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Segmentati

Snakes

Manasi Datar's webpage.

Theory

When the snake coordinate vector is defined parametrically as $v(s) = (x(s), y(s))$, the total energy of the snake is defined as $$ E^*_{snake} = \int E_{snake}(v(s))ds = \int E_{int}(v(s))ds + \int E_{ext}(v(s))ds $$ $$ E_{int} = E_{cont} + E_{curv} $$ The two energies are given by the first and second derivatives of the contour v(s). $$ E_{ext} = -|| \nabla I || $$

Discrete implementation

Model the contour as $ c = {p1,p2,...,pN} $, now the cost function becomes $$ E = \sum_{i=1}^{N} (\alpha_i E_{cont} + \beta_i E_{curv} + \gamma_i E_{image}) $$