The International Arab Journal of Information Technology (IAJIT)


Speed up of Reindexing in Adaptive Particle Swarm Optimization

 Palette re ordering is a class of pre processing me thod with the objective to manipulate the palette index such that the adjacent symbols are assigned close indices in the symbol space, thus enhancing the compressibilit y of the image with many lossless compressors. Finding an exact reorder ed palette would certainly be exhaustive and computationally complex. A solution to this NP hard problem is presented by us ing an Adaptive Particle Swarm Optimization (APSO) to achieve fast global convergence by maximizing the co occurrences . A new algorithm with improved inertia factor is presented here to accelerate the convergence speed of the reindexing scheme. In this algorithm, the key parameter inertia weight is formulated as a factor of gradient based rate of particle conv ergence. Experimental results assert that the propo sed modification helps in improving APSO performance in terms of solution qua lity and convergence to global optima.   Key  words : Reindexing, palette indexed image, cross entropy, r ate of particle convergence (k), improved inertia weight adaptive particle swarm optimization.    Received April 3, 2013; accepted November10, 2014; published online March 19, 2015     1. Introduction  A  colour-mapped  (pseudo-colour)  image  is  composed  of  colour  information  contained  in  a  look-up  table  and  pixel  values  that  are  indices,  which  point  to  colou r  values  in  the  look-up  table.  In  most  computer  applications,  images  are  used  to  help  stimulate  hum an  visual  perception.  A  true  color  image  is  a  matrix  o f  pixels,  each  consisting  of  red,  green  and  blue  colo r  triplets.  Each  component  ( Ri,  Gi, Bi)  triplet  has  a  range  between  0  and  255  and  is  represented  with  a  byte.  Since,  a  color-mapped  image  utilises  approximately  one  third  of  memory  space  of  its  corresponding  true- colour  representation,  colour-mapped  images  are  use d  as  user  interface  elements  of  most  windowing  operating systems .  A  color-quantized  image  is  generally  represented  with  a  color  index  map  each  element  of  which  serves   as  an  index  to  select  a  color  from  a  predefined  set   of  colors  to  represent  the  color  of  a  pixel  in  the  ima ge.  The  predefined  set  of  colors  is  called  a  palette.  T o  reduce  the  size  of  a  color-indexed  image  further,  lossless  compression  techniques  are  generally  used  because the index used to pick a particular palette  color  must be exact in decoding. A minor difference betwe en  two index values may result in a serious color shif t.  In  a  standard  image  coding  scenario,  pixel-to-pixel   correlation  nearly  always  exists  in  the  data,  espec ially  if the image is a natural scene. This correlation i s what  allows  predictive  coding  schemes  (e.g.,  DPCM)  to  perform  efficient  compression.  In  a  color  mapped  image,  the  values  stored  in  the  pixel  array  are  no  longer  directly  related  to  the  pixel  intensity.  For   each  pixel in the image, only the index of the correspon ding color  needs  to  be  stored.  Two  color  indices  which  a re  numerically  adjacent  (close)  may  point  to  two  very  different  colors.  The  correlation  still  exists,  but   only  via  the  color  map.  The  efficiency  of  a  lossless  compression algorithm for indexed images may greatl y  depend  on  the  assignment  of  indexes  in  the  relative   lookup table [2].   Palette  reordering  is  a  well-known  and  very  effective  approach  for  improving  the  compression  of   color-indexed  images.  Highly  compressed  palettized  images  are  needed  in  many  applications  such  as  game   cartridges,  computer  graphics  and  World  Wide  Web  (WWW) on-line services.  The  bottleneck  of  this  solution  is  the  intrinsic  inefficiency  to  numerically  optimize  the  palette  re- indexing. If the optimal palette configuration is s ought,  the computational  complexity  involved  would  be  high .  As  a  matter  of  fact,  a  table  of  M colors  corresponds  to  M! Configurations [26]. Clearly, this exhaustive sea rch  is  impractical  and  thus  transforms  to  an  NP  hard  problem.   In  typical  applications  where  the  search  space  is  large  and  multidimensional,  prior  information  about   the  function  is  not  available  and  traditional  mathematical  techniques  are  not  applicable.  Global  optimization  is  a  NP  complete  problem  and  heuristic  

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