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• Basic Video Palette Conversion

  20 août 2011, par Multimedia Mike — General, Python

  How do you take a 24-bit RGB image and convert it to an 8-bit paletted image for the purpose of compression using a codec that requires 8-bit input images ? Seems simple enough and that’s what I’m tackling in this post.

  Ask FFmpeg/Libav To Do It
  Ideally, FFmpeg / Libav should be able to handle this automatically. Indeed, FFmpeg used to be able to, at least at the time I wrote this post about ZMBV and was unhappy with FFmpeg’s default results. Somewhere along the line, FFmpeg and Libav lost the ability to do this. I suspect it got removed during some swscale refactoring.

  Still, there’s no telling if the old system would have computed palettes correctly for QuickTime files.

  Distance Approach
  When I started writing my SMC video encoder, I needed to convert RGB (from PNG files) to PAL8 colorspace. The path of least resistance was to match the pixels in the input image to the default 256-color palette that QuickTime assumes (and is hardcoded into FFmpeg/Libav).

  How to perform the matching ? Find the palette entry that is closest to a given input pixel, where "closest" is the minimum distance as computed by the usual distance formula (square root of the sum of the squares of the diffs of all the components).

  
  
  

  That means for each pixel in an image, check the pixel against 256 palette entries (early termination is possible if an acceptable threshold is met). As you might imagine, this can be a bit time-consuming. I wondered about a faster approach...

  Lookup Table
  I think this is the approach that FFmpeg used to use, but I went and derived it for myself after studying the default QuickTime palette table. There’s a pattern there— all of the RGB entries are comprised of combinations of 6 values — 0x00, 0x33, 0x66, 0x99, 0xCC, and 0xFF. If you mix and match these for red, green, and blue values, you come up with 6 * 6 * 6 = 216 different colors. This happens to be identical to the web-safe color palette.

  The first (0th) entry in the table is (FF, FF, FF), followed by (FF, FF, CC), (FF, FF, 99), and on down to (FF, FF, 00) when the green component gets knocked down and step and the next color is (FF, CC, FF). The first 36 palette entries in the table all have a red component of 0xFF. Thus, if an input RGB pixel has a red color closest to 0xFF, it must map to one of those first 36 entries.

  I created a table which maps indices 0..215 to values from 5..0. Each of the R, G, and B components of an input pixel are used to index into this table and derive 3 indices ri, gi, and bi. Finally, the index into the palette table is given by :

    index = ri * 36 + gi * 6 + bi
  

  For example, the pixel (0xFE, 0xFE, 0x01) would yield ri, gi, and bi values of 0, 0, and 5. Therefore :

    index = 0 * 36 + 0 * 6 + 5
  

  The palette index is 5, which maps to color (0xFF, 0xFF, 0x00).

  Validation
  So I was pretty pleased with myself for coming up with that. Now, ideally, swapping out one algorithm for another in my SMC encoder should yield identical results. That wasn’t the case, initially.

  One problem is that the regulation QuickTime palette actually has 40 more entries above and beyond the typical 216-entry color cube (rounding out the grand total of 256 colors). Thus, using the distance approach with the full default table provides for a little more accuracy.

  However, there still seems to be a problem. Let’s check our old standby, the Big Buck Bunny logo image :

  
  
  Distance approach using the full 256-color QuickTime default palette
  
  
  Distance approach using the 216-color palette
  
  
  Table lookup approach using the 216-color palette
  

  I can’t quite account for that big red splotch there. That’s the most notable difference between images 1 and 2 and the only visible difference between images 2 and 3.

  To prove to myself that the distance approach is equivalent to the table approach, I wrote a Python script to iterate through all possible RGB combinations and verify the equivalence. If you’re not up on your base 2 math, that’s 2²⁴ or 16,777,216 colors to run through. I used Python’s multiprocessing module to great effect and really maximized a Core i7 CPU with 8 hardware threads.

  So I’m confident that the palette conversion techniques are sound. The red spot is probably attributable to a bug in my WIP SMC encoder.

  Source Code
  Update August 23, 2011 : Here’s the Python code I used for proving equivalence between the 2 approaches. In terms of leveraging multiple CPUs, it’s possibly the best program I have written to date.

  PLAIN TEXT

  PYTHON :

