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146                    Chapter  6.  Multiple-Reference  motion  Estimation Techniques



                                          QSIF Foreman
                    0.5
                                                              M=50, Skip=1
                                                              M=50, Skip=4
                   0.45
                    0.4

                   0.35
                    0.3
                  p(d t )   0.25

                    0.2

                   0.15
                    0.1

                   0.05
                     0
                     0    5    10   15   20   25   30   35   40   45   50
                                              d
                                               t
               Figure 6.3:  Zero-biased distribution of  the long-term memory  temporal  displacement  d t

            in  memory)  has  the  highest  frequency  of  occurrence;  and  as  the  temporal
            displacement  increases,  its  frequency  of  occurrence  decreases.  Note  that  this
            distribution  becomes  more  spread  at  higher  frame  skips,  which  indicates  that
            the selection of  older  reference  frames  becomes  slightly more  probable.

            Property 6.3.1.3  The  long-term  memory  block-motion   eld  is  smooth  and
            varies  slowly.  In  other  words,  there  is  high  correlation  between  the  motion
            vectors  of  adjacent  blocks.  This  is  evident  from  Figure  6.4,  which  shows  the
            distribution of the di&erence between the current vector C and its left neighbor
            L.  This  is  shown  for  the  three  components:  d x  (Figure  6.4(a)),  d y  (Figure
            6.4(b)),  and  d t  (Figure  6.4(c)).  All  three  distributions  are  biased  toward  a
            zero  di&erence,  which  indicates  high  correlation.  Note  that  this  correlation  is
            slightly less in the multiple-reference case (M =50; skip = 1), compared to the
            single-reference  case  (M =1; skip = 1).  This  correlation  is  further  reduced  at
            higher frame skips, (M =50; skip = 4).

               In general, it can be concluded that moving from a single-reference system
            to  a  multiple-reference  system  does  not  signi)cantly  change  the  properties  of
            the block-motion  )eld.
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