**3.2. Simulated Quenching algorithm**

182 Simulated Annealing – Single and Multiple Objective Problems

minimum.

equation (5),

**Distortion**

The crystal can be seemed as the minimum energy state for this system. SA is especially suitable for the large scale problems with the global minimum hidden among several local minimum. The motion estimation is such kind of optimization problem that search for the optimal motion vector with minimum RD cost. However, most fast motion estimation search algorithms look for steepest descent for minimization and go downhill as far as they can go, as shown in Figure 7. Hence, these algorithms are easily trapped into a local

**Downhill Searching** 

*Global minimum*

*Prob E exp E kT* () ( ) ~ / − (3)

x

Avoiding the disadvantage stated above, SA algorithm can be viewed as a good solution to motion estimation search algorithm, in which occasional uphill moves will help the process escape from local minima. The so-called Boltzmann probability distribution as defined in

expresses that a system at temperature T has its energy probabilistically distributed among all different energy states. Even at low temperature, there is a chance for the system to get out of a local energy minimum. Therefore, the system sometimes goes uphill as well as downhill. But lower the temperature, less chances for any significant uphill to take place.

• An objective function *E s*( ) (analogy of energy) at state *s*, whose minimization is the

• A nonincreasing function *T* called cooling schedule, which controls the annealing

procedure, and *T(t)* is called the temperature at time *t*.

**Uphill Searching** 

*Local minimum*

**Figure 7.** Uphill and downhill searching on rate-distortion surface

The basic elements of simulated annealing are as follows:

• A finite solution space *S* (set of states).

• A Neighbourhood structure *N s*( ) .

goal of the procedure**.**

SA solution usually requires a large number of function evaluations to find the global minimum, which cause the speed of process is quite slow. That is the main disadvantage when using in fast motion estimation algorithm. To speed up the algorithm, a Simulated Quenching (SQ) methodology was proposed. Like SA, SQ algorithm also resembles the cooling process of molten metals through annealing. The analogy of the technique remains the same as that of SA except for quick temperature reduction annealing schedule. Thus the cooling rate becomes one of important parameters, which governs the successful working of SQ.

As in fast motion estimation algorithm, video contents and motion character are changing all the time, it's quite difficult to find a unique cooling scheme for such complicated application. In our proposed SAAS algorithm, we adaptive choose annealing schedule according to MV correlation probabilities information. For the frame with steady motion and high MV correlation, larger values of MV correlation probabilities are more easily to distribute in fewer divided regions. In this case, the faster anneal schedule will safely lead to global optimum. While a slower annealing schedule will be choosing when the frame with more irregular motion and MV correlation distribution is flat. The proposed SAAS algorithm with adaptive cooling scheme is specified in next section.
