Statistical Shape Models (SSMs)

The shape of an object is represented by a set of n points, which may be in any
dimension. Commonly the points are in two or three dimensions. Shape is usually defined as
that quality of a configuration of points which is invariant under some transformation. In two
or three dimensions we usually consider the Similarity transformation (translation, rotation and scaling). The shape of an object is not changed when it is moved, rotated or scaled.

http://www.cmlab.csie.ntu.edu.tw/~cyy/learning/papers/PCA_ASM.pdf
https://en.wikipedia.org/wiki/Statistical_shape_analysis

Active shape models (ASMs)

Active shape models are statistical models of the shape of objects which iteratively deform to fit to an example of the object in a new image, developed by Tim Cootes and Chris Taylor in 1995.[1]
The shapes are constrained by the PDM (point distribution model) Statistical Shape Model to vary only in ways seen in a training set of labelled examples. The shape of an object is represented by a set of points (controlled by the shape model). The ASM algorithm aims to match the model to a new image.

The key idea of ASMs is to constrain the behavior of deformable models using
the PDM

Active Appearance Models (AAMs)

An active appearance model (AAM) is a computer vision algorithm for matching a statistical model of object shape and appearance to a new image. They are built during a training phase. A set of images, together with coordinates of landmarks that appear in all of the images, is provided to the training supervisor.

A limitation of the ASM is that its prior model does not consider gray-level variation of the object instance across images. To overcome this difficulty, Edwards, Cootes, and Taylor [84–86] proposed an extension to the ASM, called active appearance
models (AAM). In AAM, a new prior model is constructed using both shape and grey-level information.

Active contour model (Snake)

Active contour model, also called snakes, is a framework in computer vision for delineating an object outline from a possibly noisy 2D image. The snakes model is popular in computer vision, and snakes are greatly used in applications like object tracking, shape recognition, segmentation, edge detection and stereo matching.

GVF snake model
The balloon model
Diffusion snakes model
Geometric active contours

Deformable Models

Deformable models are curves or surfaces defined within an image domain that can move under the influence of internal forces, which are defined within the curve or surface itself, and external forces, which are computed from the image data.
Snakes: Active Contours by Kass, Witkin and Terzopoulos
level set
active shape models

Various names, such as snakes, active contours or surfaces, balloons, and deformable contours or surfaces, have been used in the literature to refer to deformable models.