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Active contour model, also called snakes, is a framework for delineating an object outline from a possibly noisy 2D image.

This framework attempts to minimize an energy associated to the current contour as a sum of an internal and external energy:

• The external energy is supposed to be minimal when the snake is at the object boundary position. The most straightforward approach consists in giving low values when the regularized gradient around the contour position reaches its peak value.
• The internal energy is supposed to be minimal when the snake has a shape which is supposed to be relevant considering the shape of the sought object. The most straightforward approach grants high energy to elongated contours (elastic force) and to bended/high curvature contours (rigid force), considering the shape should be as regular and smooth as possible.

Latter can be written as:

$E_{internal} = \alpha |\textbf{v}_i - \textbf{v}_{i-1}|^2 + \beta |\textbf{v}_{i-1} - 2 \textbf{v}_{i} + \textbf{v}_{i+1}|^2$

where the v vectors are the coordinates of the contour points. The first term represents the elastic energy (increases with length), the second is the curvature (as it is an approximation for the second derivative, assuming a smooth contour).

This model is highly popular in computer vision, and led to several developments in 2D and 3D. Namely, in two dimensions, the active shape model represents a discrete version of this approach taking advantage of the point distribution model to restrict the shape range to an explicit domain learned from a training set.

• Michael Kass, Andrew Witkin and Demetri Terzopoulos (1988). "Snakes: active contour models". International Journal of Computer Vision: 321–331.   [1]

Active contour, also called snakes, is a framework for delineating an object outline from a possibly noisy 2D image.

This framework attempts to minimize an energy associated to the current contour as a sum of an internal and external energy:

• The external energy is supposed to be minimal when the snake is at the object boundary position. The most straightforward approach consists in giving low values when the regularized gradient around the contour position reaches its peak value.
• The internal energy is supposed to be minimal when the snake has a shape which is supposed to be relevant considering the shape of the sought object. The most straightforward approach grants high energy to elongated contours (elastic force) and to bended/high curvature contours (rigid force), considering the shape should be as regular and smooth as possible.

This model is highly popular in computer vision, and led to several developments in 2D and 3D. Namely, in two dimensions, the active shape model represents a discrete version of this approach taking advantage of the point distribution model to restrict the shape range to an explicit domain learned from a training set.