ASM, Active Shape Models

Active Shape Models (ASM) represent a statistically-based deformable modeling approach commonly used for object shape modeling and matching. The core concept involves learning shape variation patterns from a set of annotated training samples (such as hand contours) to construct a flexible model capable of adapting to new instances.

Using hand deformation as an example, consider having 18 hand image samples with each annotated using 72 landmarks (key points). The initial processing step requires Procrustes analysis alignment to eliminate translation, rotation, and scaling effects, preserving only genuine shape variations. This preprocessing ensures the purity of subsequent statistical analysis by normalizing all training shapes to a common coordinate frame.

Following alignment, Principal Component Analysis (PCA) extracts dominant modes of shape variation. PCA generates eigenvectors (termed "shape modes") where each vector represents a typical shape variation direction (e.g., finger bending, palm opening). The model's flexibility manifests through new shapes being synthesized as linear combinations of these principal components, enabling coverage of plausible deformations absent from the training set.

ASM's strength lies in combining prior knowledge with local search – during new image matching, the model constrains shapes according to statistical patterns while dynamically adjusting landmark positions using local features like edge detection. This methodology finds extensive applications in medical image analysis, facial feature localization, and other computer vision domains where shape variability requires statistical modeling.

Implementation typically involves: 1) Landmark configuration using Procrustes alignment via procrustes() function, 2) PCA decomposition through pca() to obtain eigenvalues/eigenvectors, 3) Iterative matching using multi-resolution search with Mahalanobis distance optimization. Key parameters include the number of principal components retained (typically 90-98% variance) and search range constraints.