168.

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Page 249

(6.31)

where κ is a small constant that determines the step size. Repeat (6.30) until finally:

(6.32)

Suppose an image contains three pixels, which form a one-dimensional intensity surface, as shown in Figure 6.10a. For simplicity, we are only concerned with the value of the central pixel (i.e. pixel value d=30) whose value is to be restored, and a quadratic function (shown in Equation (6.25)) is used for modelling the prior energy g(a−b) (which indicates that the interaction function h(a − b)=1). Let the initial value w⁽⁰⁾=d=30. Energy minimisation using a gradient descent procedure for q=0.25 and 1, respectively, is illustrated below.

 

 

The geometric interpretation of this process is illustrated in Figure 6.10b and c. It is shown that the greater the value of the weighting parameter q the greater is the smoothing effect. If q=0, there is no smoothing effect.

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