Fuzzy Connectedness Image Segmentation in Graph Cut Formulation: A Linear-Time Algorithm and a Comparative Analysis

A deep theoretical analysis of the graph cut image segmentation framework presented in this paper simultaneously translates into important contributions in several directions. The most important practical contribution of this work is a full theoretical description, and implementation, of a novel powerful segmentation algorithm, GC(max). The output of GC(max) coincides with a version of a segmentation algorithm known as Iterative Relative Fuzzy Connectedness, IRFC. However, GC(max) is considerably faster than the classic IRFC algorithm, which we prove theoretically and show experimentally. Specifically, we prove that, in the worst case scenario, the GC(max) algorithm runs in linear time with respect to the variable M=|C|+|Z|, where |C| is the image scene size and |Z| is the size of the allowable range, Z, of the associated weight/affinity function. For most implementations, Z is identical to the set of allowable image intensity values, and its size can be treated as small with respect to |C|, meaning that O(M)=O(|C|). In such a situation, GC(max) runs in linear time with respect to the image size |C|. We show that the output of GC(max) constitutes a solution of a graph cut energy minimization problem, in which the energy is defined as the a"" (a) norm ayenF (P) ayen(a) of the map F (P) that associates, with every element e from the boundary of an object P, its weight w(e). This formulation brings IRFC algorithms to the realm of the graph cut energy minimizers, with energy functions ayenF (P) ayen (q) for qa[1,a]. Of these, the best known minimization problem is for the energy ayenF (P) ayen(1), which is solved by the classic min-cut/max-flow algorithm, referred to often as the Graph Cut algorithm. We notice that a minimization problem for ayenF (P) ayen (q) , qa[1,a), is identical to that for ayenF (P) ayen(1), when the original weight function w is replaced by w (q) . Thus, any algorithm GC(sum) solving the ayenF (P) ayen(1) minimization problem, solves also one for ayenF (P) ayen (q) with qa[1,a), so just two algorithms, GC(sum) and GC(max), are enough to solve all ayenF (P) ayen (q) -minimization problems. We also show that, for any fixed weight assignment, the solutions of the ayenF (P) ayen (q) -minimization problems converge to a solution of the ayenF (P) ayen(a)-minimization problem (ayenF (P) ayen(a)=lim (q -> a)ayenF (P) ayen (q) is not enough to deduce that). An experimental comparison of the performance of GC(max) and GC(sum) algorithms is included. This concentrates on comparing the actual (as opposed to provable worst scenario) algorithms' running time, as well as the influence of the choice of the seeds on the output.

Riverbed: A Novel User-Steered Image Segmentation Method Based on Optimum Boundary Tracking

This paper presents an optimum user-steered boundary tracking approach for image segmentation, which simulates the behavior of water flowing through a riverbed. The riverbed approach was devised using the image foresting transform with a never-exploited connectivity function. We analyze its properties in the derived image graphs and discuss its theoretical relation with other popular methods such as live wire and graph cuts. Several experiments show that riverbed can significantly reduce the number of user interactions (anchor points), as compared to live wire for objects with complex shapes. This paper also includes a discussion about how to combine different methods in order to take advantage of their complementary strengths.

Segmentação de imagens pela transformada imagem-floresta com faixa de restrição geodésica

Vários métodos tradicionais de segmentação de imagens, como a transformada de watershed de marcado- res e métodos de conexidade fuzzy (Relative Fuzzy Connectedness- RFC, Iterative Relative Fuzzy Connected- ness - IRFC), podem ser implementados de modo eficiente utilizando o método em grafos da Transformada Imagem-Floresta (Image Foresting Transform - IFT). No entanto, a carência de termos de regularização de fronteira em sua formulação fazem com que a borda do objeto segmentado possa ser altamente irregular. Um modo de contornar isto é por meio do uso de restrições de forma do objeto, que favoreçam formas mais regulares, como na recente restrição de convexidade geodésica em estrela (Geodesic Star Convexity - GSC). Neste trabalho, apresentamos uma nova restrição de forma, chamada de Faixa de Restrição Geodésica (Geodesic Band Constraint - GBC), que pode ser incorporada eficientemente em uma sub-classe do fra- mework de corte em grafos generalizado (Generalized Graph Cut - GGC), que inclui métodos pela IFT. É apresentada uma prova da otimalidade do novo algoritmo em termos de um mínimo global de uma função de energia sujeita às novas restrições de borda. A faixa de restrição geodésica nos ajuda a regularizar a borda dos objetos, consequentemente melhorando a segmentação de objetos com formas mais regulares, mantendo o baixo custo computacional da IFT. A GBC pode também ser usada conjuntamente com um mapa de custos pré estabelecido, baseado em um modelo de forma, de modo a direcionar a segmentação a seguir uma dada forma desejada, com grau de liberdade de escala e demais deformações controladas por um parâmetro único. Essa nova restrição também pode ser combinada com a GSC e com as restrições de polaridade de borda sem custo adicional. O método é demonstrado em imagens naturais, sintéticas e médicas, sendo estas provenientes de tomografias computadorizadas e de ressonância magnética.

