Variational approaches have been proposed for solving many inverse problems in early vision, such as in the computation of optical flow, shape from shading, and energy-minimizing active contour models. In general however, variational approaches do not guarantee global optimality of the solution, require estimates of higher order derivatives of the discrete data, and do not allow direct and natural enforcement of constraints.

A decision is made from only m possible choices corresponding to the possible places to move the snaxel. The energy function is evaluated at each of these and the point with the smallest energy is chosen. This decision is made for each snaxel in the snake.

Exhaustive enumeration involves trying each possible combination of each snaxel moved within its neighborhood. This involves m raised to the n different computations of the energy function. This is generally too computationally intensive to be used.

In order to reduce the effort required to search over all the different possibilities to which each snaxel can be moved, the movement in a single iteration of each snaxel is generally constrained to be within some neighborhood (containing m points) of the snaxel's current location. This neighborhood is commonly taken to be a 3x3 grid centered at the current location. This allows the snaxel to move at most to an immediately adjacent location. Now, for each snaxel, one position from only m possible positions must be chosen.

The portion of the energy function representing constraints internal to the snake.