Lengthsshape

Lengthsshape is a descriptor used in geometry and pattern analysis to encode both the extent and the form of an object or region. It blends measurements of length with quantitative shape features to create a compact representation that supports comparison, classification, and retrieval across varying sizes and orientations.

Typically, lengthsshape combines a length measure, such as the major axis length of a fitted ellipse or the object's bounding-box length, with a set of shape descriptors, such as aspect ratio, curvature statistics, and Fourier or Zernike shape moments. Depending on the application, the descriptor can be scalar (a single length value plus one shape score) or vector-valued (a multi-dimensional feature vector). Normalization is common to achieve invariance to scale, translation, and rotation.

Computation workflow: obtain a segmented region or contour, compute a length feature (e.g., major axis length, perimeter-to-area ratio), compute shape features (curvature distribution, Fourier descriptors), and fuse them into the lengthsshape vector used by downstream tasks such as classification or matching.

Applications include biology (morphology of leaves or cells), materials inspection (elongated fibers), and computer vision (object recognition of elongated shapes). Limitations include sensitivity to segmentation quality and potential loss of local detail if the representation is overly compact. See also: shape descriptor, aspect ratio, eccentricity, Fourier descriptor.