LMS uses a negative feedback to diminish the error by altering the filter coefficients in the way of the negative of the

gradient vector to get the least mean square error (MSE).

The direction of an edge at an arbitrary point (x, y) is orthogonal to the direction, [theta](x, y), of the

gradient vector at the point.

The improved cost function integrates both modulus and phase components of the

gradient vector and then combines them with SAD cost, leading to a superior accuracy.

However, there exist boundary problems on computing the

gradient vector of powers for derivative based methods.

At each point in space (FIGURE 1) where there exists a heat flux vector and temperature

gradient vector, the Bn scalar at that point is calculated as:

7) Finally, the

gradient vector is normalized and threshold to a particular level for display of edge map information.

which shows that X is a

gradient vector field in the sense of Okumura (see [7]).

The direction of the

gradient vector is combined with the light-direction vector to produce a shading effect in which boundaries facing the light source are enhanced and those facing away from the light source are diminished.

They define the components of the

gradient vector as:

Having fixed a certain direction, we should consider the scalar product of the unit vector of this direction and

gradient vector [F'.

To make the final result relatively insensitive to the initial conditions, Xu and Prince 8,9] proposed the

Gradient Vector Field (GVF) model, which allows for flexible initialization of the snake and helps convergence to boundary concavities.

One of the significant variables is the angular difference among the velocity vector and the gap thickness

gradient vector.