Editing Image segmentation (section)

=== Parametric methods ===
[[Lagrangian relaxation|Lagrangian]] techniques are based on parameterizing the contour according to some sampling strategy and then evolving each element according to image and internal terms. Such techniques are fast and efficient, however the original "purely parametric" formulation (due to Kass, [[Andrew Witkin|Witkin]] and [[Demetri Terzopoulos|Terzopoulos]] in 1987 and known as "[[Snake (computer vision)|snakes]]"), is generally criticized for its limitations regarding the choice of sampling strategy, the internal geometric properties of the curve, topology changes (curve splitting and merging), addressing problems in higher dimensions, etc.. Nowadays, efficient "discretized" formulations have been developed to address these limitations while maintaining high efficiency. In both cases, energy minimization is generally conducted using a steepest-gradient descent, whereby derivatives are computed using, e.g., finite differences.