**1.1.5 2D logarithmic search**

2D Logarithmic (Alois, 2009) search is another algorithm, which tests limited candidates. It is similar to the three-step search. During the first iteration, a total of five candidates are tested. The candidates are centered on the current block location in a diamond shape. The step size for first iteration is set equal to half the search range. For the second iteration, the centre of the diamond is shifted to the best matching candidate. The step size is reduced by half only if the best candidate happens to be the centre of the diamond. If the best candidate is not the diamond centre, same step size is used even for second iteration. In this case, some of the diamond candidates are already evaluated during first iteration. Hence, there is no need for block matching calculation for these candidates during the second iteration. The results from the first iteration can be used for these candidates. The process continues till the step size becomes equal to one pixel. For this iteration all eight surrounding candidates are evaluated. The best matching candidate from this iteration is selected for the current block. The number of evaluated candidate is variable for the 2D logarithmic search. However, the worst case and best case candidates can be calculated.
