Influence of the Processes Parameters on the Properties of The ...
Influence of the Processes Parameters on the Properties of The ...
Influence of the Processes Parameters on the Properties of The ...
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Chapter 3.<br />
Analytical Methods and Designs <str<strong>on</strong>g>of</str<strong>on</strong>g> Experiments<br />
background. Otsu’s method can be used if <str<strong>on</strong>g>the</str<strong>on</strong>g> histogram has even <strong>on</strong>e or two modes. Figure 3.15 shows an<br />
example <str<strong>on</strong>g>of</str<strong>on</strong>g> thresholding [Niemistö, 2006].<br />
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(A)-Original image (B)-Threshold image (C)- Histogram <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> pore data obtained<br />
Figure 3.15: SCION ® Image processing and pore data retrieval.<br />
5.2.2 Morphological Filtering<br />
<strong>The</strong> two fundamental morphological operati<strong>on</strong>s are erosi<strong>on</strong> and dilati<strong>on</strong>. Erosi<strong>on</strong> is thus<br />
equivalent to <str<strong>on</strong>g>the</str<strong>on</strong>g> minimum filter having a sliding window that is equivalent to <str<strong>on</strong>g>the</str<strong>on</strong>g> structuring element.<br />
Dilati<strong>on</strong> is thus equivalent to <str<strong>on</strong>g>the</str<strong>on</strong>g> maximum filter having a sliding window that is equivalent to <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
structuring element. In <str<strong>on</strong>g>the</str<strong>on</strong>g> case <str<strong>on</strong>g>of</str<strong>on</strong>g> binary images, <str<strong>on</strong>g>the</str<strong>on</strong>g> output <str<strong>on</strong>g>of</str<strong>on</strong>g> erosi<strong>on</strong> is zero unless all <str<strong>on</strong>g>the</str<strong>on</strong>g> samples in <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
sliding window are <strong>on</strong>es, whereas <str<strong>on</strong>g>the</str<strong>on</strong>g> output <str<strong>on</strong>g>of</str<strong>on</strong>g> dilati<strong>on</strong> is <strong>on</strong>e unless all <str<strong>on</strong>g>the</str<strong>on</strong>g> samples are zeros. Erosi<strong>on</strong><br />
shrinks foreground objects and expands <str<strong>on</strong>g>the</str<strong>on</strong>g>ir background, whereas dilati<strong>on</strong> expands <str<strong>on</strong>g>the</str<strong>on</strong>g> foreground objects<br />
and shrinks <str<strong>on</strong>g>the</str<strong>on</strong>g>ir background.<br />
Figure 3.16 (A) depicts a binary image and a square-shaped structuring element (top left corner).<br />
Figure 3.16 (B) and (C) show <str<strong>on</strong>g>the</str<strong>on</strong>g> erosi<strong>on</strong> and dilati<strong>on</strong> <str<strong>on</strong>g>of</str<strong>on</strong>g> this image by <str<strong>on</strong>g>the</str<strong>on</strong>g> square-shaped structuring<br />
element. <strong>The</strong> morphological opening and closing are morphological operati<strong>on</strong>s that are very useful in image<br />
processing. Erosi<strong>on</strong> first removes all objects in <str<strong>on</strong>g>the</str<strong>on</strong>g> image that cannot c<strong>on</strong>tain <str<strong>on</strong>g>the</str<strong>on</strong>g> structuring element and<br />
shrinks all <str<strong>on</strong>g>the</str<strong>on</strong>g> o<str<strong>on</strong>g>the</str<strong>on</strong>g>r objects. When <str<strong>on</strong>g>the</str<strong>on</strong>g> obtained image is dilated by <str<strong>on</strong>g>the</str<strong>on</strong>g> reflected structuring element, <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
objects that have been removed are naturally not recovered. <strong>The</strong> objects that have not been removed by<br />
erosi<strong>on</strong> are restored in such a way that protrusi<strong>on</strong>s that cannot c<strong>on</strong>tain <str<strong>on</strong>g>the</str<strong>on</strong>g> structuring element remain<br />
removed. <strong>The</strong> morphological opening can thus be used to remove small objects and to smoo<str<strong>on</strong>g>the</str<strong>on</strong>g>n <str<strong>on</strong>g>the</str<strong>on</strong>g><br />
c<strong>on</strong>tours <str<strong>on</strong>g>of</str<strong>on</strong>g> larger objects. An example is shown in Figure 3.16 (D).<br />
Bin<br />
(A) (B) (C) (D) (E)<br />
Figure 3.16: (A): A binary image and a structuring element (top left corner).(B): Erosi<strong>on</strong> (C): Dilati<strong>on</strong><br />
(D): Opening (E): Closing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> original image.<br />
<strong>The</strong> morphological closing <str<strong>on</strong>g>of</str<strong>on</strong>g> <str<strong>on</strong>g>the</str<strong>on</strong>g> structuring element is defined as <str<strong>on</strong>g>the</str<strong>on</strong>g> dilati<strong>on</strong> followed by<br />
erosi<strong>on</strong> by <str<strong>on</strong>g>the</str<strong>on</strong>g> reflected structuring element. Dilati<strong>on</strong> first fills all background structures that cannot c<strong>on</strong>tain<br />
<str<strong>on</strong>g>the</str<strong>on</strong>g> structuring element and expands all objects. When <str<strong>on</strong>g>the</str<strong>on</strong>g> obtained image is eroded by <str<strong>on</strong>g>the</str<strong>on</strong>g> reflected<br />
structuring element, <str<strong>on</strong>g>the</str<strong>on</strong>g> filled background structures naturally remain filled. <strong>The</strong> expanded objects are<br />
restored in such a way that indentati<strong>on</strong>s that cannot c<strong>on</strong>tain <str<strong>on</strong>g>the</str<strong>on</strong>g> structuring element remain filled. <strong>The</strong><br />
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