Tail-Preserving Shape Partitioning via Multi-Orientation Centroid-Line Extraction and Fuzzy Influence-Zone Assignment

Meaningful partitioning of 2D binary shapes remains a challenging problem in shape analysis because many existing methods rely mainly on local geometric rules or skeleton simplification, which often struggle to separate the main body of a shape from its protruding parts in a perceptually meaningful way. This limitation becomes more evident in shapes with thin limbs, branching structures, or irregular extensions, where preserving topology while achieving human-consistent decomposition is difficult. We present a fully automatic framework for the hierarchical partitioning of 2D binary shapes into semantically meaningful core bodies and protruding limbs (tails). The pipeline begins by generating candidate structural lines through multi-directional centroid tracking along horizontal, vertical, and diagonal (±45°) bands. Three direction-specific Sugeno fuzzy controllers first evaluate these lines based on normalized length, angular alignment, and minimum distance to the boundary. A second pair of fuzzy systems then classifies segments as either tails or core parts using thickness statistics derived from the distance transform. For ambiguous merged tail groups, iterative midpoint splitting is applied until stable labeling is achieved. High-curvature boundary corners are then detected via signed turning-angle analysis, and candidate cutting rays are assessed through exact region splitting, tail area measurement, and label purity analysis. An adaptive third-stage fuzzy controller ranks these candidates according to cut length, purity, and area. The highest-scoring non-overlapping cuts are executed iteratively, progressively peeling peripheral parts while preserving the overall topology and symmetry of the shape. The proposed framework is evaluated on a targeted subset of 32 categories from the 2D Shape Structure Dataset Results on this evaluated subset indicate that the method produces coherent and topologically consistent partitions, with competitive agreement with the available human-annotated references. This training-free framework provides an interpretable tool for 2D shape analysis, with potential applications in object recognition, computer animation, and symmetry studies.