21-06-2012, 01:52 PM
Digital Image Processing
[attachment=24982]
Mathematic Morphology
used to extract image components that are useful in the representation and description of region shape, such as
boundaries extraction
skeletons
convex hull
morphological filtering
thinning
pruning
Mathematic Morphology
mathematical framework used for:
pre-processing
noise filtering, shape simplification, ...
enhancing object structure
skeletonization, convex hull...
Segmentation
watershed,…
quantitative description
area, perimeter, ...
Z2 and Z3
set in mathematic morphology represent objects in an image
binary image (0 = white, 1 = black) : the element of the set is the coordinates (x,y) of pixel belong to the object Z2
gray-scaled image : the element of the set is the coordinates (x,y) of pixel belong to the object and the gray levels Z3
Basic idea
in parallel for each pixel in binary image:
check if SE is ”satisfied”
output pixel is set to 0 or 1 depending on used operation
How to describe SE
many different ways!
information needed:
position of origo for SE
positions of elements belonging to SE
Basic morphological operations
Erosion
Dilation
combine to
Opening object
Closening background
Erosion
Does the structuring element fit the set?
erosion of a set A by structuring element B: all z in A such that B is in A when origin of B=z
shrink the object
Dilation
Does the structuring element hit the set?
dilation of a set A by structuring element B: all z in A such that B hits A when origin of B=z
grow the object
useful
erosion
removal of structures of certain shape and size, given by SE
Dilation
filling of holes of certain shape and size, given by SE
Combining erosion and dilation
WANTED:
remove structures / fill holes
without affecting remaining parts
SOLUTION:
combine erosion and dilation
(using same SE)
Opening
erosion followed by dilation, denoted ∘
eliminates protrusions
breaks necks
smoothes contour
Closing
dilation followed by erosion, denoted •
smooth contour
fuse narrow breaks and long thin gulfs
eliminate small holes
fill gaps in the contour
Duality
Opening and closing are dual with respect to complementation and reflection
Hit-or-Miss Transformation ⊛ (HMT)
find location of one shape among a set of shapes ”template matching
composite SE: object part (B1) and background part (B2)
does B1 fits the object while, simultaneously, B2 misses the object, i.e., fits the background?
Convex hull
A set A is is said to be convex if the straight line segment joining any two points in A lies entirely within A.
[attachment=24982]
Mathematic Morphology
used to extract image components that are useful in the representation and description of region shape, such as
boundaries extraction
skeletons
convex hull
morphological filtering
thinning
pruning
Mathematic Morphology
mathematical framework used for:
pre-processing
noise filtering, shape simplification, ...
enhancing object structure
skeletonization, convex hull...
Segmentation
watershed,…
quantitative description
area, perimeter, ...
Z2 and Z3
set in mathematic morphology represent objects in an image
binary image (0 = white, 1 = black) : the element of the set is the coordinates (x,y) of pixel belong to the object Z2
gray-scaled image : the element of the set is the coordinates (x,y) of pixel belong to the object and the gray levels Z3
Basic idea
in parallel for each pixel in binary image:
check if SE is ”satisfied”
output pixel is set to 0 or 1 depending on used operation
How to describe SE
many different ways!
information needed:
position of origo for SE
positions of elements belonging to SE
Basic morphological operations
Erosion
Dilation
combine to
Opening object
Closening background
Erosion
Does the structuring element fit the set?
erosion of a set A by structuring element B: all z in A such that B is in A when origin of B=z
shrink the object
Dilation
Does the structuring element hit the set?
dilation of a set A by structuring element B: all z in A such that B hits A when origin of B=z
grow the object
useful
erosion
removal of structures of certain shape and size, given by SE
Dilation
filling of holes of certain shape and size, given by SE
Combining erosion and dilation
WANTED:
remove structures / fill holes
without affecting remaining parts
SOLUTION:
combine erosion and dilation
(using same SE)
Opening
erosion followed by dilation, denoted ∘
eliminates protrusions
breaks necks
smoothes contour
Closing
dilation followed by erosion, denoted •
smooth contour
fuse narrow breaks and long thin gulfs
eliminate small holes
fill gaps in the contour
Duality
Opening and closing are dual with respect to complementation and reflection
Hit-or-Miss Transformation ⊛ (HMT)
find location of one shape among a set of shapes ”template matching
composite SE: object part (B1) and background part (B2)
does B1 fits the object while, simultaneously, B2 misses the object, i.e., fits the background?
Convex hull
A set A is is said to be convex if the straight line segment joining any two points in A lies entirely within A.