7,676 research outputs found
Image Thresholding Technique Based On Fuzzy Partition And Entropy Maximization
Thresholding is a commonly used technique in image segmentation because of its fast and easy application. For this reason threshold selection is an important issue. There are two general approaches to threshold selection. One approach is based on the histogram of the image while the other is based on the gray scale information located in the local small areas. The histogram of an image contains some statistical data of the grayscale or color ingredients. In this thesis, an adaptive logical thresholding method is proposed for the binarization of blueprint images first. The new method exploits the geometric features of blueprint images. This is implemented by utilizing a robust windows operation, which is based on the assumption that the objects have "e;C"e; shape in a small area. We make use of multiple window sizes in the windows operation. This not only reduces computation time but also separates effectively thin lines from wide lines. Our method can automatically determine the threshold of images. Experiments show that our method is effective for blueprint images and achieves good results over a wide range of images. Second, the fuzzy set theory, along with probability partition and maximum entropy theory, is explored to compute the threshold based on the histogram of the image. Fuzzy set theory has been widely used in many fields where the ambiguous phenomena exist since it was proposed by Zadeh in 1965. And many thresholding methods have also been developed by using this theory. The concept we are using here is called fuzzy partition. Fuzzy partition means that a histogram is parted into several groups by some fuzzy sets which represent the fuzzy membership of each group because our method is based on histogram of the image . Probability partition is associated with fuzzy partition. The probability distribution of each group is derived from the fuzzy partition. Entropy which originates from thermodynamic theory is introduced into communications theory as a commonly used criteria to measure the information transmitted through a channel. It is adopted by image processing as a measurement of the information contained in the processed images. Thus it is applied in our method as a criterion for selecting the optimal fuzzy sets which partition the histogram. To find the threshold, the histogram of the image is partitioned by fuzzy sets which satisfy a certain entropy restriction. The search for the best possible fuzzy sets becomes an important issue. There is no efficient method for the searching procedure. Therefore, expansion to multiple level thresholding with fuzzy partition becomes extremely time consuming or even impossible. In this thesis, the relationship between a probability partition (PP) and a fuzzy C-partition (FP) is studied. This relationship and the entropy approach are used to derive a thresholding technique to select the optimal fuzzy C-partition. The measure of the selection quality is the entropy function defined by the PP and FP. A necessary condition of the entropy function arriving at a maximum is derived. Based on this condition, an efficient search procedure for two-level thresholding is derived, which makes the search so efficient that extension to multilevel thresholding becomes possible. A novel fuzzy membership function is proposed in three-level thresholding which produces a better result because a new relationship among the fuzzy membership functions is presented. This new relationship gives more flexibility in the search for the optimal fuzzy sets, although it also increases the complication in the search for the fuzzy sets in multi-level thresholding. This complication is solved by a new method called the "e;Onion-Peeling"e; method. Because the relationship between the fuzzy membership functions is so complicated it is impossible to obtain the membership functions all at once. The search procedure is decomposed into several layers of three-level partitions except for the last layer which may be a two-level one. So the big problem is simplified to three-level partitions such that we can obtain the two outmost membership functions without worrying too much about the complicated intersections among the membership functions. The method is further revised for images with a dominant area of background or an object which affects the appearance of the histogram of the image. The histogram is the basis of our method as well as of many other methods. A "e;bad"e; shape of the histogram will result in a bad thresholded image. A quadtree scheme is adopted to decompose the image into homogeneous areas and heterogeneous areas. And a multi-resolution thresholding method based on quadtree and fuzzy partition is then devised to deal with these images. Extension of fuzzy partition methods to color images is also examined. An