Generalizations of Choquet-like Integrals by Restricted Dissimilarity Functions Applied to Multi-Channel Edge Detection Problems

Edge detection is a fundamental component of vision tasks, yet the fusion stage that combines multi-cue evidence has received limited attention. We explore the use of a family of Choquet-based fusion operators generalised by restricted dissimilarity functions for robust, training-free, single-scale edge detection on the BSDS500 dataset. Local cues are extracted from eight connected neighbours after Gaussian or Gravitational smoothing; ordered samples are aggregated with a fuzzy power measure using three operator families: d-CF, d-XC, and d-CC integrals. Binary edge maps are obtained through non-maximum suppression and Rosin thresholding. Evaluation follows the Bezdek framework for edge detection, utilising the Estrada–Jepson correspondence, and extracts precision, recall, and the F-score. All inferential statistics are restricted to within-family comparisons among our variants. The main results are that gravitational smoothing consistently improves performance, and the best performance is achieved with the absolute-difference restricted dissimilarity under gravitational smoothing. Under Gaussian smoothing, the best performance is obtained with the modulus of the squared difference and with the squared difference of the roots. These findings indicate that restricted-dissimilarity-based Choquet operators, particularly d-CC integrals with gravitational smoothing, form a straightforward and interpretable fusion mechanism, motivating further analysis of component interactions and multi-scale extensions.