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<title>What's In A GIF - LZW Image Data</title>
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<td><h2>What's In A GIF</h2></td>
<td align="center"><img src="../giflib-logo.gif"></td>
<td align="right">(LZW image data)</td>
</tr>
</table>
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<div style="text-align:center; margin-top: 10px; padding-top: 10px; border-top: #cecece 1px solid">
<p><a href="index.html">Back to the GIF index page.</a></p>
</div>
<p>Now let's look at exactly how we go about storing an image in a GIF
file. The GIF format is a raster format, meaning it stores image data
by remembering the color of every pixel in the image. More
specifically, GIF files remember the index of the color in a color
table for each pixel. To make that clearer, let's review the
sample image we used in the <a href="bits_and_bytes.html">first
section</a>.</p>
<table style="margin-left: auto; margin-right:auto;">
<tr>
<td style="text-align:center; vertical-align: top; padding: 5px;width:30%">
<h3>Actual Size</h3>
<img src="sample_1.gif" alt="sample gif, actual size" title="Actual Size"
width="10" height="10" style="padding: 20px" /><br/>(10x10)</td>
<td style="text-align:center; vertical-align: top; padding: 5px;; width:40%">
<h3>Enlarged</h3>
<img src="sample_1_enlarged.gif" alt="sample gif, enlarged"
title="Enlarged" width="100" height="100" /><br/>(100x100)</td>
<td style="vertical-align: top; padding: 5px; width:30%">
<h3>Color Table</h3>
<table>
<tr><th>Index</th><th>Color</th></tr>
<tr><td>0</td><td><span style="color:#FFFFFF; background: #000000; font-weight: bold">White</span></td></tr>
<tr><td>1</td><td><span style="color:#FF0000; font-weight: bold">Red</span></td></tr>
<tr><td>2</td><td><span style="color:#0000FF; font-weight: bold">Blue</span></td></tr>
<tr><td>3</td><td><span style="font-weight: bold">Black</span></td></tr>
</table>
</td>
</tr></table>
<p>The color table came from the global color table block. The colors
are listed in the order which they appear in the file. The first color
is given an index of zero. When we send the codes, we always start at
the top left of the image and work our way right. When we get to the
end of the line, the very next code is the one that starts the next
line. (The decoder will "wrap" the image based on the image
dimensions.) We could encode our sample image in the following
way:</p>
<blockquote><p>1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1,
1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1,
0, 0, 0, 0, 2, 2, 2, ...</p></blockquote>
<p>The above listing shows the sequence required to render the first five
lines of the image. We could continue with this method until we've
specified the color for every pixel; however, this can result in a
rather large file. Luckily for us, the GIF format allows us to take
advantage of repetition in our output and to compress our data.</p>
<p>Much of the following information came from John Barkaus's tutorial
<cite>LZW and GIF Explained</cite>, which seems to have fallen off the
web. I've tried to provide more detailed samples as well
as illustrations to make the process even clearer</p>
<h2><a name="lzw_compression">LZW Compression</a></h2>
<p>The compression method GIF use is a variant of LZW
(Lempel-Ziv-Welch) compression. To start using this method, we need a
<strong>code table</strong>. This code table will allow us to use
special codes to indicate a sequence of colors rather than just one at
a time. The first thing we do is to <em>initialize the code
table</em>. We start by adding a code for each of the colors in the
color table. This would be a local color table if one was provided, or
the global color table. (I will be starting all codes with
"#" to distinguish them from color indexes.)</p>
<table class="code_table">
<tr><th>Code</th><th>Color(s)</th></tr>
<tr><td>#0</td><td>0</td></tr>
<tr><td>#1</td><td>1</td></tr>
<tr><td>#2</td><td>2</td></tr>
<tr><td>#3</td><td>3</td></tr>
<tr><td>#4</td><td>Clear Code</td></tr>
<tr><td>#5</td><td>End Of Information Code</td></tr>
</table>
<p>I added a code for each of the colors in the global color table of
our sample image. I also snuck in two special control codes. (These
special codes are only used in the GIF version of LZW, not in standard
LZW compression.) Our code table is now considered initialized.</p>
<p>Let me now explain what those special codes are for. The first new code
is the <em>clear code</em> (CC). Whenever you come across the clear code
