Extended filters in bounded commutative Rl-monoids

The notion of extended filter of a filter associated to a subset of Rl-monoids is defined and related properties are investigated. Rachunek and Salounova proved that positive implicative filters and Boolean filters in Rl-monoids coincide with a condition in Rachunek and Salounova (Acta Univ Palacki Olomuc Fac rer nat Math 48(1):93–107, 2009). In this paper, we prove that positive implicative filters and Boolean filters coincide without any condition and get some results on various types of filters.     

Filter theory of BL algebras

In this paper we consider fundamental properties of some types of filters (Boolean, positive implicative, implicative and fantastic filters) of BL algebras defined in Haveshki et al. (Soft Comput 10:657–664, 2006) and Turunen (Arch Math Logic 40:467–473, 2001). It is proved in Haveshki et al. (2006) that if F is a maximal and (positive) implicative filter then it is a Boolean filter. In that paper there is an open problem Under what condition are Boolean filters positive implicative filters? One of our results gives an answer to the problem, that is, we need no more conditions. Moreover, we give simple characterizations of those filters by an identity form ? x, y(t(x, y) ∈ F), where t(x, y) is a term containing x, y.      

Image denoising with neighbour dependency and customized wavelet and threshold

Image denoising by means of wavelet transforms has been an active research topic for many years. For a given noisy image, which kind of wavelet and what threshold we use should have significant impact on the quality of the denoised image. In this paper, we use Simulated Annealing to find the customized wavelet filters and the customized threshold corresponding to the given noisy image at the same time. Also, we propose to consider a small neighbourhood around the customized wavelet coefficient to be thresholded for image denoising. Experimental results show that our approach is better than VisuShrink, our NeighShrink with fixed wavelet, and the wiener2 filter that is available in Matlab Image Processing Toolbox. In addition, our NeighShrink with fixed wavelet already outperforms VisuShrink for all the experiments.     

An effective and objective criterion for evaluating the performance of denoising filters

Denoising filters are useful for reducing noise; however, they often blur and smear the edges and boundaries, which are necessary for segmenting or locating the objects. In order to overcome above problem, many filters with contrast enhancement capability have been developed, and they have wide applications in related fields. Recently, researchers found that the traditional criteria, such as mean squared error (MSE), signal-to-noise ratio (SNR), are not suitable for evaluating such filters.Due to lack of effective metrics for such tasks, visual inspection by human and some newly proposed image quality assessment (QA) criteria, such as structural similarity (SSIM) index are utilized. However, visual inspection depends on the subjectivity of observers heavily.This paper has proved that evaluating denoising filters is different from image quality assessment, i.e., existing image quality assessment criteria cannot effectively evaluate the performance of denoising filters, especially, of the filters having contrast enhancement capability; and new criteria should be established. Further, it proposes a novel objective and effective assessment criterion, homogeneity mean difference (HMD), to evaluate the performance of the filters since it can describe the textual and structural information and/or the changes in textual and structural information well. We have employed 503 images from three databases to demonstrate the superiority of the proposed metric over the existing ones, and to prove that HMD is an effective and useful metric for assessing denoising filters with/without contrast enhancement, which may find wide applications in image processing and computer vision.     

Designing spectral sensitivity curves for use with Artificial Color

Artificial Color uses data from two or more spectrally overlapping sensitivity curves to assign class membership to pixels and ultimately to images. The usefulness of Artificial Color for various scene segmentation tasks has been shown in several recent papers, but those demonstrations all used sensitivity curves not optimized for the particular task, i.e. the R, G, B filters of commercial color cameras. This paper explores means to evolve suitable spectral sensitivity curves suited to any specialized task and illustrates that method with synthetic data chosen to be very hard to discriminate spectrally. Two special cases are illustrated. In one, a single Gaussian curve is used for a dichroic beamsplitter, so that the curve and its complement are used for discrimination. In the other case, two essentially orthogonal curves are utilized for the same task. The single Gaussian curve leads to poorer discrimination but better light efficiency relative to the two curves. Both do quite well on the difficult target problem.     

泛逻辑学中UB代数系统的(∈,∈∨q)-fuzzy滤子

何华灿教授给出了理想状态下的泛逻辑学的形式演绎系统β,并证明了该系统的可靠性。并且提出了理想状态下的泛逻辑学对应的代数系统-UB代数,并讨论了它们的性质。在以上这些结果的基础上,引入UB代数的(∈,∈∨q)-fuzzy滤子和(∈,∈∨q)-fuzzy关联滤子的概念,获得了它们的若干等价刻画,证明了(∈,∈∨q)-fuzzy关联滤子的扩张定理。     

Fast Algorithm for Local Statistics Calculation for N -Dimensional Images

Local mean and variance measures are frequently required in multi-dimensional image analysis. These measures are needed when calculating correlation coefficients for local image matching purposes. Other measures such as skewness and autocorrelation are useful for texture analysis. This paper presents a fast algorithm for calculating these local statistics in a window of an N -dimensional image. The new algorithm, which is called the plunger method, recursively reduces the dimensions of the input N -dimensional image to achieve fast computation. The speed of the algorithm is independent of the window size. Another advantage of the algorithm is that it calculates the local statistics in one pass. Real image tests have been performed.     

