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162                  Chapter  7.  Reduced-Complexity  Motion Estimation  Techniques



                                      Horizontal displacement, d
                                                        x
                     -6   -5   -4   -3   -2   -1  0   +1  +2  +3  +4  +5  +6
                   -6
                                             3        4
                   -5
                                                  5   5   5
                   -4
                                    3        2    5   3   5       4
                   -3
                                                  5   5    5
                   -2
                 Vertical displacement, d y   +1
  1   1   1
                                                      2
                                     2
                                             1
                   -1
                   0


                   +2
                                             1
                   +3

                   +4
                   +5

                   +6

                           searched location         minimum at a given step


                           direction of minimum at   final motion vector
                           a given step
                        Figure 7.1:  An example of  the TDL search with d m = 6 pels



            the search pattern of the )rst step. At each step, the search pattern is centered
            around the minimum of the previous step. In the given example, the minimum
            in  the  )rst  step  is  at  (0; −2).  Thus,  the  search  pattern  in  the  second  step  is
            centered  around  this  minimum  location.  The  step  size  is  reduced  by  a  factor
            of 2 if the minimum is in the center of the search pattern or at the boundary
            of  the  search  window.  In  the  fourth  step  of  the  given  example,  the  mini-
            mum is at (+2; −4), which is the center of the search pattern. Therefore, the
            spacing between the search locations is halved in the )fth step. Since halving
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