in the image data, it's your cue to reinitialize the code table. (I'll
explain why you might need to do this in a bit.) The second new code
is the <em>end of information code</em> (EOI). When you come across
this code, this means you've reached the end of the image. Here I've placed
the special codes right after the color codes, but actually the value of
the special codes depends on the value of the LZW minimum code size
from the image data block. If the LZW minimum code size is the same as
the color table size, then special codes immediatly follow the colors; however
it is possible to specify a larger LWZ minimum code size which may leave
a gap in the codes where no colors are assigned. This can be
summarizaed in the <a name="color_table_size">following table</a>.</p>
<div style="text-align:center">
<table id="global_color_size">
<tr><th>LWZ Min Code<br/>Size</th><th>Color<br/>Codes</th><th>Clear<br/>Code</th><th>EOI<br/>Code</th></tr>
<tr><td>2</td><td>#0-#3</td><td>#4</td><td>#5</td></tr>
<tr><td>3</td><td>#0-#7</td><td>#8</td><td>#9</td></tr>
<tr><td>4</td><td>#0-#15</td><td>#16</td><td>#17</td></tr>
<tr><td>5</td><td>#0-#31</td><td>#32</td><td>#33</td></tr>
<tr><td>6</td><td>#0-#63</td><td>#64</td><td>#65</td></tr>
<tr><td>7</td><td>#0-#127</td><td>#128</td><td>#129</td></tr>
<tr><td>8</td><td>#0-#255</td><td>#256</td><td>#257</td></tr>
</table>
</div>
<p>Before we proceed, let me define two more terms. First the <strong>index
stream</strong> will be the list of indexes of the color for each of
the pixels. This is the input we will be compressing. The <strong>code
stream</strong> will be the list of codes we generate as output. The
<strong>index buffer</strong> will be the list of color indexes
we care "currently looking at." The index buffer will contain a list
of one or more color indexes. Now we can step though the LZW
compression algorithm. First, I'll just list the steps. After that
I'll walk through the steps with our specific example.</p>
<ul>
<li>Initialize code table</li>
<li>Always start by sending a clear code to the code stream.</li>
<li>Read first index from index stream. This value is now the value
for the index buffer</li>
<li><LOOP POINT></li>
<li>Get the next index from the index stream to the index buffer. We will
call this index, K</li>
<li>Is index buffer + K in our code table?</li>
<li>Yes:
<ul>
<li>add K to the end of the index buffer</li>
<li>if there are more indexes, return to LOOP POINT</li>
</ul>
</li>
<li>No:
<ul>
<li>Add a row for index buffer + K into our code table with
the next smallest code</li>
<li>Output the code for just the index buffer to our code steam</li>
<li>Index buffer is set to K</li>
<li>K is set to nothing</li>
<li>if there are more indexes, return to LOOP POINT</li>
</ul>
</li>
<li>Output code for contents of index buffer</li>
<li>Output end-of-information code</li>
</ul>
<p>Seems simple enough, right? It really isn't all that bad. Let's
walk though our sample image to show you how this works. (The steps I
will be describing are summarized in the following table. Numbers
highlighted in green are in the index buffer; numbers in purple are
the current K value.) We have already initialized our code table. We
start by doing two things: we output our clear code (#4) to the code
stream, and we read the first color index from the index stream, 1,
into our index buffer [Step 0].</p>
<p>Now we enter the main loop of the algorithm. We read the next index
in the index stream, 1, into K [Step 1]. Next we see if we have a
record for the index buffer plus K in the code stream. In this case we
looking for 1,1. Currently our code table only contains single colors
so this value is not in there. Now we will actually add a new row to
our code table that does contain this value. The next available code
is #6, we will let #6 be 1,1. Note that we do not actually send this
code to the code stream, instead we send just the code for the
value(s) in the index buffer. The index buffer is just 1 and the code
for 1 is #1. This is the code we output. We now reset the index buffer
to just the value in K and K becomes nothing. [Step 2].</p>
<p>We continue by reading the next index into K. [Step 3]. Now K is 1 and the
index buffer is 1. Again we look to see if there is a value in our code
table for the buffer plus K (1,1) and this time there is. (In fact we just
added it.) Therefore we add K to the end of the index buffer and clear out
K. Now our index buffer is 1,1. [Step 4].</p>
<p>The next index in the index stream is yet another 1. This is our
new K [Step 5]. Now the index buffer plus K is 1,1,1 which we do not