Fast mean filtering technique (FMFT)

This article presents a novel method for mean filtering that reduces the required number of additions and eliminates the need for division altogether. The time reduction is achieved using basic store-and-fetch operations and is irrespective of the image or neighbourhood size. This method has been tested on a variety of greyscale images and neighbourhood sizes with promising results. These results indicate that the relative time requirement reduces with increase in image size. The method's efficiency also improves significantly with increase in neighbourhood size thereby making it increasingly useful when dealing with large images.     

General Adaptive Neighborhood Choquet Image Filtering

A novel framework entitled General Adaptive Neighborhood Image Processing (GANIP) has been recently introduced in order to propose an original image representation and mathematical structure for adaptive image processing and analysis. The central idea is based on the key notion of adaptivity which is simultaneously associated with the analyzing scales, the spatial structures and the intensity values of the image to be addressed. In this paper, the GANIP framework is briefly exposed and particularly studied in the context of Choquet filtering (using fuzzy measures), which generalizes a large class of image filters. The resulting spatially-adaptive operators are studied with respect to the general GANIP framework and illustrated in both the biomedical and materials application areas. In addition, the proposed GAN-based filters are practically applied and compared to several other denoising methods through experiments on image restoration, showing a high performance of the GAN-based Choquet filters.

From binary to grey tone image processing using fuzzy logic concepts

The concept of fuzzy logic was introduced by Zadeh in 1965 as a tool for analysing complex systems and decision processes. In fuzzy set theory, the binary Boolean operations of OR and AND generalise to the min and max functions. Nakagawa(⁸) later introduced the idea of local min and max operators to image processing as the grey equivalents to the parallel binary operations of shrinking and expanding. In this paper the ideas of min and max are further investigated and their usefulness in image processing assessed by extending some already well known binary processes into grey level algorithms. The functions of min_π and max_π are introduced (deleted neighbourhood min_π and max_π) as the analogues of nearest neighbour “propagation” signals of binary images. Examples of grey edge detection, spatial filtering, object labelling and grey thinning algorithms are given.     

Relationships between generalized Bosbach states and <Emphasis Type="Italic">L</Emphasis>-filters on residuated lattices

Generalized Bosbach states and filters on residuated lattices have been extensively studied in the literature. In this paper, relationships between generalized Bosbach states and residuated-lattice-valued filters, also called L-filters, on residuated lattices are investigated. Particularly, type I and type II L-filters and their subclasses are defined, and some their properties are obtained. Then relationships between special types of L-filters and the generalized Bosbach states are considered where generalized Bosbach states are characterized by some type I or type II L-filters with additional conditions. Associated with these relationships, new subclasses of generalized Bosbach states such as implicative type IV, V, VI states, fantastic type IV states and Boolean type IV states are introduced, and the relationships between various types of generalized Bosbach states are investigated in detail. In particular, the existence of several generalized Bosbach states is provided and, as application, some typical subclasses of residuated lattices such as Rl-monoids, Heyting algebras and Boolean algebras are characterized by these generalized Bosbach states.     

Cell Histograms Versus Color Histograms for Image Representation and Retrieval

This paper presents a new approach for content-based image retrieval, which is based on the well-known and widely used color histograms. Previous approaches have used a single global color histogram (GCH) for the whole image, or local color histograms (LCHs) for cells within a grid of fixed size. Our approach is also based on a grid of cells, but unlike the latter it uses a cell histogram for each of the colors actually present in the images, representing how that color is distributed among the image cells -- hence the name Cell/Color Histograms. Our experiments have shown that the actual number of colors present in images is often low. Thus we are able to achieve performance comparable to using LCHs within a grid, but with a much smaller space overhead. Furthermore, the proposed approach is very flexible in the sense that the user has alternative ways to calibrate the trade-off between space overhead and retrieval effectiveness. In fact, we have been able to outperform GCHs (typically a compact representation) in terms of effectiveness requiring less storage space.     

Orthogonal Algorithm of Logic Probability and Syndrome-Testable Analysis

A new method,orthogonal algoritm,is presented to compute the logic probabilities(i.e.signal probabilities)accurately,The transfer properties of logic probabilities are studied first,which are useful for the calculation of logic probability of the circuit with random independent inputs.Then the orthogonal algoritm is described to compute the logic probability of Boolean function realized by a combinational circuit.This algorithm can make Boolean function “ORTHOGONAL”so that the logic probabilities can be easily calculated by summing up the logic probabilities of all orthogonal terms of the Booleam function.     