  1. # !/usr/bin/python
  2.  
  3. from multiprocessing import Pool
  4.  
  5. palette = []
  6. pal8_table = []
  7.  
  8. def process_r(r) :
  9.  counts = []
  10.  
  11.  for i in xrange(216) :
  12.   counts.append(0)
  13.  
  14.  print "r = %d" % (r)
  15.  for g in xrange(256) :
  16.   for b in xrange(256) :
  17.    min_dsqrd = 0xFFFFFFFF
  18.    best_index = 0
  19.    for i in xrange(len(palette)) :
  20.     dr = palette[i][0] - r
  21.     dg = palette[i][1] - g
  22.     db = palette[i][2] - b
  23.     dsqrd = dr * dr + dg * dg + db * db
  24.     if dsqrd <min_dsqrd :
  25.      min_dsqrd = dsqrd
  26.      best_index = i
  27.    counts[best_index] += 1
  28.  
  29.    # check if the distance approach deviates from the table-based approach
  30.    i = best_index
  31.    r = palette[i][0]
  32.    g = palette[i][1]
  33.    b = palette[i][2]
  34.    ri = pal8_table[r]
  35.    gi = pal8_table[g]
  36.    bi = pal8_table[b]
  37.    table_index = ri * 36 + gi * 6 + bi ;
  38.    if table_index != best_index :
  39.     print "(0x%02X 0x%02X 0x%02X) : distance index = %d, table index = %d" % (r, g, b, best_index, table_index)
  40.  
  41.  return counts
  42.  
  43. if __name__ == ’__main__’ :
  44.  counts = []
  45.  for i in xrange(216) :
  46.   counts.append(0)
  47.  
  48.  # initialize reference palette
  49.  color_steps = [ 0xFF, 0xCC, 0x99, 0x66, 0x33, 0x00 ]
  50.  for r in color_steps :
  51.   for g in color_steps :
  52.    for b in color_steps :
  53.     palette.append([r, g, b])
  54.  
  55.  # initialize palette conversion table
  56.  for i in range(0, 26) :
  57.   pal8_table.append(5)
  58.  for i in range(26, 77) :
  59.   pal8_table.append(4)
  60.  for i in range(77, 128) :
  61.   pal8_table.append(3)
  62.  for i in range(128, 179) :
  63.   pal8_table.append(2)
  64.  for i in range(179, 230) :
  65.   pal8_table.append(1)
  66.  for i in range(230, 256) :
  67.   pal8_table.append(0)
  68.  
  69.  # create a pool of worker threads and break up the overall job
  70.  pool = Pool()
  71.  it = pool.imap_unordered(process_r, range(256))
  72.  try :
  73.   while 1 :
  74.    partial_counts = it.next()
  75.    for i in xrange(216) :
  76.     counts[i] += partial_counts[i]
  77.  except StopIteration :
  78.   pass
  79.  
  80.  print "index, count, red, green, blue"
  81.  for i in xrange(len(counts)) :
  82.   print "%d, %d, %d, %d, %d" % (i, counts[i], palette[i][0], palette[i][1], palette[i][2])

• Piwik Mobile est maintenant disponible !

  18 août 2010, par SteveG — Développement

  Après quelques mois de développement, l’équipe Piwik est fière de vous présenter le client mobile.

  Piwik Mobile est déjà disponible pour les markets des différents téléphones avec IOS (comme iPhone, iPod et iPad) ou Android (1.6 ou supérieure).

  Piwik Mobile dans les markets :
  Android : http://www.androidpit.com/en/android/market/apps/app/org.piwik.mobile/Piwik-Mobile-Beta
  iOS : http://itunes.apple.com/us/app/piwikmobile/id385536442?mt=8

  

  Piwik Mobile a été développé en utilisant Titanium et fournit aujourd’hui les principaux graphiques et rapports. Comme Piwik Mobile est toujours en développement et ce n’est que la première version, tous les rapports ne sont pas disponibles. L’application utilise la traduction inclue dans Piwik. Ainsi, il est disponible dans toutes les langues supportées par Piwik.

  D’autres améliorations suivront. Il n’est pas possible pour nous de tester l’application sur tous les téléphones, il peut y avoir des problèmes avec certains d’entre eux. Si vous trouvez des erreurs dans l’application ou si vous avez des suggestions pour l’améliorer, n’hésitez pas à nous contacter par courriel à mobileatpiwik.org ou créer un ticket.

  Piwik Mobile a été développé par Thomas et Stefan, qui ont rejoins l’équipe Piwik avec l’idée du client mobile. Ils vont superviser et maintenir les développements en tant que meneurs de ce projet.

  Un grand merci à Mayflower, une société de développement Web Allemande, qui a sponsorisé les heures de travail des développeurs Thomas et Stefan.

  

• Understanding the VP8 Token Tree

  7 juin 2010, par Multimedia Mike — VP8

  I got tripped up on another part of the VP8 decoding process today. So I drew a picture to help myself understand it. Then I went back and read David Conrad’s comment on my last post regarding my difficulty understanding the VP8 spec and saw that he ran into the same problem. Since we both experienced the same hindrance in trying to sort out this matter, I thought I may as well publish the picture I drew.

  VP8 defines various trees for decoding different syntax elements. There is one tree for decoding the tokens and it is expressed in the VP8 spec as such :

  PLAIN TEXT

  C :

  1. const tree_index coef_tree [2 * (num_dct_tokens - 1)] =
  2. {
  3.  -dct_eob, 2,        /* eob = "0"  */
  4.   -DCT_0, 4,        /* 0  = "10" */
  5.   -DCT_1, 6,        /* 1  = "110" */
  6.    8, 12,
  7.    -DCT_2, 10,      /* 2  = "11100" */
  8.     -DCT_3, -DCT_4,    /* 3  = "111010", 4 = "111011" */
  9.    14, 16,
  10.     -dct_cat1, -dct_cat2, /* cat1 = "111100", cat2 = "111101" */
  11.    18, 20,
  12.     -dct_cat3, -dct_cat4, /* cat3 = "1111100", cat4 = "1111101" */
  13.     -dct_cat5, -dct_cat6 /* cat4 = "1111110", cat4 = "1111111" */
  14. } ;

  Here is what the table looks like when you make a tree out of it (click for full size image) :

  
  
  

  The catch is that it makes no sense for an end-of-block (EOB) token to follow a 0 token since EOB already indicates that the remainder of the coefficients should be 0 anyway. Thus, the spec states that, "decoding of certain DCT coefficients may skip the first branch, whose preceding coefficient is a DCT_0." I confess, I didn’t understand what "skip the first branch" meant until I drew the tree.

  
  
  

  For those wondering why it might be sub-optimal (clarity-wise) for a spec to simply regurgitate vast chunks of C code, this makes a decent case. As you can see, the spec makes certain assumptions about how a binary tree should be organized in a static array (node n points to elements n*2 and n*2+1 as its branches ; leaves are either negative or 0). This is the second method I have seen ; another piece of code (not the VP8 spec) had the nodes in the first half of the array and pointed to leaves in the second half. There must be other arrangements.