Análise da dinâmica e quantificação metabólica de imagens de medicina nuclear na modalidade PET/CT.

A presença da Medicina Nuclear como modalidade de obtenção de imagens médicas é um dos principais procedimentos utilizados hoje nos centros de saúde, tendo como grande vantagem a capacidade de analisar o comportamento metabólico do paciente, traduzindo-se em diagnósticos precoces. Entretanto, sabe-se que a quantificação em Medicina Nuclear é dificultada por diversos fatores, entre os quais estão a correção de atenuação, espalhamento, algoritmos de reconstrução e modelos assumidos. Neste contexto, o principal objetivo deste projeto foi melhorar a acurácia e a precisão na análise de imagens de PET/CT via processos realísticos e bem controlados. Para esse fim, foi proposta a elaboração de uma estrutura modular, a qual está composta por um conjunto de passos consecutivamente interligados começando com a simulação de phantoms antropomórficos 3D para posteriormente gerar as projeções realísticas PET/CT usando a plataforma GATE (com simulação de Monte Carlo), em seguida é aplicada uma etapa de reconstrução de imagens 3D, na sequência as imagens são filtradas (por meio do filtro de Anscombe/Wiener para a redução de ruído Poisson caraterístico deste tipo de imagens) e, segmentadas (baseados na teoria Fuzzy Connectedness). Uma vez definida a região de interesse (ROI) foram produzidas as Curvas de Atividade de Entrada e Resultante requeridas no processo de análise da dinâmica de compartimentos com o qual foi obtida a quantificação do metabolismo do órgão ou estrutura de estudo. Finalmente, de uma maneira semelhante imagens PET/CT reais fornecidas pelo Instituto do Coração (InCor) do Hospital das Clínicas da Faculdade de Medicina da Universidade de São Paulo (HC-FMUSP) foram analisadas. Portanto, concluiu-se que a etapa de filtragem tridimensional usando o filtro Anscombe/Wiener foi relevante e de alto impacto no processo de quantificação metabólica e em outras etapas importantes do projeto em geral.

A calibration approach based on Takagi-Sugeno fuzzy inference system for digital electronic compasses

Recently, the development of industrial processes brought on the outbreak of technologically complex systems. This development generated the necessity of research relative to the mathematical techniques that have the capacity to deal with project complexities and validation. Fuzzy models have been receiving particular attention in the area of nonlinear systems identification and analysis due to it is capacity to approximate nonlinear behavior and deal with uncertainty. A fuzzy rule-based model suitable for the approximation of many systems and functions is the Takagi-Sugeno (TS) fuzzy model. IS fuzzy models are nonlinear systems described by a set of if then rules which gives local linear representations of an underlying system. Such models can approximate a wide class of nonlinear systems. In this paper a performance analysis of a system based on IS fuzzy inference system for the calibration of electronic compass devices is considered. The contribution of the evaluated IS fuzzy inference system is to reduce the error obtained in data acquisition from a digital electronic compass. For the reliable operation of the TS fuzzy inference system, adequate error measurements must be taken. The error noise must be filtered before the application of the IS fuzzy inference system. The proposed method demonstrated an effectiveness of 57% at reducing the total error based on considered tests. (C) 2011 Elsevier Ltd. All rights reserved.

Prediction of PM10 concentrations using Fuzzy c-Means and ANN

Salamanca has been considered among the most polluted cities in Mexico. The vehicular park, the industry and the emissions produced by agriculture, as well as orography and climatic characteristics have propitiated the increment in pollutant concentration of Particulate Matter less than 10 μg/m3 in diameter (PM10). In this work, a Multilayer Perceptron Neural Network has been used to make the prediction of an hour ahead of pollutant concentration. A database used to train the Neural Network corresponds to historical time series of meteorological variables (wind speed, wind direction, temperature and relative humidity) and air pollutant concentrations of PM10. Before the prediction, Fuzzy c-Means clustering algorithm have been implemented in order to find relationship among pollutant and meteorological variables. These relationship help us to get additional information that will be used for predicting. Our experiments with the proposed system show the importance of this set of meteorological variables on the prediction of PM10 pollutant concentrations and the neural network efficiency. The performance estimation is determined using the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). The results shown that the information obtained in the clustering step allows a prediction of an hour ahead, with data from past 2 hours

A fuzzy MCDA framework for safety assessment in the remediation of a uranium mill tailings site in Ukraine

The Pridneprovsky Chemical Plant was one of the largest uranium processing enterprises in the former USSR, producing a huge amount of uranium residues. The Zapadnoe tailings site contains most of these residues. We propose a theoretical framework based on multicriteria decision analysis and fuzzy logic to analyze different remediation alternatives for the Zapadnoe tailings, which simultaneously accounts for potentially conflicting economic, social and environmental objectives. We build an objective hierarchy that includes all the relevant aspects. Fuzzy rather than precise values are proposed for use to evaluate remediation alternatives against the different criteria and to quantify preferences, such as the weights representing the relative importance of criteria identified in the objective hierarchy. Finally, we suggest that remediation alternatives should be evaluated by means of a fuzzy additive multi-attribute utility function and ranked on the basis of the respective trapezoidal fuzzy number representing their overall utility.