adaptive thresholding method for color images based on fuzzy partition is proposed which can determine the number of thresholding levels automatically. This thesis concludes that the "e;C"e; shape assumption and varying sizes of windows for windows operation contribute to a better segmentation of the blueprint images. The efficient search procedure for the optimal fuzzy sets in the fuzzy-2 partition of the histogram of the image accelerates the process so much that it enables the extension of it to multilevel thresholding. In three-level fuzzy partition the new relationship presentation among the three fuzzy membership functions makes more sense than the conventional assumption and, as a result, performs better. A novel method, the "e;Onion-Peeling"e; method, is devised for dealing with the complexity at the intersection among the multiple membership functions in the multilevel fuzzy partition. It decomposes the multilevel partition into the fuzzy-3 partitions and the fuzzy-2 partitions by transposing the partition space in the histogram. Thus it is efficient in multilevel thresholding. A multi-resolution method which applies the quadtree scheme to distinguish the heterogeneous areas from the homogeneous areas is designed for the images with large homogeneous areas which usually distorts the histogram of the image. The new histogram based on only the heterogeneous area is adopted for partition and outperforms the old one. While validity checks filter out the fragmented points which are only a small portion of the whole image. Thus it gives good thresholded images for human face images
Image Thresholding Technique Based On Fuzzy Partition And Entropy Maximization
Thresholding is a commonly used technique in image segmentation because of its fast and easy application. For this reason threshold selection is an important issue. There are two general approaches to threshold selection. One approach is based on the histogram of the image while the other is based on the gray scale information located in the local small areas. The histogram of an image contains some statistical data of the grayscale or color ingredients. In this thesis, an adaptive logical thresholding method is proposed for the binarization of blueprint images first. The new method exploits the geometric features of blueprint images. This is implemented by utilizing a robust windows operation, which is based on the assumption that the objects have "e;C"e; shape in a small area. We make use of multiple window sizes in the windows operation. This not only reduces computation time but also separates effectively thin lines from wide lines. Our method can automatically determine the threshold of images. Experiments show that our method is effective for blueprint images and achieves good results over a wide range of images. Second, the fuzzy set theory, along with probability partition and maximum entropy theory, is explored to compute the threshold based on the histogram of the image. Fuzzy set theory has been widely used in many fields where the ambiguous phenomena exist since it was proposed by Zadeh in 1965. And many thresholding methods have also been developed by using this theory. The concept we are using here is called fuzzy partition. Fuzzy partition means that a histogram is parted into several groups by some fuzzy sets which represent the fuzzy membership of each group because our method is based on histogram of the image . Probability partition is associated with fuzzy partition. The probability distribution of each group is derived from the fuzzy partition. Entropy which originates from thermodynamic theory is introduced into communications theory as a commonly used criteria to measure the information transmitted through a channel. It is adopted by image processing as a measurement of the information contained in the processed images. Thus it is applied in our method as a criterion for selecting the optimal fuzzy sets which partition the histogram. To find the threshold, the histogram of the image is partitioned by fuzzy sets which satisfy a certain entropy restriction. The search for the best possible fuzzy sets becomes an important issue. There is no efficient method for the searching procedure. Therefore, expansion to multiple level thresholding with fuzzy partition becomes extremely time consuming or even impossible. In this thesis, the relationship between a probability partition (PP) and a fuzzy C-partition (FP) is studied. This relationship and the entropy approach are used to derive a thresholding technique to select the optimal fuzzy C-partition. The measure of the selection quality is the entropy function defined by the PP and FP. A necessary condition of the entropy function arriving at a maximum is derived. Based on this condition, an efficient search procedure for two-level thresholding is derived, which makes the search so efficient that extension to multilevel