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On analysis of discrete spatial fuzzy sets in 2 and 3 dimensions

Sladoje, Nataša (2005). On analysis of discrete spatial fuzzy sets in 2 and 3 dimensions. Diss. (sammanfattning/summary) Uppsala : Sveriges lantbruksuniv., Acta Universitatis agriculturae Sueciae, 1652-6880 ; 2005:112
ISBN 91-576-6911-2
[Doctoral thesis]

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Abstract

The use of fuzzy set theoretical approaches for representing spatial relationships provides an intuitive way of expressing the diffuse localization and limits of image components. Fuzziness can be present in images as a consequence of noise introduced during the imaging process, in which case it should preferably be removed, and as imprecision inherent to the observed objects, in which case it provides important information that should be utilized during the image analysis process. A general goal for the research presented in this thesis has been to develop shape analysis methods that can be applied to fuzzy segmented images in 2D and 3D. A demand for the developed methods has been to respect the specific nature of a fuzzy representation of the studied shapes and, especially, the consequences of discretization. We have studied representation and reconstruction of a shape by using moments of both its crisp and fuzzy discretization. We show, both theoretically and statistically, that the precision of estimation of moments of a shape is increased if a fuzzy representation of a shape is used, instead of a crisp one. The signature of a shape based on the distance from the shape centroid is studied and two approaches for its calculation for fuzzy shapes are proposed. A comparison of the performance of fuzzy and crisp approaches is carried out through a statistical study, where a higher precision of shape signature estimation is observed for the fuzzy approaches. The measurements of area, perimeter, and compactness, as well as of volume, surface area, and sphericity, are considered, too. New methods are developed for the estimation of perimeter and surface area of a discrete fuzzy shape. It is shown through statistical studies that the precision of all the observed estimates increases if a fuzzy representation is used and that the improvement is more significant at low spatial resolutions. In addition, a defuzzification method based on feature invariance is designed, utilizing the improved estimates of shape characteristics from fuzzy sets to generate crisp discrete shapes with the most similar shape characteristics. This defuzzification method, performed on a fuzzy segmentation, can be seen as an alternative to a crisp segmentation of an image. The presented results can be applied wherever precise estimates of shape properties are required, especially in conditions of limited spatial resolution. We have showed, either theoretically, or empirically, that membership resolution available can be successfully utilized to overcome a lack of spatial resolution.

Authors/Creators:Sladoje, Nataša
Title:On analysis of discrete spatial fuzzy sets in 2 and 3 dimensions
Year of publishing :October 2005
Volume:2005:112
Number of Pages:85
Papers/manuscripts:
NumberReferences
ALL1. Žunić, J., Sladoje, N. (2000). Efficiency of Characterising Ellipses and Ellipsoids by Discrete Moments. IEEE Trans. on Pattern Analysis and Machine Intelligence 22(4):407–414. 2. Sladoje, N., Lindblad, J. (2005). Estimation of Moments of Digitized Objects with Fuzzy Borders. In Proc. 13th Intern. Conf. on Image Analysis and Processing, Lecture Notes in Computer Science 3617:188–195. Springer-Verlag. 3. Sladoje, N., Lindblad, J. (2005). Representation and Reconstruction of Disks by Fuzzy Discrete Moments. Submitted for journal publication. 4. Chanussot, J., Nyström, I., Sladoje, N. (2005). Shape Signatures of Fuzzy Star-Shaped Sets Based on Distance from the Centroid. Pattern Recognition Letters 26(6):735–746. 5. Sladoje, N., Nyström, I., Saha, P. K. (2003). Perimeter and Area Estimations of Digitized Objects with Fuzzy Border. In Proc. Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science 2886:368–377. Springer-Verlag. 6. Sladoje, N., Nyström, I., Saha, P. K. (2005). Measurements of Digitized Objects with Fuzzy Borders in 2D and 3D. Image and Vision Computing 23:123–132. 7. Sladoje, N., Lindblad, J., Nyström, I. (2005). Defuzzification of Spatial Fuzzy Sets by Feature Invariance. Manuscript.
Place of Publication:Uppsala
ISBN for printed version:91-576-6911-2
ISSN:1652-6880
Language:English
Publication Type:Doctoral thesis
Full Text Status:Public
Agris subject categories.:U Auxiliary disciplines > U40 Surveying methods
U Auxiliary disciplines > U10 Mathematical and statistical methods
Subjects:Not in use, please see Agris categories
Agrovoc terms:image analysis, imagery, methods, mathematical models, surface area, volume, measurement
Keywords:digital image analysis, shape description, fuzzy sets, moments, signature, area, perimeter, volume, surface area, defuzzification, multiple criteria evaluation
URN:NBN:urn:nbn:se:slu:epsilon-776
Permanent URL:
http://urn.kb.se/resolve?urn=urn:nbn:se:slu:epsilon-776
ID Code:963
Department:(S) > Centrum för bildanalys (900701-031231?)
Deposited By: Natasa Sladoje
Deposited On:26 Oct 2005 00:00
Metadata Last Modified:02 Dec 2014 10:08

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