formmatching

Formmatching is the computational task of determining correspondences between shapes or forms in data, with the goal of identifying whether shapes are the same or how they relate to one another. It is used across pattern recognition, computer vision, computational geometry, and morphometrics. Depending on the domain, form matching may seek invariance to transformations such as translation, rotation, scaling, or more complex non-rigid deformations.

Forms can be represented as point clouds, meshes, curves, graphs, or implicit functions. Matching proceeds by describing each form with features or descriptors, computing a similarity measure, and searching for a correspondence or alignment. Common approaches include rigid matching (Procrustes analysis, Iterative Closest Point), non-rigid or elastic matching, and graph or spectral matching. Local descriptors such as Shape Context, Spin Images, or histogram-based features are often used to compare partial views. In 3D, distance measures such as Chamfer distance, Earth Mover's Distance, and spectral similarity are typical scoring tools.

Applications span 3D object recognition and retrieval, medical image analysis for matching anatomical structures, biometric identification, handwriting or symbol recognition, manufacturing quality control, morphometric analysis in biology, and cultural heritage digitization.

Key challenges include noise and occlusion, incomplete data, large intra-class variation, non-rigid deformation, and computational complexity. Selecting robust representations and descriptors suitable to a domain, as well as reliable evaluation benchmarks, remains an active area of research.

See also: pattern recognition, shape matching, point set registration, morphometrics, computer vision, computational geometry.