Chapter 11
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08/03/04
Morphological image processing
o nonlinear techniques dealing with the shape/structure/form of features in an image
o usually applied to binary images resulting from segmentation process
o may also be applied to grayscale images
o probe an image with a structuring element
 small array containing a shape template
 has an origin that may be outside the array
 position the origin at each pixel in the image and compare structuring element to image
neighborhood
 logical comparison
 locations where structuring element is zero are ignored
 fit - every non-zero structuring element value corresponds to a non-zero neighborhood value
 hit - any non-zero structuring element value corresponds to a non-zero neighborhood value
o StructElement.java
o StructElementTypes.java
o BinaryStructElement.java
Fundamental operations
o erosion
 given an image f and a structuring element s,
 if s fits f at x,y then g(x,y) = 1
 else g(x,y) = 0
 must deal with access outside image boundaries
 erodes pixels away from boundaries of regions
 removes small extrusions at region boundary
 could use this to find region boundaries by subtracting eroded image from original image
o dilation
 given an image f and a structuring element s,
 if s hits f at x,y then g(x,y) = 1
 else g(x,y) = 0
 opposite of erosion - adds a layer of pixels to region boundaries
o shape of the structuring element affects the results of erosion or dilation
 dilation by a disc - smooths convex corners
 erosion by a disc - smooths concave corners
o dilation is the dual of erosion
o BinaryMorphologicalOp.java
o BinaryErodeOp.java
o BinaryDilateOp.java
Set theory is the language of mathematical morphology
o a binary image is represented as the set of all black (or white) pixels
o each element of the set is a 2D vector whose coordinates are the (x,y) coordinates of a pixel
o basic definitions include
 translation
 reflection
 complement
 intersection
 union
 difference
o dilation and erosion can be defined in terms of these basic definitions
o dilation of A by B
 all x such that the intersection of A with the reflection of B translated by x in not null
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set of all x displacements such that the reflection of B and A overlap by at least one nonzero
element
erosion of A by B
 all x such that B translated by x is a subset of A
 set of all x such that B, translated by x, is contained in A
dilation and erosion are duals of each other with respect to complementation and reflection
 we can perform dilation by performing erosion on the complement of the image
 if our structuring element is not symmetric with respect to rotation, we need to reflect it first
compound operations
 opening
 an erosion followed by a dilation
 breaks narrow isthmuses, eliminates thin protrusions
 can open a gap between two regions joined by a narrow bridge of pixels
 can be used to separate two regions that should be distinct
 advantage over erosion is that the regions are returned to their original size, minus
the connecting pixels
 closing
 a dilation followed by an erosion
 closes narrow gaps, eliminates small holes
 advantage over dilation is that the region is restored to its original size
 opening and closing are idempotent
 once an image has been opened, further openings with the same structuring element
have no effect
 once an image has been closed, further closings with the same structuring element
have no effect
 opening and closing are duals of each other with respect to complementation and reflection
 hit or miss transform
 probes both the inside and the outside of a region
 used for shape detection
 uses two structuring elements - s1 probes inside the regions - s2 probes outside the
region
 other compound operations include
 boundary extraction
 region filling
 extraction of connected components
 convex hull
 thinning
 thickening
 skeletons
 pruning
examples of morphological filtering
 optical character recognition
 analysis of a printed circuit board image
 analysis of cookies
BinaryOpenUp.java
BinaryCloseUp.java
HitAndMiss.java application
BinaryMorphologyTool application
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Grayscale morphology
o apply morphological processing concepts to grayscale images
o adds another dimension
o visualize the image as a height field
o the structuring element is now 3D - structuring function
o erosion
 darkens image, reduces or eliminates small bright structure
 maximum distance the structuring element can be pushed up and stay under the height field
 computed as the minimum of the differences of neighborhood values and corresponding
structuring element values
 structuring element of all zeros produces same result as the minimum rank filter
o dilation
 lightens image, reduces or eliminates small dark structure
 structuring element must be reflected (if not symmetrical)
 minimum distance the structuring element must be pushed up to be above the height field
 computed as the maximum of the sums of neighborhood values and corresponding
(reflected) structuring element values
 structuring element of all zeros produces the same result as the maximum rank filter
o opening
 defined as before - erosion followed by dilation
 reduces or eliminates small bright structure, leaving dark features undisturbed
o closing
 defined as before - dilation followed by erosion
 reduces or eliminates small dark structure, leaving bright features undisturbed
o compound operations
 morphological smoothing
 opening followed by closing
 attenuates both bright and dark artifacts or noise
 morphological gradient
 subtract erosion from dilation of image
 highlights sharp gray-level transitions
 top-hat transformation
 name comes from use of a cylindrical structuring element with a flat top
 subtract the opening of an image from the original image
 leaves just the small bright structure
o GreyStructElement.java
o GreyErodeOp.java
o GreyDilateOp.java
o GreyOpenOp.java
o GreyCloseOp.java