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<h1>mmregmin
<br>
<span class="subtitle">Regional Minimum (with generalized dynamics).
</span>
</h1>
<div class="synopsis">
<H2>Synopsis</H2>
<div class="H2">
<div class="prototype">y =
<span class="fun">mmregmin</span>(
<span class="par">f</span>,
<span class="par">Bc</span> = None,
<span class="par">option</span> = "binary"
)
</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) image.
</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>
<tr>
<td class="term"><span class="par">option</span></td>
<td class="def"><span class="type"><a href="../mmtypes/mmString.html">String</a></span><p>Choose one of: BINARY: output a binary image; VALUE: output a grayscale image with points at the regional minimum with the pixel values of the input image; DYNAMICS: output a grayscale image with points at the regional minimum with its dynamics; AREA-DYN: int32 image with the area-dynamics; VOLUME-DYN: int32 image with the volume-dynamics.</p><p>Default:
<code>"binary"</code>
</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> Gray-scale (uint8 or uint16) or binary image.
</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
<div class="descr">
<H2>Description</H2>
<div class="H2">
<p>
<span class="fun">mmregmin</span> creates a binary image
<code>f</code> by computing the regional minima of
<code>f</code>, according to the connectivity defined by the structuring element
<code>Bc</code>. A regional minimum is a flat zone not surrounded by flat zones of lower gray values. A flat zone is a maximal connected component of a gray-scale image with same pixel values. There are three output options: binary image; valued image; and generalized dynamics. The dynamics of a regional minima is the minimum height a pixel has to climb in a walk to reach another regional minima with a higher dynamics. The area-dyn is the minimum area a catchment basin has to raise to reach another regional minima with higher area-dynamics. The volume-dyn is the minimum volume a catchment basin has to raise to reach another regional minima with a higher volume dynamics.
<br>The dynamics concept was first introduced in Grimaud:92 and it is the basic notion for the hierarchical or multiscale watershed transform.
</p>
</div>
</div>
<div class="examples">
<H2>Examples</H2>
<div class="H2">
<p>
<div class="bridge">Numerical example:</div>
<div class="example">
<div class="listing">
<pre class="user">>>> a = uint8([
[10, 10, 10, 10, 10, 10, 10],
[10, 9, 6, 18, 6, 5, 10],
[10, 9, 6, 18, 6, 5, 10],
[10, 9, 9, 15, 4, 9, 10],
[10, 9, 9, 15, 12, 10, 10],
[10, 10, 10, 10, 10, 10, 10]])</pre>
<pre class="computer"></pre>
<pre class="user">>>> print mmregmin(a)</pre>
<pre class="computer">[[0 0 0 0 0 0 0]
[0 0 1 0 0 1 0]
[0 0 1 0 0 1 0]
[0 0 0 0 1 0 0]
[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]]</pre>
<pre class="user">>>> print mmregmin(a,mmsecross(),'value')</pre>
<pre class="computer">[[0 0 0 0 0 0 0]
[0 0 6 0 0 5 0]
[0 0 6 0 0 5 0]
[0 0 0 0 4 0 0]
[0 0 0 0 0 0 0]
[0 0 0 0 0 0 0]]</pre>
<pre class="user">>>> print mmregmin(a,mmsecross(),'dynamics')</pre>
<pre class="computer">[[ 0 0 0 0 0 0 0]
[ 0 0 4 0 0 1 0]
[ 0 0 4 0 0 1 0]
[ 0 0 0 0 14 0 0]
[ 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0]]</pre>
</div>
</div>
<div class="bridge">Image example, filtering the regional minima:</div>
<br>Typically, the regional minima is very numerous in a real image. To filter the regional minima, one can use the
<span class="fun">mmhmin</span>,
<span class="fun">mmclose</span>,
<span class="fun">mmareaclose</span>, or other functions that simplifies basins.