have a code for in our code table. As we did before, we define a new
code and add it to the code table. The next code would be #7; thus #7
= 1, 1, 1. Now we kick out the code for just the values in the index
buffer (#6 = 1,1) to the code stream and set the index buffer to be
K. [Step 6].</p>
<table class="alg_steps" cellspacing="0">
<tbody>
<tr>
<th>Step</th>
<th>Action</th>
<th>Index Stream</th>
<th>New Code Table Row</th>
<th>Code Stream</th>
</tr>
<tr>
<td>0</td>
<td>Init</td>
<td><span class="processed"></span>
<span class="buffer"><span class="index">1</span></span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4</td>
</tr>
<tr>
<td>1</td>
<td>Read</td>
<td><span class="processed"></span>
<span class="buffer"><span class="index">1</span></span>
<span class="current"><span class="index">1</span></span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4</td>
</tr>
<tr>
<td>2</td>
<td>Not Found</td>
<td><span class="processed"><span class="index">1</span></span>
<span class="buffer"><span class="index">1</span></span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td>#6 - 1, 1</td>
<td>#4 #1</td>
</tr>
<tr>
<td>3</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span></span>
<span class="buffer"><span class="index">1</span></span>
<span class="current"><span class="index">1</span></span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1</td>
</tr>
<tr>
<td>4</td>
<td>Found</td>
<td><span class="processed"><span class="index">1</span></span>
<span class="buffer"><span class="index">1</span>
<span class="index">1</span></span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1</td>
</tr>
<tr>
<td>5</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span></span>
<span class="buffer"><span class="index">1</span>
<span class="index">1</span></span>
<span class="current"><span class="index">1</span></span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1</td>
</tr>
<tr>
<td>6</td>
<td>Not Found</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span></span>
<span class="buffer"><span class="index">1</span></span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td>#7 - 1, 1, 1</td>
<td>#4 #1 #6</td>
</tr>
</tbody>
<tbody id="compress_more">
<tr>
<td>7</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span></span>
<span class="buffer"><span class="index">1</span></span>
<span class="current"><span class="index">1</span></span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6</td>
</tr>
<tr>
<td>8</td>
<td>Found</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span></span>
<span class="buffer"><span class="index">1</span>
<span class="index">1</span></span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6</td>
</tr>
<tr>
<td>9</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span></span>
<span class="buffer"><span class="index">1</span>
<span class="index">1</span></span>
<span class="current"><span class="index">2</span></span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6</td>
</tr>
<tr>
<td>10</td>
<td>Not Found</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span></span>
<span class="buffer"><span class="index">2</span></span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td>#8 - 1, 1, 2</td>
<td>#4 #1 #6 #6</td>
</tr>
<tr>
<td>11</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span></span>
<span class="buffer"><span class="index">2</span></span>
<span class="current"><span class="index">2</span></span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6</td>
</tr>
<tr>
<td>12</td>
<td>Not Found </td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">2</span></span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td>#9 - 2, 2</td>
<td>#4 #1 #6 #6 #2</td>
</tr>
<tr>
<td>13</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">2</span></span>
<span class="current"><span class="index">2</span></span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2</td>
</tr>
<tr>
<td>14</td>
<td>Found </td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">2</span>
<span class="index">2</span></span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2</td>
</tr>
<tr>
<td>15</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">2</span>
<span class="index">2</span></span>
<span class="current"><span class="index">2</span></span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2</td>
</tr>
<tr>
<td>16</td>
<td>Not Found</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">2</span></span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td>#10 - 2, 2, 2</td>
<td>#4 #1 #6 #6 #2 #9</td>
</tr>
