Linear Diophantine Fuzzy Graph Connectedness for Uncertainty‑Aware Kidney Segmentation in CT Images with LDF‑TOPSIS Method Selection
Keywords:
Diophantine fuzzy graph, Fuzzy connectedness, Image segmentation, Kidney tumor, Computed tomography, TOPSIS, Decision analyticsAbstract
We introduce a linear Diophantine fuzzy (LDF) graph model for the segmentation of kidneys and renal masses in computed tomography (CT) and use the same LDF framework for the selection of a segmentation method. A CT slice is represented by a superpixel graph whose vertices and edges carry LDF values: the membership and non-membership degrees describe photometric evidence, while the reference parameters, coupled by the Diophantine constraint, describe geodesic and boundary evidence. We prove that the construction satisfies the axioms of an LDF graph and that it reduces to the intuitionistic fuzzy case when no topological information is present. The segmentation is defined through LDF fuzzy connectedness, with the threshold determined by a stability criterion on the nested family of ε-clusters (LDF-FC). On thirteen test targets taken from public kidney CT collections, LDF-FC attained a mean Dice coefficient of 0.718 and a 95th percentile Hausdorff distance of 20.4 pixels, compared with 0.669 and 41.8 for the random walker and 0.603 and 40.1 for the intuitionistic variant. Under four noise models the method was significantly better than each of the eight competing methods (Wilcoxon signed-rank test, p < 0.03). For the selection problem we propose an LDF-TOPSIS model with entropy weights in which the reference parameters encode the dispersion of the observed performance. The model ranked LDF-FC first (closeness coefficient 0.904), and the ranking was stable with respect to the reference parameters and the criteria weights.
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