<br>
<div class="example">
<div class="listing">
<pre class="user">>>> f1=mmreadgray('bloodcells.tif')</pre>
<pre class="computer"></pre>
<pre class="user">>>> m1=mmregmin(f1,mmsebox())</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(f1,m1)</pre>
<pre class="computer"></pre>
<pre class="user">>>> f2=mmhmin(f1,70)</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(f2)</pre>
<pre class="computer"></pre>
<pre class="user">>>> m2=mmregmin(f2,mmsebox())</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(f2,m2)</pre>
<pre class="computer"></pre>
</div>
<table class="images">
<tbody align="center">
<tr class="image" valign="bottom">
<td><img width="256" src="../images/img_mmregmin_001.jpg"></td>
<td><img width="256" src="../images/img_mmregmin_002.jpg"></td>
<td class="spare"></td>
</tr>
<tr class="title" valign="baseline">
<td><a href="../images/img_mmregmin_001.jpg">f1,m1</a></td>
<td><a href="../images/img_mmregmin_002.jpg">f2</a></td>
<td class="spare"></td>
</tr>
</tbody>
</table>
<table class="images">
<tbody align="center">
<tr class="image" valign="bottom">
<td><img width="256" src="../images/img_mmregmin_003.jpg"></td>
<td class="spare"></td>
</tr>
<tr class="title" valign="baseline">
<td><a href="../images/img_mmregmin_003.jpg">f2,m2</a></td>
<td class="spare"></td>
</tr>
</tbody>
</table>
</div>
<div class="bridge">Multiscale watershed</div>
<br>To build a pyramid of nested segmentations, use the marker for the watershed only the minima above a given dynamic. Two levels of this pyramid are build below, one with dynamic above 20 and the other, above 40.
<br>
<div class="example">
<div class="listing">
<pre class="user">>>> f=mmreadgray('cameraman.tif')</pre>
<pre class="computer"></pre>
<pre class="user">>>> g=mmgradm(f)</pre>
<pre class="computer"></pre>
<pre class="user">>>> mh=mmregmin(g,mmsecross(),'dynamics')</pre>
<pre class="computer"></pre>
<pre class="user">>>> ws1=mmcwatershed(g, mmbinary(mh, 20))</pre>
<pre class="computer"></pre>
<pre class="user">>>> ws2=mmcwatershed(g, mmbinary(mh, 40))</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(ws1)</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(ws2)</pre>
<pre class="computer"></pre>
</div>
<table class="images">
<tbody align="center">
<tr class="image" valign="bottom">
<td><img width="256" src="../images/img_mmregmin_004.jpg"></td>
<td><img width="256" src="../images/img_mmregmin_005.jpg"></td>
<td class="spare"></td>
</tr>
<tr class="title" valign="baseline">
<td><a href="../images/img_mmregmin_004.jpg">ws1</a></td>
<td><a href="../images/img_mmregmin_005.jpg">ws2</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_mmregmin001.png">
</div>
</p>
</div>
</div>
<div class="sourcecode">
<H2>Source Code</H2>
<div class="H2">
<pre class="listing">
def mmregmin(f, Bc=None, option="binary"):
if Bc is None: Bc = mmsecross()
fplus = mmaddm(f,1)
g = mmsubm(mmsuprec(fplus,f,Bc),f)
y = mmunion(mmthreshad(g,1),mmthreshad(f,0,0))
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/mmregmax.html">mmregmax</a></td>
<td class="def">Regional Maximum.</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/mmhmin.html">mmhmin</a></td>
<td class="def">Remove basins with contrast less than h.</td>
</tr>
<tr>
<td class="term"><a href="../morph/mmareaclose.html">mmareaclose</a></td>
<td class="def">Area closing</td>
</tr>
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</table>
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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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distrib
>
Mandriva
>
2010.0
>
i586
>
media
>
contrib-release
>
by-pkgid
>
4a71d9984febeb5a206904a5a379841a
>
files
>
727