<tr>
<td>17</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">2</span></span>
<span class="current"><span class="index">2</span></span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2 #9</td>
</tr>
<tr>
<td>18</td>
<td>Found</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">2</span>
<span class="index">2</span></span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2 #9</td>
</tr>
<tr>
<td>19</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">2</span>
<span class="index">2</span></span>
<span class="current"><span class="index">1</span></span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2 #9</td>
</tr>
<tr>
<td>20</td>
<td>Not Found</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">1</span></span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td>#11 - 2, 2, 1</td>
<td>#4 #1 #6 #6 #2 #9 #9</td>
</tr>
<tr>
<td>21</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">1</span></span>
<span class="current"><span class="index">1</span></span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2 #9 #9</td>
</tr>
<tr>
<td>22</td>
<td>Found</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">1</span>
<span class="index">1</span></span>
<span class="index">1</span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2 #9 #9</td>
</tr>
<tr>
<td>23</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">1</span>
<span class="index">1</span></span>
<span class="current"><span class="index">1</span></span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2 #9 #9</td>
</tr>
<tr>
<td>24</td>
<td>Found</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span></span>
<span class="index">1</span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2 #9 #9</td>
</tr>
<tr>
<td>25</td>
<td>Read</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span></span>
<span class="buffer"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span></span>
<span class="current"><span class="index">1</span></span>...</td>
<td> </td>
<td>#4 #1 #6 #6 #2 #9 #9</td>
</tr>
<tr>
<td>26</td>
<td>Not Found</td>
<td><span class="processed"><span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">2</span>
<span class="index">1</span>
<span class="index">1</span>
<span class="index">1</span></span>
<span class="buffer"><span class="index">1</span></span>...</td>
<td>#12 - 1, 1, 1, 1</td>
<td>#4 #1 #6 #6 #2 #9 #9 #7</td>
</tr>
</tbody>
</table>
<p>I've included a few more steps to help you see the pattern. You
keep going until you run out of indexes in the index stream. When
there is nothing new to read, you simply write out the code for
whatever values you may have in your index buffer. Finally you should
send the end-of-information code to the code stream. In this example,
that code is #5. (View the <a href="lzw_image_data_code_table.html">
complete code table</a>.)</p>
<p>As you can see we dynamically built many new codes for our code
table as we compressed the data. For large files this can turn into a
large number of codes. It turns out that the GIF format specifies a
maximum code of #4095 (this happens to be the largest 12-bit
number). If you want to use a new code, you have to clear out all of
your old codes. You do this by sending the clear code (which for our
sample was the #4). This tells the decoder that you are reinitializing
your code table and it should too. Then you start building your own
codes again starting just after the value for your end-of-information
code (in our sample, we would start again at #6).</p>
<p>The final code stream would look like this:</p>
<blockquote><p>#4 #1 #6 #6 #2 #9 #9 #7 #8 #10 #2 #12 #1 #14 #15 #6 #0 #21 #0 #10 #7 #22 #23
#18 #26 #7 #10 #29 #13 #24 #12 #18 #16 #36 #12 #5</p></blockquote>
<p>This is only 36 codes versus the 100 that would be required without compression.</p>
<h2><a name="lzw_decompression">LZW Decompression</a></h2>
<p> At some point we will need to turn this code stream back into
a picture. To do this, we only need to know the values in the stream
and the size of the color table that was used. That's it. You remember that
big code table we built during compression? We actually have enough information
in the code stream itself to be able to rebuild it.</p>
<p>Again, i'll list the algorithm and then we will walk though an example. Let
me define a few terms i will be using. CODE will be current code we're working
with. CODE-1 will be the code just before CODE in the code stream. {CODE}
will be the value for CODE in the code table. For example, using the code
table we created during compression, if CODE=#7 then {CODE}=1,1,1.
