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118                             Chapter 4.  Basic  Motion  Estimation  Techniques


            DFA  This  is  an  implementation  of  the  di erential  method  of  Ca orio  and
                Rocca  as  given  by  Equation  (4.12).  In  this  case,  the  moving  area,  A,
                was  set  to a block of  16 × 16 pels.
            PRA  This  is  an  implementation  of  the  pel-recursive  algorithm  of  Netravali
                and Robbins as given by Equation (4.20). In this case, the motion vector
                                                                           ˆ i
                of the previous pel in the line was taken as the initial motion estimate, d ,
                of the current pel, the update step size was set to   =1=1024, the update
                term  was  calculated  and  averaged  over  an  area  of  3 × 3 pels  centered
                around the current pel, and  ve  iterations were  performed per  pel.
            PCA  This  is  an  implementation  of  the  phase  correlation  method  as  given
                by  Equations  (4.24)  and  (4.25).  In  this  case,  a  window  of  32 × 32 pels
                centered around the current 16 × 16 block was used to generate the phase
                correlation  surface.  The  three  most  dominant  peaks  in  this  surface  were
                detected  and  the  corresponding  motion  displacements  were  unwrapped
                using Equation (4.27). The three candidate displacements were then tested
                using  the  SAD  between  the  current  block  and  the  candidate  displaced
                block in the reference frame. The candidate displacement with the lowest
                SAD was chosen  as  the motion vector  of  the current block.
            BMA  This  is  an  implementation  of  a  full-search  block-matching  algorithm.
                In  this  case,  the  block  size  was  16 × 16  pels  and  the  matching  criterion
                was the SAD.
               In  each  case,  the  maximum  allowed  motion  displacement  was  set  to
            ± 15  pels  in  each  direction  and  the  motion  vectors  were  allowed  to  point
            outside  the  reference  frame  (i.e.,  unrestricted  motion  vectors).  To  provide  a
            fair  comparison  and  to  ease  motion  vector  coding,  all  displacements  were
            estimated  with  half-pel  accuracy.  In  DFA  and  PRA  this  was  achieved  by
            rounding  the  subpel  accurate  motion  estimates  to  the  nearest  half-pel  accu-
            rate  motion  vectors.  In  PCA  and  BMA  this  was  achieved  using  a  re nement
            stage  that  examined  the  eight  nearest  half-pel  estimates  centered  around  the
            full-pel  motion  estimate.  Bilinear  interpolation  was  used  to  obtain  intensity
            values  at  subpel  locations  of  the  reference  frame.  To  mask  the  e ect  of  the
            temporal  propagation  of  prediction  errors,  motion  was  estimated  and  com-
            pensated  using  original  reference  frames.  For  comparison  purposes,  motion
            vectors  were  coded  using  the  median  predictor  and  the  VLC  table  of  the
            H.263  standard.  The  DFD  signal  was  also  transform  encoded  according  to
            the  H.263  standard  and  a  quantization  parameter  of  QP =10.  All  quoted  re-
            sults  refer  to  the  luma  components  of  sequences.  No  chroma  encoding  was
            performed.
               Care  should  be  taken  when  interpreting  the  results  of  this  study.  Di erent
            simulation parameters will lead to di erent results. For example, at the expense
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