shapedefined

Shapedefined is a conceptual framework used in geometry and vision research to assign a formal, canonical definition to a geometric shape by encoding its structural properties into a compact representation. The aim is to represent a shape by a descriptor vector that is stable under common transformations, such as translation, rotation, and scaling, allowing shapes that are geometrically equivalent to share the same or closely related identifiers.

Key components include invariant features that capture boundary shape and topology. Examples often used include curvature distribution along the boundary, Fourier descriptors of the boundary, Zernike moments for radial and angular structure, as well as topological measures like Euler characteristic and genus. By combining these features and applying normalization, shapedefined produces a canonical form or label for the shape within a chosen equivalence class.

Typical workflow involves extracting the region or boundary, computed descriptors, normalization to achieve invariance, and generation of the canonical representation. The resulting descriptor can be used for shape retrieval, classification, or matching in databases, computer-aided design, and 3D object recognition.

Limitations include sensitivity to noise, partial occlusion, non-rigid deformations, and the choice of descriptors affecting discriminability. No single set of features fully captures all aspects of shape, so multiple descriptor schemes may be combined.

See also: shape descriptor, isometry, topology, pattern recognition, computer vision.