In the same way, {CODE-1} would be the value in the code table for the
code that came before CODE. Looking at step 26 from the compression,
if CODE=#7, then {CODE-1} would be {#9}, not {#6}, which was 2,2.</p>
<ul>
<li>Initialize code table</li>
<li>let CODE be the first code in the code stream</li>
<li>output {CODE} to index stream</li>
<li><LOOP POINT></li>
<li>let CODE be the next code in the code stream</li>
<li>is CODE in the code table?</li>
<li>Yes:
<ul>
<li>output {CODE} to index stream</li>
<li>let K be the first index in {CODE}</li>
<li>add {CODE-1}+K to the code table</li>
</ul>
</li>
<li>No:
<ul>
<li>let K be the first index of {CODE-1}</li>
<li>output {CODE-1}+K to index stream</li>
<li>add {CODE-1}+K to code table</li>
</ul>
</li>
<li>return to LOOP POINT</li>
</ul>
<p>Let's start reading though the code stream we've created to show how to
turn it back into a list of color indexes. The first value in the code
stream should be a clear code. This means we should initialize our code
table. To do this we must know how many colors are in our color table.
(This information comes from the first byte in the image data block in
the file. More on this later.) Again we will set up codes #0-#3 to be each
of the four colors and add in the clear code (#4)
and end of information code (#5).</p>
<p>The next step is to read the first color code. In the following table you
will see the values of CODE highlighted in purple, and the values for
CODE-1 highlighted in green. Our first CODE value is #1. We then output
{#1}, or simply 1, to the index stream [Step 0].</p>
<p>Now we enter the main loop of the algorithm. The next code gets assigned
to CODE which now makes that value #6. Next we check to see if this value
is in our code table. At this time, it is not. This means we must find the
first index in the value of {CODE-1} and call this K. Thus K = first index of
{CODE-1} = first index of {#1} = 1. Now we output {CODE-1} + K to the index
stream and add this value to our code table. The means we output 1,1 and
give this value a code of #6 [Step 1].</p>
<table class="alg_steps" cellspacing="0">
<tr>
<th>Step</th>
<th>Action</th>
<th>Code Stream</th>
<th>New Code Table Row</th>
<th>Index Stream</th>
</tr>
<tr>
<td>0</td>
<td>Init</td>
<td><span class="processed">#4</span> <span class="current">#1</span> #6 #6 #2 #9 #9 #7 ...</td>
<td> </td>
<td>1</td>
</tr>
<tr>
<td>1</td>
<td>Not Found</td>
<td><span class="processed">#4</span> <span class="buffer">#1</span> <span class="current">#6</span> #6 #2 #9 #9 #7 ...</td>
<td>#6 - 1, 1</td>
<td>1, 1, 1</td>
</tr>
<tr>
<td>2</td>
<td>Found</td>
<td><span class="processed">#4 #1</span> <span class="buffer">#6</span> <span class="current">#6</span> #2 #9 #9 #7 ...</td>
<td>#7 - 1, 1, 1</td>
<td>1, 1, 1, 1, 1</td>
</tr>
<tr>
<td>3</td>
<td>Found</td>
<td><span class="processed">#4 #1 #6</span> <span class="buffer">#6</span> <span class="current">#2</span> #9 #9 #7 ...</td>
<td>#8 - 1, 1, 2</td>
<td>1, 1, 1, 1, 1, 2</td>
</tr>
<tr>
<td>4</td>
<td>Not Found</td>
<td><span class="processed">#4 #1 #6 #6</span> <span class="buffer">#2</span> <span class="current">#9</span> #9 #7 ...</td>
<td>#9 - 2, 2</td>
<td>1, 1, 1, 1, 1, 2, 2, 2</td>
</tr>
<tr>
<td>5</td>
<td>Found</td>