Fuzzy MCDA for remediation of a uranium tailing

The Pridneprovsky Chemical Plant was a largest uranium processing enterprises, producing a huge amount of uranium residues. The Zapadnoe tailings site contains the majority of these residues. We propose a theoretical framework based on Multi-Criteria Decision Analysis and fuzzy logic to analyse different remediation alternatives for the Zapadnoe tailings, in which potentially conflicting economic, radiological, social and environmental objectives are simultaneously taken into account. An objective hierarchy is built that includes all the relevant aspects. Fuzzy rather than precise values are proposed for use to evaluate remediation alternatives against the different criteria and to quantify preferences, such as the weights representing the relative importance of criteria identified in the objective hierarchy. Finally, it is proposed that remediation alternatives should be evaluated by means of a fuzzy additive multi-attribute utility function and ranked on the basis of the respective trapezoidal fuzzy number representing their overall utility.

Soundscape quality analysis by fuzzy logic: A field study in Cordoba, Argentina

This research studies urban soundscapes through the comparative analysis of twelve public open spaces in the city of Córdoba (Argentina), taken as case studies. The work aims to examine selection of indicators and assessment tools intended to characterize soundscape quality. The field study was carried out through surveys and acoustic and psychoacoustic indicators, that are used together to objectively describe the sound quality of urban spaces. The study shows that, while there is a relationship of these indicators with the sound quality of the spaces, this is not linear. Their relative importance or influence depends on the interrelations occurring between the parameters studied. A model analyzing and correlating the parameters with the sound quality, based on the postulates of fuzzy logic, was applied as a tool of analysis, and it was seen to achieve a very close approximation to the subjective or perceptual response of the inhabitants. This close match between the model results and the perceptual response of the users confirms the fuzzy model as an effective tool for the study, not only of soundscapes, but also for those situations in which objective parameters must be related to the perceptual response of users.

Fuzzy data envelopment analysis:a discrete approach

Data envelopment analysis (DEA) as introduced by Charnes, Cooper, and Rhodes (1978) is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input-output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on a-cut. One drawback of the a-cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the a-cut approach. We introduce the concept of "local a-level" to develop a multi-objective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method.

A taxonomy and review of the fuzzy data envelopment analysis literature:two decades in the making

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. Crisp input and output data are fundamentally indispensable in conventional DEA. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. Many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in DEA. In this study, we provide a taxonomy and review of the fuzzy DEA methods. We present a classification scheme with four primary categories, namely, the tolerance approach, the a-level based approach, the fuzzy ranking approach and the possibility approach. We discuss each classification scheme and group the fuzzy DEA papers published in the literature over the past 20 years. To the best of our knowledge, this paper appears to be the only review and complete source of references on fuzzy DEA. © 2011 Elsevier B.V. All rights reserved.

The state of the art in fuzzy data envelopment analysis

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. Crisp input and output data are fundamentally indispensable in conventional DEA. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. Many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in DEA. This chapter provides a taxonomy and review of the fuzzy DEA (FDEA) methods. We present a classification scheme with six categories, namely, the tolerance approach, the α-level based approach, the fuzzy ranking approach, the possibility approach, the fuzzy arithmetic, and the fuzzy random/type-2 fuzzy set. We discuss each classification scheme and group the FDEA papers published in the literature over the past 30 years. © 2014 Springer-Verlag Berlin Heidelberg.

Productivity growth and efficiency measurements in fuzzy environments with an application to health care

Health care organizations must continuously improve their productivity to sustain long-term growth and profitability. Sustainable productivity performance is mostly assumed to be a natural outcome of successful health care management. Data envelopment analysis (DEA) is a popular mathematical programming method for comparing the inputs and outputs of a set of homogenous decision making units (DMUs) by evaluating their relative efficiency. The Malmquist productivity index (MPI) is widely used for productivity analysis by relying on constructing a best practice frontier and calculating the relative performance of a DMU for different time periods. The conventional DEA requires accurate and crisp data to calculate the MPI. However, the real-world data are often imprecise and vague. In this study, the authors propose a novel productivity measurement approach in fuzzy environments with MPI. An application of the proposed approach in health care is presented to demonstrate the simplicity and efficacy of the procedures and algorithms in a hospital efficiency study conducted for a State Office of Inspector General in the United States. © 2012, IGI Global.