shapematching

Shapematching is the computational task of finding correspondences between shapes or assessing similarity between shape representations. It is used for object recognition, model retrieval, alignment, deformable registration, and morphometrics. The problem can be posed for 2D shapes such as contours and boundaries or 3D shapes such as surfaces and point clouds. It may seek a rigid alignment (rotation, translation, possibly scale) or account for non-rigid deformations.

Common representations include boundary-based contours, landmark sets, surface meshes, and feature-based descriptors such as Fourier descriptors, Zernike moments, Shape Context, and spin images. Similarity measures include distance metrics (Hausdorff, Chamfer), Procrustes analysis for alignment, and more complex metrics on graphs or manifolds. Spectral approaches use eigenfunctions of Laplacians to compare shapes.

Algorithm families encompass template-based matching, correspondence estimation via feature matching, dynamic programming on sequences, graph matching, and elastic registration using thin-plate splines or non-rigid iterative closest point. More recently, learning-based shapematching uses neural networks to embed shapes in a latent space or to predict correspondences; techniques include CNNs and point-network approaches for 3D shapes and Transformer-based models.

Applications span computer vision, medical imaging, robotics, computer-aided design, animation, and morphometrics. Challenges include occlusion, partial data, noise, non-rigid deformations, invariance to scale, rotation and topology changes, and computational complexity. Evaluation typically relies on benchmark datasets with ground-truth correspondences or retrieval metrics.