<td><span class="processed">#4 #1 #6 #6 #2</span> <span class="buffer">#9</span> <span class="current">#9</span> #7 ...</td>
<td>#10 - 2, 2, 2</td>
<td>1, 1, 1, 1, 1, 2, 2, 2, 2, 2</td>
</tr>
<tr>
<td>6</td>
<td>Found</td>
<td><span class="processed">#4 #1 #6 #6 #2 #9</span> <span class="buffer">#9</span> <span class="current">#7</span> ...</td>
<td>#11 - 2, 2, 1</td>
<td>1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1</td>
</tr>
</table>
<p>We start the loop again by reading the next code. CODE now would be
#6 and this time we do have a record for this code in our code
table. Thus we dump {#6} to the index stream which would be 1,1.
Now we take the first index in {#6} and call that K. Here, {#6} has
two indexes, the first of which is 1; thus K = 1. Before moving
on, we add {CODE-1}+K to the code table. This #7 is now 1, 1, 1 [Step 2].</p>
<p>I've included a few more steps so you can see the algorithm in action. While
the explanation may sound complicated, you can see it's actually quite simple.
You'll also notice that you end up building the exact same
<a href="lzw_image_data_code_table.html">code table</a>
as the one that was created during compression. This is the reason that
LZW is so great; we can just share the codes and not the table.</p>
<h2><a name="lzw_bytes">Saving the Code Stream as Bytes</a></h2>
<p>I've shown you how to go back and forth between index and code stream, but
haven't told you what to do with them. The index stream is used to specify the
color of each of the pixel of your image and really only shows up on screen.
It is the code stream that is actually saved in the GIF files on your computer
or transmitted over the internet. In order to save these code streams, we must
turn them into bytes. The first thought might be to store each of the codes
as its own byte; however this would limit the max code to just #255 and
result in a lot of wasted bits for the small codes. To solve these problems,
the GIF file format actually uses flexible <em>code sizes</em>.</p>
<p>Flexible code sizes allow for further compression by limiting the bits
needed to save the code stream as bytes. The <em>code size</em> is the number
of bits it takes to store the value of the code. When we talk about bits,
we're referring to the 1's and 0's that make up a byte. The codes are
converted to their binary values to come up with the bits. To specify
the code for #4, you would look at this binary equivalent, which is 100,
and see that you would need three bits to store this value. The largest code
value in our sample code stream is #36 (binary: 100100) which would
take 6 bits to encode. Note that the number of bits i've just given is
the minimum number. You can make the number take up more bits by adding
zeros to the front.</p>
<p style="text-align:center"><img src="image_data_block.gif" alt="GIF image data block layout" style="border: 1px solid black" /></p>
<p>We need a way to know what size each of the codes are. Recall that the
image data block begins with a single byte value called the
<em>LZW minimum code size</em>. The GIF format allows sizes as small
as 2 bits and as large as 12 bits. This minimum code size value is typically
the number of bits/pixel of the image. So if you have 32 colors in your image,
you will need 5 bits/pixel (for numbers 0-31 because 31 in binary is 11111).
