Influence of the Processes Parameters on the Properties of The ...

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