docs/UnifiedAlpha-static.html

   1 <?xml version="1.0" encoding="utf-8"?>
   2 <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
   3
   4
   5 <!-- The babl webpage is partially autogenerated
   6 -->
   7 <html>
   8   <head>
   9     <title>Unified Alpha - babl</title>
  10     <meta http-equiv="content-type" content="text/html;charset=utf-8" />
  11     <link rel="icon" href="graphics/babl-16x16.png" type="image/png" />
  12     <link rel="shortcut icon" href="graphics/babl-16x16.png" type="image/png" />
  13     <style type='text/css'>
  14        @import url(babl.css);
  15     </style>
  16   </head>
  17   <body>
  18
  19     <div class='print'>
  20       <div class='print_title'>
  21         <h1>Babl</h1>
  22       </div>
  23     </div>
  24 <!--TOC-->
  25
  26     <div class='paper'>
  27   <div class='content'>
  28
  29   <h2>Symmetric transformations for floating point alpha</h2>
  30
  31
  32   <p> babl clamps the alpha used when going from separate alpha to associated
  33 alpha or from associated alpha to separate alpha to BABL_ALPHA_FLOOR. This
  34 replaces asymptotic behavior and direct precision loss of color precision when
  35 multiplying or dividing by alphas near 0.0 with a consistent symmetric
  36 transformation.</p>
  37
  38 <p>Original intent of data as well as non-asymptotic precision loss is thus
  39 maintained when the processing chain might temporarily use the other alpha
  40 representation.</p>
  41
  42 <pre>
  43     #define BABL_ALPHA_FLOOR    (1.0/65536.0)
  44     #define BABL_ALPHA_FLOOR_F  (1.0f/65536.0f)
  45 </pre>
  46
  47 <p>The deviation from not clamping near 0.0 is within the quantization margin
  48 of 16bit integer alpha, thus no adaptations for any SIMD or and similar 8bit
  49 and 16bit extensions of pixel format conversions are needed.
  50   </p>
  51
  52    <p>This is the clamping function in use:</p>
  53 <pre>
  54 static inline float
  55 babl_epsilon_for_zero_float (float value)
  56 {
  57  if (value &lt;= BABL_ALPHA_FLOOR_F &amp;&amp;
  58      value &gt;= -BABL_ALPHA_FLOOR_F)
  59    return BABL_ALPHA_FLOOR_F;
  60  else
  61    return value;
  62 }
  63 </pre>
  64 <p>And an example use of this clamping function that is consistent with babls behavior:</p>
  65 <pre>
  66 static inline void
  67 associated_to_separate_rgba (const float *associated_rgba,
  68                                    float *separate_rgba)
  69 {
  70   float alpha = associated_rgba[3];
  71   float reciprocal_alpha = 1.0f / babl_epsilon_for_zero_float (alpha);
  72
  73   separate_rgba[0] = associated_rgba[0] * reciprocal_alpha;
  74   separate_rgba[1] = associated_rgba[1] * reciprocal_alpha;
  75   separate_rgba[2] = associated_rgba[2] * reciprocal_alpha;
  76   separate_rgba[3] = alpha;
  77 }
  78
  79
  80 static inline void
  81 separate_to_associated_rgba (const float *separate_rgba,
  82                                    float *associated_rgba)
  83 {
  84   float alpha = associated_rgba[3];
  85   float limited_alpha = babl_epsilon_for_zero_float (alpha);
  86
  87   associated_rgba[0] = separate_rgba[0] * limited_alpha;
  88   associated_rgba[1] = separate_rgba[1] * limited_alpha;
  89   associated_rgba[2] = separate_rgba[2] * limited_alpha;
  90   associated_rgba[3] = alpha;
  91 }
  92 </pre>
  93
  94
  95 <p>For more detils see <a href='https://gitlab.gnome.org/GNOME/babl/commit/a4d607843d3cab18745d547fc8a46dec51dcea5e'>the commit message of the most recent refinement</a> as well as <a href='https://www.patreon.com/posts/premultiplied-in-21014115'>blog post with further background</a>.</p>
  96
  97
  98
  99   <a href='graphics/index.html'><img class='BablFish' alt='/babl' title='babl' src='graphics/babl-48x48.png'/></a>
 100   </div>
 101   </div>
 102
 103     <div class='graphic'>
 104       <div class='print'>
 105         <img src='graphics/babl-a4poster.png' alt=' '/>
 106       </div>
 107     </div>
 108
 109   </body>
 110 </html>