Fuzzy Circularity: A New Fuzzy Shape-Based Descriptor of the Object

This paper introduces a new family of fuzzy shape measures, called fuzzy circularity, to evaluate the degree to which a considered fuzzy shape matches a fuzzy disk. A new family of fuzzy shape-based measures ranges the interval (0, 1] where a maximum value equal to 1 is reached if and only if the shape under consideration is a fuzzy disk. This family is theoretically well grounded having the behavior that corresponds to human perception and can be predicted in advance. Additionally, a new family of fuzzy shape-based measures is invariant to rotation, translation, and scaling of the considered fuzzy shape. Various experiments on both synthetically generated and real images are included to provide a better understanding of the behavior of the new measures and to confirm the theoretically proven results. The performance of the new family of fuzzy circularity is extensively tested on several standard, well-known image datasets such as MPEG-7 CE-1, Animal, Swedish Leaf, and Galaxy Zoo datasets. Experimental evaluations also illustrate the effectiveness and advantages of the new shape descriptors in various object classification and recognition tasks by comparing them with other known analysis approaches.