thresholding becomes possible. A novel fuzzy membership function is proposed in three-level thresholding which produces a better result because a new relationship among the fuzzy membership functions is presented. This new relationship gives more flexibility in the search for the optimal fuzzy sets, although it also increases the complication in the search for the fuzzy sets in multi-level thresholding. This complication is solved by a new method called the "e;Onion-Peeling"e; method. Because the relationship between the fuzzy membership functions is so complicated it is impossible to obtain the membership functions all at once. The search procedure is decomposed into several layers of three-level partitions except for the last layer which may be a two-level one. So the big problem is simplified to three-level partitions such that we can obtain the two outmost membership functions without worrying too much about the complicated intersections among the membership functions. The method is further revised for images with a dominant area of background or an object which affects the appearance of the histogram of the image. The histogram is the basis of our method as well as of many other methods. A "e;bad"e; shape of the histogram will result in a bad thresholded image. A quadtree scheme is adopted to decompose the image into homogeneous areas and heterogeneous areas. And a multi-resolution thresholding method based on quadtree and fuzzy partition is then devised to deal with these images. Extension of fuzzy partition methods to color images is also examined. An adaptive thresholding method for color images based on fuzzy partition is proposed which can determine the number of thresholding levels automatically. This thesis concludes that the "e;C"e; shape assumption and varying sizes of windows for windows operation contribute to a better segmentation of the blueprint images. The efficient search procedure for the optimal fuzzy sets in the fuzzy-2 partition of the histogram of the image accelerates the process so much that it enables the extension of it to multilevel thresholding. In three-level fuzzy partition the new relationship presentation among the three fuzzy membership functions makes more sense than the conventional assumption and, as a result, performs better. A novel method, the "e;Onion-Peeling"e; method, is devised for dealing with the complexity at the intersection among the multiple membership functions in the multilevel fuzzy partition. It decomposes the multilevel partition into the fuzzy-3 partitions and the fuzzy-2 partitions by transposing the partition space in the histogram. Thus it is efficient in multilevel thresholding. A multi-resolution method which applies the quadtree scheme to distinguish the heterogeneous areas from the homogeneous areas is designed for the images with large homogeneous areas which usually distorts the histogram of the image. The new histogram based on only the heterogeneous area is adopted for partition and outperforms the old one. While validity checks filter out the fragmented points which are only a small portion of the whole image. Thus it gives good thresholded images for human face images
Semi-supervised cross-entropy clustering with information bottleneck constraint
In this paper, we propose a semi-supervised clustering method, CEC-IB, that
models data with a set of Gaussian distributions and that retrieves clusters
based on a partial labeling provided by the user (partition-level side
information). By combining the ideas from cross-entropy clustering (CEC) with
those from the information bottleneck method (IB), our method trades between
three conflicting goals: the accuracy with which the data set is modeled, the
simplicity of the model, and the consistency of the clustering with side
information. Experiments demonstrate that CEC-IB has a performance comparable
to Gaussian mixture models (GMM) in a classical semi-supervised scenario, but
is faster, more robust to noisy labels, automatically determines the optimal
number of clusters, and performs well when not all classes are present in the
side information. Moreover, in contrast to other semi-supervised models, it can
be successfully applied in discovering natural subgroups if the partition-level
side information is derived from the top levels of a hierarchical clustering
One-class classifiers based on entropic spanning graphs
One-class classifiers offer valuable tools to assess the presence of outliers
in data. In this paper, we propose a design methodology for one-class
classifiers based on entropic spanning graphs. Our approach takes into account
the possibility to process also non-numeric data by means of an embedding
procedure. The spanning graph is learned on the embedded input data and the
outcoming partition of vertices defines the classifier. The final partition is
derived by exploiting a criterion based on mutual information minimization.
