Modeling and measuring the spatial relation "along": Regions, contours and fuzzy sets

The analysis of spatial relations among objects in an image is an important vision problem that involves both shape analysis and structural pattern recognition. In this paper, we propose a new approach to characterize the spatial relation along, an important feature of spatial configurations in space that has been overlooked in the literature up to now. We propose a mathematical definition of the degree to which an object A is along an object B, based on the region between A and B and a degree of elongatedness of this region. In order to better fit the perceptual meaning of the relation, distance information is included as well. In order to cover a more wide range of potential applications, both the crisp and fuzzy cases are considered. In the crisp case, the objects are represented in terms of 2D regions or ID contours, and the definition of the alongness between them is derived from a visibility notion and from the region between the objects. However, the computational complexity of this approach leads us to the proposition of a new model to calculate the between region using the convex hull of the contours. On the fuzzy side, the region-based approach is extended. Experimental results obtained using synthetic shapes and brain structures in medical imaging corroborate the proposed model and the derived measures of alongness, thus showing that they agree with the common sense. (C) 2011 Elsevier Ltd. All rights reserved.

Fuzzy linguistic model for bioelectrical impedance vector analysis

Backgrounds Ea aims: The boundaries between the categories of body composition provided by vectorial analysis of bioimpedance are not well defined. In this paper, fuzzy sets theory was used for modeling such uncertainty. Methods: An Italian database with 179 cases 18-70 years was divided randomly into developing (n = 20) and testing samples (n = 159). From the 159 registries of the testing sample, 99 contributed with unequivocal diagnosis. Resistance/height and reactance/height were the input variables in the model. Output variables were the seven categories of body composition of vectorial analysis. For each case the linguistic model estimated the membership degree of each impedance category. To compare such results to the previously established diagnoses Kappa statistics was used. This demanded singling out one among the output set of seven categories of membership degrees. This procedure (defuzzification rule) established that the category with the highest membership degree should be the most likely category for the case. Results: The fuzzy model showed a good fit to the development sample. Excellent agreement was achieved between the defuzzified impedance diagnoses and the clinical diagnoses in the testing sample (Kappa = 0.85, p < 0.001). Conclusions: fuzzy linguistic model was found in good agreement with clinical diagnoses. If the whole model output is considered, information on to which extent each BIVA category is present does better advise clinical practice with an enlarged nosological framework and diverse therapeutic strategies. (C) 2012 Elsevier Ltd and European Society for Clinical Nutrition and Metabolism. All rights reserved.