Perspectives on the theory and practice of belief functions

Shafer, Glenn

doi:10.1016/0888-613x(90)90012-q

Cited by 337 publications

(160 citation statements)

References 83 publications

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“…An integrated edge filter is proposed to improve the accuracy of vessel edge detection by combining the outputs of a Laplacian of Gaussian (LoG) filter and a Canny filter via a probability-based fusion method, known as Dempster-Shafer fusion (D-S) [14]. To make edge detection more accurate on diameter measurement and more robust to noise, edge thinning and noise reduction operations are integrated in the filter as well.…”

Section: Generating Vascular Map Via a Dempster-shafer-based Edge Detmentioning

confidence: 99%

“…Depmster-Shafer theory developed by Arthur P. Dempster and Glenn Shafer is a mathematical theory of evidence based on belief functions and plausible reasoning, which is used to combine separate pieces of information (evidence) to calculate the probability density of an event. More details of the D-S theory can be found in [14]. Since LoG filter applies the second spatial derivative of a Gaussian for edge detection while Canny filter focuses on using the first spatial derivative of a Gaussian for edge detection, they are two independent methods.…”

Section: D-s-based Fusion For Edge Detectionmentioning

confidence: 99%

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Retinal Vessel Detection and Measurement for Computer-aided Medical Diagnosis

Wee

2013

J Digit Imaging

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Since blood vessel detection and characteristic measurement for ocular retinal images is a fundamental problem in computer-aided medical diagnosis, automated algorithms/systems for vessel detection and measurement are always demanded. To support computer-aided diagnosis, an integrated approach/solution for vessel detection and diameter measurement is presented and validated. In the proposed approach, a Dempster-Shafer (D-S)-based edge detector is developed to obtain initial vessel edge information and an accurate vascular map for a retinal image. Then, the appropriate path and the centerline of a vessel of interest are identified automatically through graph search. Once the vessel path has been identified, the diameter of the vessel will be measured accordingly by the algorithm in real time. To achieve more accurate edge detection and diameter measurement, mixed Gaussian-matched filters are designed to refine the initial detection and measures. Other important medical indices of retinal vessels can also be calculated accordingly based on detection and measurement results. The efficiency of the proposed algorithm was validated by the retinal images obtained from different public databases. Experimental results show that the vessel detection rate of the algorithm is 100 % for large vessels and 89.9 % for small vessels, and the error rate on vessel diameter measurement is less than 5 %, which are all well within the acceptable range of deviation among the human graders.

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Section: Generating Vascular Map Via a Dempster-shafer-based Edge Detmentioning

confidence: 99%

Section: D-s-based Fusion For Edge Detectionmentioning

confidence: 99%

Retinal Vessel Detection and Measurement for Computer-aided Medical Diagnosis

Wee

2013

J Digit Imaging

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“…However, they relax the additive assumption (Tversky and Koehler 1994). Among them, the Dempster-Shafer Theory (Dempster 1967(Dempster , 1968Shafer 1976) is the most systematic (Mongin 1994;Huber 2012). The Dempster-Shafer (DS) Theory offers an alternative way to assigning likelihoods to events.…”

Section: Dempster-shafer Theorymentioning

confidence: 99%

“…The entire frame  in our example might be a binary setting of ignored (a1) and not ignored (a2) for a specific attribute associated with an alternative and/or a choice task. (It could also be degrees of attribute relevance (a1, a2 ,…, an) from totally relevant (not ignored) to totally irrelevant (ignored)).These belief masses define a function called the basic belief mass function (Shafer, 1976). We write a belief mass assigned to a subset B as m(B), where B could be a single element, or a subset of two, a sub-set of three (e.g., degrees of attribute preservation), and so on, or the entire frame, .…”

Section: An Illustration Of How D-s May Be Implemented In a Travel Chmentioning

confidence: 99%

“…A number of theories have been developed that focus on degrees of belief including Subjective Probability Theory (Ramsey 1931;Savage 1954), Dempster-Shafer Theory (Dempster 1967, 1968Shafer 1976), and Possibility Theory (Zadeh 1978;Dubois and Prade 1988). The essential difference between the three theories can be best summarized as different mathematical properties (defined in detail in later sections but noting that A and B are any two variables or events or subsets of variables) that are used to account for degrees of belief.…”

Section: Introductionmentioning

confidence: 99%

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A scoping inquiry into the potential contribution of Subjective Probability Theory, Dempster–Shafer Theory and Possibility Theory in accommodating degrees of belief in traveller behaviour research

Hensher

2014

Travel Behaviour and Society

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There is a small but growing interest in traveller behaviour research on investigating ways to identify and quantify degrees of belief (as subjective probabilities or other propositions) associated with behavioural responses, especially in the context of popular travel choice methods such as stated choice experiments, as a way of adding to our understanding of decision making in real-world contexts that are associated with inevitable risk and uncertainty. This paper reviews three major theories that are not well known in the transportation literature that have been developed in psychology and decision sciences to accommodate belief, namely Subjective Probability Theory, Dempster-Shafer Theory and Possibility Theory. We focus on how degrees of belief are measured in these theories. The key elements of each theoretical approach are compared, including their mathematical properties and evidence patterns. Despite their being few applications to date in transportation, the review promotes the relevance of accounting for degrees of belief in travel choice analysis. Keyword: belief, degree of belief, Subjective Probability Theory, Dempster-Shafer Theory, Possibility TheoryAcknowledgment: This study is supported by the Australian Research Council Discovery Program Grant DP110100454 titled "Assessment of the commuter's willingness to pay a congestion charge under alternative pricing regimes and revenue disbursement plans". We also thank two referees and the Becky Loo for comments.

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The average decision maker and its properties utilizing the generalized information system model

Yovits¹,

Kleyle²

1993

J. Am. Soc. Inf. Sci.

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Perspectives on the theory and practice of belief functions

Cited by 337 publications

References 83 publications

Retinal Vessel Detection and Measurement for Computer-aided Medical Diagnosis

Retinal Vessel Detection and Measurement for Computer-aided Medical Diagnosis

A scoping inquiry into the potential contribution of Subjective Probability Theory, Dempster–Shafer Theory and Possibility Theory in accommodating degrees of belief in traveller behaviour research

The average decision maker and its properties utilizing the generalized information system model

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