Encoding deductive argumentation in quantified Boolean formulae

There are a number of frameworks for modelling argumentation in logic. They incorporate a formal representation of individual arguments and techniques for comparing conflicting arguments. A common assumption for logic-based argumentation is that an argument is a pair 〈Φ,α〉 where Φ is minimal subset of the knowledge-base such that Φ is consistent and Φ entails the claim α. Different logics provide different definitions for consistency and entailment and hence give us different options for argumentation. Classical propositional logic is an appealing option for argumentation but the computational viability of generating an argument is an issue. To better explore this issue, we use quantified Boolean formulae to characterise an approach to argumentation based on classical logic.     

Algebraic models of deviant modal operators based on de Morgan and Kleene lattices

An algebraic model of a kind of modal extension of de Morgan logic is described under the name MDS5 algebra. The main properties of this algebra can be summarized as follows: (1) it is based on a de Morgan lattice, rather than a Boolean algebra; (2) a modal necessity operator that satisfies the axioms N, K, T, and 5 (and as a consequence also B and 4) of modal logic is introduced; it allows one to introduce a modal possibility by the usual combination of necessity operation and de Morgan negation; (3) the necessity operator satisfies a distributivity principle over joins. The latter property cannot be meaningfully added to the standard Boolean algebraic models of S5 modal logic, since in this Boolean context both modalities collapse in the identity mapping. The consistency of this algebraic model is proved, showing that usual fuzzy set theory on a universe U can be equipped with a MDS5 structure that satisfies all the above points (1)-(3), without the trivialization of the modalities to the identity mapping. Further, the relationship between this new algebra and Heyting-Wajsberg algebras is investigated. Finally, the question of the role of these deviant modalities, as opposed to the usual non-distributive ones, in the scope of knowledge representation and approximation spaces is discussed.     

二值命题逻辑中基于条件真度的近似推理

以公式真度为基础,给出了二值命题逻辑中基于条件真度的逻辑度量的真度表示式,提出了两类在信息Г下的误差不大于ε结论模式,证明了两类结论模式的等价性,并讨论了基于条件真度和真度的近似推理及其关系问题。     

The Strong Property of Morphological Connected Alternated Filters

This paper studies connectivity aspects that arise in image operators that process connected components. The focus is on morphological image analysis (i.e., on increasing image operators) and, in particular, on a robustness property satisfied by certain morphological filters that is denominated the strong property. The behavior of alternated compositions of openings and closings is investigated under certain assumptions, particularly connectedness and a connected component preserving condition. It is shown that these conditions cannot in general guarantee the strong property of certain connected alternated filters because of issues related to the locality of the filters. As treated in the paper, there have been a series of misunderstandings in the literature concerning this topic, and it is important to clarify them. The root cause of those problems is discussed, and a solution is indicated. The class of connected openings and closings used to build connected alternated filters should therefore be defined to avoid such situations, since the strong property of alternated filters should be a distinctive characteristic of this class.

A stock selection strategy using fuzzy neural networks

This paper describes, from a general system-design perspective, an artificial neural network (ANN) approach to a stock selection strategy. The paper suggests a concept of neural gates which are similar to the processing elements in ANN, but generalized into handling various types of information such as fuzzy logic, probabilistic and Boolean information together. Forecasting of stock market returns, assessing of country risk and rating of stocks based on fuzzy rules, probabilistic and Boolean data can be done using the proposed neural gates. Fuzzy logic is known to be useful for decision-making where there is a great deal of uncertainty as well as vague phenomena, but lacks the learning capability; on the other hand, neural networks are useful in constructing an adaptive system which can learn from historical data, but are not able to process ambiguous rules and probabilistic data sets. This paper describes how these problems can be solved using the proposed neural gates.     

A new generalised α scale spaces quadrature filters

The α   scale spaces is a recent theory that open new possibilities of phase-based image processing. It is a parameterised class (α∈]0,1])$(\alpha \in ]0,1\left]\right)$ of linear scale space representations, which allows a continuous connection beyond the well-known Gaussian scale space (α=1$\alpha =1$). In this paper, we make use of this unified representation to derive new families of band pass quadrature filters, built from derivatives and difference of the α scale space generating kernels. This construction leads to generalised α kernel filters including the commonly known families derived from the Gaussian and the Poisson kernels. The properties of each family are first studied and then experiments on one- and two-dimensional signals are shown to exemplify how the suggested filters can be used for edge detection. This work is complemented by an experimental evaluation, which demonstrates that the new proposed filters are a good alternative to the commonly used Log-Gabor filter.