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138                      Chapter 5.  Warping-Based  Motion  Estimation  Techniques

            uncovered background. In fact, poor compensation of covered and uncovered
            objects  is  one  of  the  main  disadvantages  of  the  continuous  warping-based
            method. In particular, the method performs poorly whenever there are objects
            disappearing  from  the  scene  because  it  can  deform  objects  but  cannot  easily
            remove them completely [111].
               Another  obvious  disadvantage  of  the  continuous  warping-based  method  is
            the lack of motion  (eld  segmentation.  A  number  of  methods  have  been  pro-
            posed to overcome this problem. For example, NiewFeg lowski and Haavisto [110]
            use adaptive motion  (eld interpolation  to  introduce  discontinuities  within  the
            nodal motion (eld. Adaptivity is achieved by switching between bilinear inter-
            polation and nearest-neighbor interpolation of the nodal vectors at the vertices
            of  a  patch.  The  latter  interpolation  method  e>ectively  splits  the  motion  (eld
            within the patch into four quadrants. A similar e>ect can be achieved by using a
            hierarchical (e.g., quad-tree) motion-based adaptive mesh [109, 120, 115, 123].
               It is interesting at this point to compare the computational complexity of the
            preceding  three  algorithms.  Table  5.2  compares  the  complexity  of  the  three
            algorithms  in  terms  of  encoding  time  per  frame.  The  results  were  obtained
            using  the  pro(ler  of  the  Visual  C++  5.0compiler  run  on  a  PC  with  Pentium
            100-MHz  processor,  64 MB  of  RAM,  and  a  Windows  98  operating  system.
            The  results  were  averaged  over  10runs,  where  each  run  was  used  to  encode
            the 8.33-frames=sFOREMAN  sequence. Care should be taken when interpreting
            the  results  as  they  depend  heavily  on  the  implementation  and  the  hardware
            platform.
               The  BMA  requires  about  2.16  seconds=frame.  Most  of  this  time  (about
            1.76  seconds)  is  consumed  by  the  full-pel  full-search  block-matching  motion
            estimation process.
               The BMA-HO algorithm requires about 3.56 seconds=frame. This increase
            of about 1.4 seconds over the BMA is due mainly to two reasons. The half-pel
            re(nement stage and the associated bilinear interpolation process increase the
            motion  estimation  time  by  about  0.98  seconds.  In  addition,  the  overlapping
            process increases the motion compensation time by about 0.42 seconds.

               Table 5.2: Comparison between BMA and WBA in terms of computational complexity
                                             CPU time (in seconds) per frame
                                            when encoding FOREMAN  at 8.33 f.p.s
                                       BMA           BMA-HO           WBA
            BMA motion estimation      1.76            2.74             1.86
            WBA iterative re(nement    0.00            0.00           116.00
            Motion compensation        0.01            0.43             0.60
            Others                     0.39            0.38             0.37
            Total                      2.16            3.56           118.83
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