and can enhance the overall interactive experience through fast feedback, and (iii) the filter-refinement scheme makes our proposed approach more robust than conventional approaches.

Classification as Clustering: A Pareto Cooperative-Competitive GP Approach

Intuitively population based algorithms such as genetic programming provide a natural environment for supporting solutions that learn to decompose the overall task between multiple individuals, or a team. This work presents a framework for evolving teams without recourse to prespecifying the number of cooperating individuals. To do so, each individual evolves a mapping to a distribution of outcomes that, following clustering, establishes the parameterization of a (Gaussian) local membership function. This gives individuals the opportunity to represent subsets of tasks, where the overall task is that of classification under the supervised learning domain. Thus, rather than each team member representing an entire class, individuals are free to identify unique subsets of the overall classification task. The framework is supported by techniques from evolutionary multiobjective optimization (EMO) and Pareto competitive coevolution. EMO establishes the basis for encouraging individuals to provide accurate yet nonoverlaping behaviors; whereas competitive coevolution provides the mechanism for scaling to potentially large unbalanced datasets. Benchmarking is performed against recent examples of nonlinear SVM classifiers over 12 UCI datasets with between 150 and 200,000 training instances. Solutions from the proposed coevolutionary multiobjective GP framework appear to provide a good balance between classification performance and model complexity, especially as the dataset instance count increases.

Identification of Nonlinear Static Processes with Local Polynomial Regression and Subset Selection

The presented method for nonlinear system identification is based on the LOLIMOT algorithm introduced by Nelles and Isermann [1996]. The LOLIMOT algorithm divides the input space by a tree-construction algorithm and interpolates the local linear models by local membership functions. Instead of assuming local linear models, the presented algorithm utilizes general local nonlinear functions, which make the algorithm more flexible. These are approximated by a multidimensional Taylor series. Since the amount of regressors grows fast with the number of inputs and the expansion order, a subset selection procedure is introduced. It reveals significant regressors and gives information about the local functional behavior. The local subset selection is implemented as a stepwise regression with replacement of regressors. Mallows’ Cp-statistic is used for the subset selection algorithm and is also implemented for final model selection. The benefit of the extended algorithm lies in the higher flexibility in the local models, which results in less partitions of the input space by a similar approximation quality.