active shape model

An active shape model (Cootes and Taylor) fits a flexible outline to the boundary of an object in an image — the contour of a face, the silhouette of a hand, the edge of a heart chamber — while only allowing it to deform in ways that real examples of that object actually deform. The intuition is a smart elastic band: you mark the object with a fixed set of landmark points (corners of the eyes, tip of the nose), learn from many annotated training shapes how those points are allowed to move together, and then let the band snap to image edges, but only into shapes that look plausible. A naive snake or edge-follower would happily contort into nonsense; an ASM is constrained to stay shaped like the thing it models.

The statistical core is a point distribution model. You represent each training shape as the concatenated coordinates of its landmarks, align all the training shapes to remove differences of position, scale, and rotation (Procrustes analysis), and run PCA on the aligned landmark coordinates. The result is a mean shape plus a few principal modes of variation — directions in which the whole set of points moves in a correlated way (a mouth opening, a face turning). Any valid shape is then the mean plus a small weighted sum of these modes, and crucially the weights are clamped to a sensible range (typically within about three standard deviations) so the model can only produce shapes statistically like the training set. Fitting alternates two steps: for each landmark, search a short profile across the image boundary to find the nearest strong edge and propose moving the point there; then project that proposed shape back onto the allowed model (re-estimate pose and the mode weights, clamping them), which pulls any implausible suggestions back into a legal shape. Repeat until it settles.

Active shape models matter because they cleanly separate appearance evidence (where the edges are) from a learned shape prior (what shapes are allowed), and they introduced landmark-based, statistically constrained fitting that became central to face analysis and medical image segmentation. Their weaknesses are the cost of dense manual landmark annotation, sensitivity to initialization (a bad start lands in the wrong local optimum), and reliance on edge profiles that can be fooled by clutter. The active appearance model extended ASM by also modeling the texture inside the shape; and modern landmark localization (cascaded regression, and CNN/heatmap-based face-alignment networks) learns the shape-and-appearance mapping directly, but the point-distribution-model concept of a low-dimensional, constrained shape space endures.