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130                      Chapter 5.  Warping-Based  Motion  Estimation  Techniques









                    Reference     Current         Reference     Current
                     patches      patches          patches      patches


                      (a)  Discontinuous method     (b)  Continuous method
                      Figure 5.2:  Continuous versus discontinuous warping-based methods



            5.2.5  Backward Versus Forward Node Tracking
            The  process  of  estimating  the  motion  of  a  grid  or  a  node  point  is  called
            node  tracking.  There  are  two  types  of  node-tracking  algorithms:  backward
            and forward node tracking.
               In  backward  node  tracking,  nodes  are  (rst  placed  on  the  current  frame
            and  then  they  are  matched  to  points  in  the  reference  frame.  During  motion
            compensation, a pel (x; y) in the current patch is copied from a corresponding
            pel  (u; v)=(g x  (x; y);g y  (x; y))  in  the  reference  patch.  Note  that  in  this  case,
            (x; y)  is  a  sampling  spatial  position,  whereas  (u; v)  may  be  a  nonsampling
            spatial  position.  Interpolation,  e.g.,  bilinear,  can  be  used  to  obtain  pel  values
            at nonsampling positions of the reference frame. This process is repeated for
            all pels within the current patch. Since backward tracking starts with a mesh
            on the current frame (which is not available at the decoder), this technique is
            usually used in combination with a (xed mesh.
               In  forward  node  tracking,  nodes  are  (rst  placed  on  the  reference  frame
            and  then  matched  to  points  in  the  current  frame.  During  motion  compen-
            sation,  a  pel  (u; v)  in  the  reference  patch  is  copied  to  a  corresponding  pel
            (x; y)=(g x (u; v);g y  (u; v)) in the current patch. Since, in this case, (x; y) may
            be  a  nonsampling  spatial  position,  the  compensated  current  patch  will  nor-
            mally contain holes (i.e., noncompensated pels at sampling spatial positions).
            Techniques that can be used to recover pel values at sampling spatial positions
            from  values  at  nonsampling  spatial  positions  are  discussed  and  compared  by
            Sharaf and Marvasti in Ref. 116. Due to the use of such techniques, forward
            node tracking and compensation is computationally more complex than back-
            ward node tracking and compensation. Since forward node tracking starts with
            a mesh on the reference frame, this technique is usually used in combination
            with  an  adaptive  mesh.  Although  the  combination  of  forward  tracking  and
            adaptive  meshes  can  provide  some  prediction-quality  improvement  over  the
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