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110                             Chapter 4.  Basic  Motion  Estimation  Techniques



                       Foreman @ 8.33 f.p.s.             Foreman @ 8.33 f.p.s.
              36                              1800
                  +/15                              +/15
              34   +/5                              +/5
                                              1600
              32                              1400
             PSNR Y  (dB)   28                Motion overhead (bits)   1200
              30
                                              1000
              26
              24                               800
              22                               600
              20
              18                               400
              16                               200
                1  10  20  30  40  50  60  70  80  90 99   1   10  20  30  40  50  60  70  80  90 99
                            Frame                            Frame
                      (a) Prediction quality           (b) Motion overhead
                       Figure 4.5:  Performance  of  the BMA with di erent  search ranges

            displacement  of  d m  = ± 15  pels  is  su!cient  for  low-bit-rate  applications.  As
            already discussed, the H.263 standard uses a maximum displacement of about
            ± 15 pels, although this range can optionally be doubled with the unrestricted
            motion  vector mode.

            4.6.4  Search Accuracy

            Initially, the BMA was designed to estimate motion displacements with full-pel
            accuracy. Clearly, this limits the performance of the algorithm, since in reality
            the motion of objects is completely unrelated to the sampling grid. A number
            of workers in the  eld have proposed to extend the BMA to subpel accuracy.
            For  example,  Ericsson  [100]  demonstrated  that  a  prediction  gain  of  about
            2 dB can be obtained by moving from full-pel to 1=8-pel accuracy. Girod [92]
            presented  an  elegant  theoretical  analysis  of  motion-compensating  prediction
            with  subpel  accuracy.  He  termed  the  resulting  prediction  gain  the  accuracy
            e ect.  He  also  showed  that  there  is  a  “critical  accuracy”  beyond  which  the
            possibility  of  further  improving  prediction  is  very  small.  He  concluded  that
            with  block  sizes  of  16 × 16,  quarter-pel  accuracy  is  desirable  for  broadcast
            TV signals, whereas half-pel accuracy appears to be su!cient for videophone
            signals. Today, most video coding standards adopt subpel accuracy in its half-
            pel  form.  In  fact,  it  has  been  shown  [65]  that  most  of  the  performance  gain
            of  H.263  over  H.261  can  be  attributed  to  the  move  from  full-pel  to  half-pel
            accuracy.
               It  should  be  pointed  out,  however,  that  the  improved  prediction  quality  of
            subpel accuracy comes at the expense of a signi cant increase in computational
            complexity.  This  increase  is  due  to  two  reasons.  First,  the  reference  frame
            intensities  have  to  be  interpolated  at  subpel  locations.  Second,  there  are  now
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