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‘Morphology’ - a branch of Biology which deals withthe form and structure of plants and animals. Here, it is used as a tool for extracting imagecomponents useful in describing image shape. Programme chart• Dilation and Erosion• Opening and Closing• Hit or Miss transformation• Morph. algorithms
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DilationIn dilation, a small image called structuring element is used as a localmaximum operator. As the structuring element is scanned over theimage, we compute the maximal pixel value overlapped by B andreplace the image pixel under the anchor point with that maximalvalue. Structuring element B
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Dilation contd...Dilation gradually enlarges the boundaries of regions of foreground pixels.Thus areas of foreground regions grow in size while holes within thoseregions become smaller.
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ErosionErosion is the converse of dilation. The action of the erosion operatoris equivalent to computing a local minimum over the area of thekernel. As the kernel is scanned over the image, we compute theminimal pixel value overlapped by B and replace the image pixelunder the anchor point with that minimal value.
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Erosion contd…Erosion is the converse of dilation. The action of the erosion operatoris equivalent to computing a local minimum over the area of thekernel. As the kernel is scanned over the image, we compute theminimal pixel value overlapped by B and replace the image pixelunder the anchor point with that minimal value.
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OpeningOpening generally smoothens the contour of an object, breaks narrowisthmuses, and eliminates thin protrusions.The opening of set A by structuring element B, denoted A ◦ B, is defined as,
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Opening – geometrical interpretationSuppose that we view the structuring element B as a (flat) "rolling ball."The boundary of A ◦ B is then established by the points in B that reach thefarthest into the boundary of A as B is rolled around the inside of thisboundary.
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ClosingClosing also tends to smooth sections of contours but, as opposed toopening, it generally fuses narrow breaks and long thin gulfs, eliminates smallholes, and fills gaps in the contour. The closing of set A by structuring element B, denoted A • B, is defined as,
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Closing – geometrical interpretationClosing has a similar geometric interpretation, except that now we roll B onthe outside of the boundary.
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A morphological filterWe have a binary image showing a section of a fingerprint corruptedby noise. The noise manifests itself as light elements on a darkbackground and as dark elements on the light components of thefingerprint. The objective is to eliminate the noise and its effects onthe print while distorting it as little as possible. A morphological filterconsisting of opening followed by closing can be used to accomplishthis objective. Noisy image Structuring element
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A morphological filter Noisy image Eroded image Opening Dilation of opening Closing
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The Hit-or-Miss TransformationBasic tool for shape detection.Our aim is to find the center of gravity of X in the image. Here dark is “1”.