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<td class="title">Connected Operators</td>
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</table>
<h1>mmareaopen
<br>
<span class="subtitle">Area opening
</span>
</h1>
<div class="synopsis">
<H2>Synopsis</H2>
<div class="H2">
<div class="prototype">y =
<span class="fun">mmareaopen</span>(
<span class="par">f</span>,
<span class="par">a</span>,
<span class="par">Bc</span> = None
)
</div>
<p>Implemented in
<b>Python.</b>
</p>
<div class="input">
<H3>Input</H3>
<div class="H3">
<table class="deflist">
<tbody valign="baseline">
<tr>
<td class="term"><span class="par">f</span></td>
<td class="def"><span class="type"><a href="../mmtypes/mmImage.html">Image</a></span> Gray-scale (uint8 or uint16) or binary image.
</td>
</tr>
<tr>
<td class="term"><span class="par">a</span></td>
<td class="def"><span class="type"><a href="../mmtypes/mmDouble.html">Double</a></span><p>non negative integer.</p></td>
</tr>
<tr>
<td class="term"><span class="par">Bc</span></td>
<td class="def"><span class="type"><a href="../mmtypes/mmSe.html">Structuring Element</a></span><p>( connectivity).</p><p>Default:
<code>None</code> (3x3 elementary cross)
</p></td>
</tr>
</tbody>
</table>
</div>
</div>
<div class="output">
<H3>Output</H3>
<div class="H3">
<table class="deflist">
<tbody valign="baseline">
<tr>
<td class="term"><span class="par">y</span></td>
<td class="def"><span class="type"><a href="../mmtypes/mmImage.html">Image</a></span><p>Same type of
<code>f</code>
</p></td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
<div class="descr">
<H2>Description</H2>
<div class="H2">
<p>
<span class="fun">mmareaopen</span> removes any grain (i.e., connected component) with area less than
<code>a</code> of a binary image
<code>f</code>. The connectivity is given by the structuring element
<code>Bc</code>. This operator is generalized to gray-scale images by applying the binary operator successively on slices of
<code>f</code> taken from higher threshold levels to lower threshold levels.
</p>
</div>
</div>
<div class="examples">
<H2>Examples</H2>
<div class="H2">
<p>
<div class="bridge">Numerical examples:</div>
<div class="example">
<div class="listing">
<pre class="user">>>> f=mmbinary(uint8([
[1, 1, 0, 0, 0, 0, 1],
[1, 0, 1, 1, 1, 0, 1],
[0, 0, 0, 0, 1, 0, 0]]))</pre>
<pre class="computer"></pre>
<pre class="user">>>> y=mmareaopen(f,4,mmsecross())</pre>
<pre class="computer"></pre>
<pre class="user">>>> print y</pre>
<pre class="computer">[[0 0 0 0 0 0 0]
[0 0 1 1 1 0 0]
[0 0 0 0 1 0 0]]</pre>
</div>
</div>
<div class="example">
<div class="listing">
<pre class="user">>>> f=uint8([
[10, 11, 0, 0, 0, 0, 20],
[10, 0, 5, 8, 9, 0, 15],
[10, 0, 0, 0, 10, 0, 0]])</pre>
<pre class="computer"></pre>
<pre class="user">>>> y=mmareaopen(f,4,mmsecross())</pre>
<pre class="computer"></pre>
<pre class="user">>>> print y</pre>
<pre class="computer">[[10 10 0 0 0 0 0]
[10 0 5 5 5 0 0]
[10 0 0 0 5 0 0]]</pre>
</div>
</div>
<div class="bridge">Binary image</div>
<div class="example">
<div class="listing">
<pre class="user">>>> a=mmreadgray('form-1.tif');</pre>
<pre class="computer"></pre>
<pre class="user">>>> b=mmareaopen(a,500);</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(a);</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(b);</pre>
<pre class="computer"></pre>