Thus, this will most likely be one more than the bit value for the size of the
color table you are using. (Even if you only have two colors, the minimum
code size most be at least 2.) Refer to the <a href="#color_table_size">
code table above</a> to remind yourself how that works.</p>
<p>Here's the funny thing: the value for minimum code size isn't
actually the smallest code size that's used in the encoding
process. Because the minimum code size tells you how many bits are
needed just for the different colors of the image, you still have to
account for the two special codes that we always add to the code
table. Therefore the actual smallest code size that will be used is
one more than the value specified in the "minimum" code size
byte. I'll call this new value the <em>first code size</em>.</p>
<p>We now know how many bytes the first code will be. This size will probably
work for the next few codes as well, but recall that the GIF format
allows for flexible code sizes. As larger code values get added to your
code table, you will soon realize that you need larger code sizes if you
were to output those values. When you are encoding the data, you increase
your code size as soon as your write out the code equal to
2^(current code size)-1. If you are decoding from codes to indexes,
you need to increase your code size as soon as you add the code value that
is equal to 2^(current code size)-1 to your code table. That is, the next
time you grab the next section of bits, you grab one more.</p>
<p>Note that the largest code size allowed is 12 bits. If you get to this
limit, the next code you encounter should be the <em>clear code</em> which
would tell you to reinitialize the code table. You then go back to using
the first code size and grow again when necessary.</p>
<p>Jumping back to our sample image, we see that we have a minimum code
size value of 2 which means out first code size will be 3 bits long.
Out first three codes, #1 #6 and #6, would be coded as 001 110 and 110.
If you see at Step 6 of the encoding, we added a code of #7 to our code
table. This is our clue to increase our code size because 7 is equal to
2^3-1 (where 3 is our current code size). Thus, the next code we
write out, #2, will use the new code size of 4 and therefore look
like 0010. In the decoding process, we again would increase our code
size when we read the code for #7 and would read the next 4, rather than
the next 3 bits, to get the next code. In the sample table above this
occurs in Step 2.</p>
<p>Finally we must turn all these bit values into bytes. The lowest bit of the
code bit value gets placed in the lowest available bit of the byte. After
you've filled up the 8 bits in the byte, you take any left over bits and
start a new byte. Take a look at the following illustration to see
how that works with the codes from our sample image.</p>
<p style="text-align:center"><img src="lzw_encoding_codes.gif"
alt="Encoding LZW Codes" style="border: 1px solid black" / WIDTH="500"
HEIGHT="220"></p>
<p>You can see in the first byte that was returned (<span
class="byte">8C</span>) that the lowest three bits (because that was
our first code size) contain 110 which is the binary value of 4 so
that would be the clear code we started with, #4. In the three bits to
the left, you see 001 which out or first data code of #1. You can also
see when we switched into code sizes of 4 bits in the second byte
(<span class="byte">2D</span>).</p>
<p>When you run out of codes but have filled less than 8 bits of the
byte, you should just fill the remaining bits with zeros. Recall that
the image data must be broken up onto <a
href="bits_and_bytes.html#image_data_block">data sub-blocks</a>. Each
of the data sub-blocks begins with a byte that specifies how many
bytes of data. The value will be between 1 and 255. After you read
those bytes, the next byte indicates again how many bytes of data
follow. You stop when you encounter a subblock that has a lenght of
zero. That tells you when you've reached the end of the image data. In
our sample the image the byte just after the LZW code size is <span
class="byte">16</span> which indicates that 22 bytes of data
follow. After we reach those, we see the next byte is <span
class="byte">00</span> which means we are all done.</p>
<p>Return codes from bytes the basically just the same process in
reverse. A sample illustration of the process follows which shows how
you would extract codes if the first code size were 5 bits.</p>
<p style="text-align:center"><img src="lzw_decoding_bytes.gif" alt="Decoding LZW Bytes" style="border: 1px solid black" / WIDTH="500" HEIGHT="220"></p>
<h2>Next: Animation and Transparency</h2>
<p>That is pretty much everything you need to know to read or generate
a basic image file. One of the reasons the GIF becames such a popular
format was because it also allowed for "fancier" features. These
features include animation and transparency. Next we'll look
at how those work.</p>
<p><a href="animation_and_transparency.html">Continue...</a></p>
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