Shapeform

Shapeform is a term used in geometry and related fields to describe a compact descriptor that captures the essential form of a geometric object in a way that is invariant under certain transformations, such as translation, rotation, and scaling. In this sense, a shapeform acts as a concise fingerprint of a shape, emphasizing the overall silhouette and structural properties rather than exact size or position.

Although the exact definition of shapeform varies by author, it commonly consists of a vector of features derived from the object's boundary or interior, including boundary descriptors, curvature measures, Fourier descriptors, and shape moments. The goal is to produce a representation that enables reliable shape comparison and recognition across different instances of the same type of object.

Computing a shapeform typically involves normalizing the shape to remove position, orientation, and size effects, then extracting a set of invariant features and assembling them into a fixed-length vector. This can include normalization steps, computation of Hu moments or Zernike moments, and the use of Fourier descriptors on the boundary.

Shapeforms are used in object recognition, image retrieval, computer-aided design, font analysis, and pattern matching. They support tasks such as nearest-neighbor search in shape space, clustering of similar shapes, and deformation analysis. A related concept is the shape descriptor, with shapeform serving as a particular instantiation or framework for such descriptors.

Because the term is not standardized, different sources may define shapeform differently or use alternative terminology. In practice, shapeform is often described within the broader context of shape analysis, geometry processing, or computer vision.