Here, we compute the mutual information by using a convenient formulation
provided in terms of the -Jensen difference. Once training is
completed, in order to associate a confidence level with the classifier
decision, a graph-based fuzzy model is constructed. The fuzzification process
is based only on topological information of the vertices of the entropic
spanning graph. As such, the proposed one-class classifier is suitable also for
data characterized by complex geometric structures. We provide experiments on
well-known benchmarks containing both feature vectors and labeled graphs. In
addition, we apply the method to the protein solubility recognition problem by
considering several representations for the input samples. Experimental results
demonstrate the effectiveness and versatility of the proposed method with
respect to other state-of-the-art approaches.Comment: Extended and revised version of the paper "One-Class Classification
Through Mutual Information Minimization" presented at the 2016 IEEE IJCNN,
Vancouver, Canad
Observer-biased bearing condition monitoring: from fault detection to multi-fault classification
Bearings are simultaneously a fundamental component and one of the principal causes of failure in rotary machinery. The work focuses on the employment of fuzzy clustering for bearing condition monitoring, i.e., fault detection and classification. The output of a clustering algorithm is a data partition (a set of clusters) which is merely a hypothesis on the structure of the data. This hypothesis requires validation by domain experts. In general, clustering algorithms allow a limited usage of domain knowledge on the cluster formation process. In this study, a novel method allowing for interactive clustering in bearing fault diagnosis is proposed. The method resorts to shrinkage to generalize an otherwise unbiased clustering algorithm into a biased one. In this way, the method provides a natural and intuitive way to control the cluster formation process, allowing for the employment of domain knowledge to guiding it. The domain expert can select a desirable level of granularity ranging from fault detection to classification of a variable number of faults and can select a specific region of the feature space for detailed analysis. Moreover, experimental results under realistic conditions show that the adopted algorithm outperforms the corresponding unbiased algorithm (fuzzy c-means) which is being widely used in this type of problems. (C) 2016 Elsevier Ltd. All rights reserved.Grant number: 145602
Gray Image extraction using Fuzzy Logic
Fuzzy systems concern fundamental methodology to represent and process
uncertainty and imprecision in the linguistic information. The fuzzy systems
that use fuzzy rules to represent the domain knowledge of the problem are known
as Fuzzy Rule Base Systems (FRBS). On the other hand image segmentation and
subsequent extraction from a noise-affected background, with the help of
various soft computing methods, are relatively new and quite popular due to
various reasons. These methods include various Artificial Neural Network (ANN)
models (primarily supervised in nature), Genetic Algorithm (GA) based
techniques, intensity histogram based methods etc. providing an extraction
solution working in unsupervised mode happens to be even more interesting
problem. Literature suggests that effort in this respect appears to be quite
rudimentary. In the present article, we propose a fuzzy rule guided novel
technique that is functional devoid of any external intervention during
execution. Experimental results suggest that this approach is an efficient one
in comparison to different other techniques extensively addressed in
literature. In order to justify the supremacy of performance of our proposed
technique in respect of its competitors, we take recourse to effective metrics
like Mean Squared Error (MSE), Mean Absolute Error (MAE), Peak Signal to Noise
Ratio (PSNR).Comment: 8 pages, 5 figures, Fuzzy Rule Base, Image Extraction, Fuzzy
Inference System (FIS), Membership Functions, Membership values,Image coding
and Processing, Soft Computing, Computer Vision Accepted and published in
IEEE. arXiv admin note: text overlap with arXiv:1206.363
On the usage of the probability integral transform to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems
We present a new distributed fuzzy partitioning method to reduce the
complexity of multi-way fuzzy decision trees in Big Data classification
problems. The proposed algorithm builds a fixed number of fuzzy sets for all
variables and adjusts their shape and position to the real distribution of
training data. A two-step process is applied : 1) transformation of the
original distribution into a standard uniform distribution by means of the
probability integral transform. Since the original distribution is generally
unknown, the cumulative distribution function is approximated by computing the
q-quantiles of the training set; 2) construction of a Ruspini strong fuzzy
partition in the transformed attribute space using a fixed number of equally
distributed triangular membership functions. Despite the aforementioned
transformation, the definition of every fuzzy set in the original space can be
recovered by applying the inverse cumulative distribution function (also known
as quantile function). The experimental results reveal that the proposed
methodology allows the state-of-the-art multi-way fuzzy decision tree (FMDT)
induction algorithm to maintain classification accuracy with up to 6 million
fewer leaves.Comment: Appeared in 2018 IEEE International Congress on Big Data (BigData
Congress). arXiv admin note: text overlap with arXiv:1902.0935
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