{'fraction_non_alphanumeric': 0.01877346683354193, 'fraction_numerical': 0.0, 'mean_word_length': 5.6115702479338845, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Fuzzy objects and their boundaries

Measured data are inherently inaccurate. Operations done on data for defining, visualizing, manipulating and analyzing object information should attempt to retain these inaccuracies as accurately as possible. The theory of fuzzy sets is a proper mathematical vehicle for this purpose. In this attempt, topological notions such as adjacency, connectedness, and boundary need to be developed starting from fuzzy sets. We develop such a framework in this paper and present algorithms for finding fuzzy connected components and boundaries in digital imagery. We demonstrate the usefulness of these algorithms in medical applications, particularly in separating objects that come close together which are otherwise difficult to segment using hard (non-fuzzy) criteria.