Speeding up Lossless Image Compression: Experimental Results on a Parallel Machine

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Speeding up Lossless Image
CompressionExperimental Results on a Parallel
Machine

• Luigi Cinque and
  Sergio De Agostino
  Computer Science Department
  Sapienza University of Rome
  ITALY
• Luca
  Lombardi
• Computer Science
  Department
• 
  University of Pavia
• 
  ITALY

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• Lossless image compression by block matching has
  a linear time implementation on bi-level images
  by means of a square greedy matching heuristic.
• Storer 1996, Proc. IEEE Data Compression
  Conf.
• 
  how to compute a square
  match

4 x 4


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The Compression Scheme

• The image is read by a raster scan and the
  matching algorithm works with a perfect hashing
  table with one position for each possible 4x4
  subarray.
• All-zero and all-one squares are handled
  differently.
• Each pointer starts with a flag field indicating
  whether there is a monochromatic square (0 for
  white, 10 for black), a match (110) or raw data
  (111).

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If the 4 x 4 subarray in position (i,j) is
monochromatic, then we compute the largest
monochromatic square in that position and encode
the side length.Otherwise we compute the
largest square match in the position provided by
the hash table, encode its position and side
length, and update the table with the current
position.If the subarray is not hashed, then it
is left uncompressed and added to the hash table
with its current position.The positions covered
by matches are skipped in the linear scan of the
image.
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Dealing with square matches, we were able to
partition an image into up to a hundred areas and
to apply the BLOCK MATCHING heuristic
independently to each area with no loss of
compression effectiveness. In order to implement
decompression on an array of processors, we
indicate the end of the encoding of an area with
1111 changing the flag field 111 to 1110. We
obtained the expected speed up of the compression
and decompression times, achieving parallel
running times about twenty-five times faster than
the sequential ones with up to 32 processors of a
256 Intel Xeon 3.06 GHz processors machine in
Italy (avogadro.cilea.it) on a test set of large
topographic bi-level images.
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The extension of the BLOCK MATCHING method to
grey scale and color images is not feasible
since the high cardinality of the alphabet causes
an exponential blow-up of the hash table. Grey
scale and color image compression relies on the
fact that most of the times there are minimal
variations of color in the neighborood of one
pixel. There exists an extremely local procedure
which is able to achieve a satisfying degree of
compression by working independently on 8 x 8
pixels blocks. Cinque, De Agostino, Liberati and
Westgeest 2006. Int. J. Of Foundations of
Computer Science
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The PALIC Compressor

• The PALIC (Parallelizable Lossless Image
  Compression) compressor employs a header and a
  fixed length code to encode each 8 x 8 pixels
  block.
• Two different techniques may be applied to the
  block.
• One is to encode the difference between the
  pixel value and the smallest one in the block.
• The other one is the simple idea of reducing the
  alphabet size by looking at the values occurring
  in the block.

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• The heuristic may be applied to the four
  sub-blocks of 16 pixels if better compression is
  achieved.
• If this is not the case, the first bit of the
  header is set to 1.
• Then a second field of 3-bits (but 110 and 111)
  stores the number of bits required to encode the
  distance between the smallest pixel value and
  every other pixel value in the block.
• A third field of 8-bits stores the smallest
  pixel value and then the distances are given.

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• If the second field is 110, the reduced alphabet
  technique is applied.
• An additional three bits field stores the
  reduced alphabet size d in the range from 2 to 9.
• The last componenent of the header is the
  alphabet itself, a concatenation of d bytes.
• A code of fixed length log(d) is used to encode
  the block.
• If the second field is 111, the block is not
  compressed.

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• If the first bit of the header is set to 0 then
  four 3-bits fields follow the flag bit, one for
  each 4x4 block.
• If a field is 111, then it is followed by three
  more bits.
• If they are 110, the first technique with
  distances expressed by seven bits is applied to
  the sub-block.
• If they are 111, the sub-block is not
  compressed.
• Otherwise, they encode a reduced alphabet size
  in the range from 2 to 7 and the alphabet follows.

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• The PALIC compressor works on color images by
  applying the procedure to each component.
• We experimented PALIC on a test set of five
  large topographic images in RGB format (4096 x
  4096 pixels).
• We obtained the expected speed up of the
  compression and decompression times, achieving
  parallel running times about twenty-five times
  faster than the sequential ones with up to 32
  processors of the 256 Intel Xeon 3.06 GHz
  processors machine in Italy (avogadro.cilea.it)
  as with bi-level images.

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Image 1 image 2
image 3 image 4
image 4
image 1 proc. 2 proc. 4 proc. 8 proc 16 proc. 32 proc.
1 227 117 57 34 17 9
2 243 120 69 33 16 10
3 235 118 72 35 17 9
4 236 131 71 34 16 9
5 232 113 67 30 16 11
Avg. 234.6 119.8 67.2 33.2 16.4 9.6
PALIC compression times (cs.)
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Image 1 image 2
image 3 image 4
image 4
image 1 proc. 2 proc. 4 proc. 8 proc 16 proc. 32 proc.
1 128 65 32 18 11 6
2 133 66 35 21 10 6
3 130 66 44 21 13 6
4 129 91 36 20 10 5
5 123 95 46 17 10 5
Avg. 128.6 76.6 38.6 19.4 10.8 5.6
PALIC decompression times (cs.)