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ECE 6258 Russell M. Mersereau
ECE6258 Lecture 38
Mathematical Morphology IISource: Images taken from Gonzalez and Woods
ECE 6258 Russell M. Mersereau
Extraction of Connected Components ^
Let
Y
represent a connected component contained
in a set
A
^
Assume that a point
p
of
Y
is known.
^
All of the elements of
Y
can be found by the
following iterationwhere
X
p.
^
Upon convergence
Y
X
. k
ECE 6258 Russell M. Mersereau
Connected Component Extraction
ECE 6258 Russell M. Mersereau
Convex Hull^ ^
A set
A
is
convex
if a straight line segment drawn between
two points in
A
lies wholly within
A
^
The
convex hull
of
A
is the smallest convex set that contains
A
X = don’t care
ECE 6258 Russell M. Mersereau
Example Note: Convex,but larger thannecessary
ECE 6258 Russell M. Mersereau Correction^ ^ The real convex hull is achieved by limiting thehorizontal and vertical extent to that of the originalobject. 11/24/ ECE 6258 Russell M. Mersereau
Thinning ^ The thinning of a set A by a structuring element B can be defined by ^ This is typically done by thinning with a sequence of structuringelements: {B}={B 1 ,B 2 ,B 3 ,…,B n^ }.
ECE 6258 Russell M. Mersereau Example
ECE 6258 Russell M. Mersereau
Skeleton Example
ECE 6258 Russell M. Mersereau Gray-Scale Dilation ^ Consider a gray-scale function f ( s , t ) and a gray- scale structuring element b ( s , t ). 11/24/ ECE 6258 Russell M. Mersereau
1-D Dilation Example
ECE 6258 Russell M. Mersereau Gray-scale Erosion^ ^ Consider again a gray-scale function f ( s , t ) and a gray-scale structuring element b ( s , t ).
ECE 6258 Russell M. Mersereau
1-D Erosion Example
ECE 6258 Russell M. Mersereau Dilations and Erosions Dilations^ make an image brighter
reduce or eliminate dark details Erosions^ make an image darker
reduce or eliminate bright details Dilations and erosions are duals 11/24/ ECE 6258 Russell M. Mersereau
Example (5x5 box) original erosion
dilation
ECE 6258 Russell M. Mersereau Gray-scale Openings and Closings ^ Opening ^ Narrow bright areas reduced. ^ Closing ^ Narrow dark areas reduced. ^ Duality
ECE 6258 Russell M. Mersereau
Top-Hat Transformation ^ Useful for enhancing detail in the presence ofshading
ECE 6258 Russell M. Mersereau Texture Segmentation 11/24/ ECE 6258 Russell M. Mersereau
Texture Segmentation--Algorithm 1.^ Close the input image by using successively largerstructural elements. (This removes the small blobs.)
2.^ A single opening is then performed using a structuringelement that is large compared to the spacing between thelarge blobs. (This leaves a large light region on the left anda large dark region on the right.) 3.^ A simple threshold yields the boundary.
ECE 6258 Russell M. Mersereau Granulometry 1.^ Opening operations with elements of increasing size areperformed.
2.^ Differences between the original and the opening are formed ateach operation. 3.^ A histogram is constructed from the differences. 4.^ The peaks suggest three general particle sizes.
