shapeoften

Shapeoften is a proposed metric in computational geometry and pattern analysis that aims to quantify the prevalence of particular shapes within a dataset of geometric objects. It combines aspects of shape similarity and frequency to identify motifs that recur across items.

Formal definition: Given a collection S of shapes, each shape s is represented by a descriptor vector d(s) (for example Fourier descriptors, Zernike moments, or boundary-based features). A similarity relation is defined using a distance function dist(d(s1), d(s2)). Shapes are grouped into clusters of similar shapes using a threshold or a clustering algorithm. If cluster i contains n_i shapes, then a shape motif corresponding to i has a strength proportional to n_i/N, where N is the total number of shapes in S. The shapeoften score for an individual shape s in cluster i can be defined as n_i / N, while the motif frequency is the set {n_i/N} across all clusters.

Properties: Shapeoften is sensitive to the choice of descriptor and clustering threshold. Depending on the descriptor, certain transformations such as rotation or scaling may be normalized, providing partial invariance. Results can be affected by noise, sampling density, and the representation of shapes.

Applications: Identifying common motifs in design corpora, analyzing shapes in visual datasets, guiding feature extraction in computer vision, and informing generative design to reproduce prevalent shapes.

Example: In a dataset of vector graphics, circular and elliptical shapes often form large clusters. The shapeoften score for circles would be high, indicating a prevalent motif.

History and context: Shapeoften has been discussed as a concept in motif mining and shape analysis, with related ideas including shape descriptors, motif mining, and cluster-based frequency analysis.