Contribució a l'estudi dels conjunts extensionals de les relacions d'indistingibilitat i la seva aplicació a la representació d'imatges de ressonància magnètica
This thesis can be summarized in the following sentence: All scientific models, for instance structural atlases of brain MRI, can be read in terms of fuzzy extensional sets. The work done in this doctoral thesis backs up and explains how this interpretation can be performed and provides future lines...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | catalán |
| OAI Identifier: | oai:upcommons.upc.edu:2117/96314 |
| Acceso en línea: | https://hdl.handle.net/2117/96314 https://dx.doi.org/10.5821/dissertation-2117-96314 |
| Access Level: | acceso abierto |
| Palabra clave: | Cervell -- Imatges per ressonància magnètica Conjunts borrosos Àrees temàtiques de la UPC::Enginyeria biomèdica |
| Sumario: | This thesis can be summarized in the following sentence: All scientific models, for instance structural atlases of brain MRI, can be read in terms of fuzzy extensional sets. The work done in this doctoral thesis backs up and explains how this interpretation can be performed and provides future lines of application of the results developed in the field of automatized analysis of brain MRI neuroimages. Does this make any sense? Why should a framework be developed in order to apply fuzzy techniques in brain analysis? The first part of this work asks itself precisely this question, the why and for what of the thesis proposed. Uncertainty, as a multidimensional phenomenon, is studied and tried to discriminate the different sources and natures of vagueness, imprecision, partial truth and knowledge¿ These epistemological questions are studied all along the perception and knowledge construction process and analyzed why it does make sense to use fuzzy tools to represent some of these phenomena, either in the general and a medical case. To develop this part of the thesis the autor has contacted with 45 international experts on the field, who have helped to build the discourse that backs up the sense of the thesis. Following, the technical part of the thesis is developed. The main objects worked with are indistinguishability operators and those related such as extensional (observable) fuzzy subsets and upper and lower extensional approximation operators. These concepts are fundamental for the following construction proposed. One of the main results of this work is that, fixed a t-norm, there is a structural isomorphism between the lattices of indistinguishabilities, sets of extensional fuzzy subsets and upper and lower approximation operators. This result is new and enlightens the previous studies developed around these objects. It is studied as well how they are interrelated when further aggregation operators are considered such as quasi-arithmetic weighted means, either in a finite and infinite universe of discourse. An open problem of indistinguishability operators theory is how to approximate, minimizing the error, an arbitrary set by an extensional one. In the third chapter of this work 3 new methods are proposed for Archimedean t-norms and one for the Minimum t-norm. All the methods proposed improve significantly the results obtained by current methods in the literature. Given all these results, the theoretical framework that justifies the reinterpretation of scientific models proposed is solid enough. But what is a scientific model? This apparently straightforward question has no consensuated answer in the literature. In this work a definition is proposed and Wittgenstein's figurative theory is used to understand the essence and limits of the concept. The spectrum of a phenomenon is defined and its inevitability in any modelled phenomenon is justified. This spectrum is identified with observable (extensional) sets in the model and, taking into account the particular issues a specific phenomenon and model may have, this way it is possible to bring fuzzy techniques to the interpretation of the particular sample and model. An interesting and straightforward application is the definition of model-based distance functions. Finally, the proposed interpretation is applied in the specific field of analysis of of MRI brain structural atlases. It's important to highlight that this part of the work is just a proposal that should be studied further in future work in order to analyze proper and rigorously its benefits. In this proposal it is shown how an atlas can be particularized given a real human brain MRI and in the two appendices of this work two alternative future lines of research are given: how to define the atlas-based distance and use it in a segmentation process and how to build an own atlas given a local sample. |
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