</div>
<table class="images">
<tbody align="center">
<tr class="image" valign="bottom">
<td><img width="320" src="../images/img_mmareaopen_001.jpg"></td>
<td><img width="320" src="../images/img_mmareaopen_002.jpg"></td>
<td class="spare"></td>
</tr>
<tr class="title" valign="baseline">
<td><a href="../images/img_mmareaopen_001.jpg">a</a></td>
<td><a href="../images/img_mmareaopen_002.jpg">b</a></td>
<td class="spare"></td>
</tr>
</tbody>
</table>
</div>
<div class="bridge">Gray-scale image</div>
<div class="example">
<div class="listing">
<pre class="user">>>> a=mmreadgray('bloodcells.tif');</pre>
<pre class="computer"></pre>
<pre class="user">>>> b=mmareaopen(a,500);</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(a);</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(b);</pre>
<pre class="computer"></pre>
</div>
<table class="images">
<tbody align="center">
<tr class="image" valign="bottom">
<td><img width="256" src="../images/img_mmareaopen_003.jpg"></td>
<td><img width="256" src="../images/img_mmareaopen_004.jpg"></td>
<td class="spare"></td>
</tr>
<tr class="title" valign="baseline">
<td><a href="../images/img_mmareaopen_003.jpg">a</a></td>
<td><a href="../images/img_mmareaopen_004.jpg">b</a></td>
<td class="spare"></td>
</tr>
</tbody>
</table>
</div>
</p>
</div>
</div>
<div class="equation">
<H2>Equation</H2>
<div class="H2">
<p>
<div class="eqfig">
<img src="../images/eq_mmareaopen001.png">
</div>
</p>
</div>
</div>
<div class="descr">
<H2>Limitations</H2>
<div class="H2">
<p>
The structuring elements allowed are the elementary cross (4-connected) and the elementary box (8-connected).
</p>
</div>
</div>
<div class="sourcecode">
<H2>Source Code</H2>
<div class="H2">
<pre class="listing">
def mmareaopen(f, a, Bc=None):
if Bc is None: Bc = mmsecross()
if mmisbinary(f):
fr = mmlabel(f,Bc) # binary area open, use area measurement
g = mmblob(fr,'area')
y = mmthreshad(g,a)
else:
y = mmintersec(f,0)
zero = mmbinary(y)
k1 = mmstats(f,'min')
k2 = mmstats(f,'max')
for k in range(k1,k2+1): # gray-scale, use thresholding decomposition
fk = mmthreshad(f,k)
fo = mmareaopen(fk,a,Bc)
if mmisequal(fo,zero):
break
y = mmunion(y, mmgray(fo,mmdatatype(f),k))
return y
</pre>
</div>
</div>
<div class="seealso">
<H2>See also</H2>
<div class="H2">
<table class="deflist">
<tbody valign="baseline">
<tr>
<td class="term"><a href="../morph/mmfreedom.html">mmfreedom</a></td>
<td class="def">Control automatic data type conversion.</td>
</tr>
<tr>
<td class="term"><a href="../morph/mmlabel.html">mmlabel</a></td>
<td class="def">Label a binary image.</td>
</tr>
<tr>
<td class="term"><a href="../morph/mmsebox.html">mmsebox</a></td>
<td class="def">Create a box structuring element.</td>
</tr>
<tr>
<td class="term"><a href="../morph/mmsecross.html">mmsecross</a></td>
<td class="def">Diamond structuring element and elementary 3x3 cross.</td>
</tr>
<tr>
<td class="term"><a href="../morph/mmareaclose.html">mmareaclose</a></td>
<td class="def">Area closing</td>
</tr>
</tbody>
</table>
</div>
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<td class="copyright">Copyright (c) 2003, Roberto A. Lotufo, UNICAMP-University of Campinas; Rubens C. Machado, CenPRA-Renato Archer Research Center.</td>
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2010.0
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