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tutorial/chap5.html

@@ -37,7 +37,7 @@
 <div class="ContSect"><span class="tocline"><span class="nocss">&nbsp;</span><a href="chap5.html#X825C5B837A08F579">5.3 <span class="Heading">Digital image analysis</span></a>
 </span>
 <div class="ContSSBlock">
-<span class="ContSS"><br /><span class="nocss">&nbsp;&nbsp;</span><a href="chap5.html#X84F2B640851E82A6">5.3-1 <span class="Heading">Image segmentation by automatic thresholding</span></a>
+<span class="ContSS"><br /><span class="nocss">&nbsp;&nbsp;</span><a href="chap5.html#X8066F9B17B78418E">5.3-1 <span class="Heading">Naive example of image segmentation by automatic thresholding</span></a>
 </span>
 <span class="ContSS"><br /><span class="nocss">&nbsp;&nbsp;</span><a href="chap5.html#X7D512DA37F789B4C">5.3-2 <span class="Heading">Background to the data</span></a>
 </span>
@@ -181,11 +181,11 @@ <h4>5.3 <span class="Heading">Digital image analysis</span></h4>
 
 <p>The <span class="SimpleMath">20</span> persistent bars in the degree <span class="SimpleMath">0</span> barcode suggest that the image has <span class="SimpleMath">20</span> objects. The degree <span class="SimpleMath">1</span> barcode suggests that <span class="SimpleMath">14</span> (or possibly <span class="SimpleMath">17</span>) of these objects have holes in them.</p>
 
-<p><a id="X84F2B640851E82A6" name="X84F2B640851E82A6"></a></p>
+<p><a id="X8066F9B17B78418E" name="X8066F9B17B78418E"></a></p>
 
-<h5>5.3-1 <span class="Heading">Image segmentation by automatic thresholding</span></h5>
+<h5>5.3-1 <span class="Heading">Naive example of image segmentation by automatic thresholding</span></h5>
 
-<p>Assuming that short bars and isolated points in the barcodes represent noise while long bars represent essential features, a "noiseless" representation of the image should correspond to a term in the filtration corresponding to a column in the barcode incident with no short bars or isolated points. The following commands confirm that the 4th term in the filtration is such a term and display this term as a binary image.</p>
+<p>Assuming that short bars and isolated points in the barcodes represent noise while long bars represent essential features, a "noiseless" representation of the image should correspond to a term in the filtration corresponding to a column in the barcode incident all long bars but incident with no short bars or isolated points. The following commands confirm that the 4th term in the filtration is such a term and display this term as a binary image.</p>
 
 
 <div class="example"><pre>

tutorial/chap5.txt

@@ -138,14 +138,14 @@
   objects have holes in them.
 
 
-  5.3-1 Image segmentation by automatic thresholding
+  5.3-1 Naive example of image segmentation by automatic thresholding
 
   Assuming that short bars and isolated points in the barcodes represent noise
   while  long  bars represent essential features, a "noiseless" representation
   of  the image should correspond to a term in the filtration corresponding to
-  a  column in the barcode incident with no short bars or isolated points. The
-  following  commands  confirm  that  the 4th term in the filtration is such a
-  term and display this term as a binary image.
+  a  column  in  the barcode incident all long bars but incident with no short
+  bars or isolated points. The following commands confirm that the 4th term in
+  the filtration is such a term and display this term as a binary image.
 
     Example  
     gap> Y:=FiltrationTerm(F,4);            

tutorial/chap5_mj.html

@@ -40,7 +40,7 @@
 <div class="ContSect"><span class="tocline"><span class="nocss">&nbsp;</span><a href="chap5_mj.html#X825C5B837A08F579">5.3 <span class="Heading">Digital image analysis</span></a>
 </span>
 <div class="ContSSBlock">
-<span class="ContSS"><br /><span class="nocss">&nbsp;&nbsp;</span><a href="chap5_mj.html#X84F2B640851E82A6">5.3-1 <span class="Heading">Image segmentation by automatic thresholding</span></a>
+<span class="ContSS"><br /><span class="nocss">&nbsp;&nbsp;</span><a href="chap5_mj.html#X8066F9B17B78418E">5.3-1 <span class="Heading">Naive example of image segmentation by automatic thresholding</span></a>
 </span>
 <span class="ContSS"><br /><span class="nocss">&nbsp;&nbsp;</span><a href="chap5_mj.html#X7D512DA37F789B4C">5.3-2 <span class="Heading">Background to the data</span></a>
 </span>
@@ -184,11 +184,11 @@ <h4>5.3 <span class="Heading">Digital image analysis</span></h4>
 
 <p>The <span class="SimpleMath">\(20\)</span> persistent bars in the degree <span class="SimpleMath">\(0\)</span> barcode suggest that the image has <span class="SimpleMath">\(20\)</span> objects. The degree <span class="SimpleMath">\(1\)</span> barcode suggests that <span class="SimpleMath">\(14\)</span> (or possibly <span class="SimpleMath">\(17\)</span>) of these objects have holes in them.</p>
 
-<p><a id="X84F2B640851E82A6" name="X84F2B640851E82A6"></a></p>
+<p><a id="X8066F9B17B78418E" name="X8066F9B17B78418E"></a></p>
 
-<h5>5.3-1 <span class="Heading">Image segmentation by automatic thresholding</span></h5>
+<h5>5.3-1 <span class="Heading">Naive example of image segmentation by automatic thresholding</span></h5>
 
-<p>Assuming that short bars and isolated points in the barcodes represent noise while long bars represent essential features, a "noiseless" representation of the image should correspond to a term in the filtration corresponding to a column in the barcode incident with no short bars or isolated points. The following commands confirm that the 4th term in the filtration is such a term and display this term as a binary image.</p>
+<p>Assuming that short bars and isolated points in the barcodes represent noise while long bars represent essential features, a "noiseless" representation of the image should correspond to a term in the filtration corresponding to a column in the barcode incident all long bars but incident with no short bars or isolated points. The following commands confirm that the 4th term in the filtration is such a term and display this term as a binary image.</p>
 
 
 <div class="example"><pre>