CS 6723 Image Processing

CS 6723 Image Processing
Lecture 22: Introduction to Morphology

Translation: B_x = {c: c = b + x, for x in B}.
(Translation of B by x moves the set so that its origin is at x.)
Reflection: hat (B) = {x : x = -b, for b in B}.
Reflection has the effect of flipping
Complement: A^c = {x: x not in A}.
Difference: A - B = {x: x in A but x not in B}.
Difference is A intersect B^c.

Morphological image operations involve two sets: A and B. Usually A is an image and B is a structuring element.
Move position of B relative to A and perform set operations.
Matlab implements 4 morphological operations for binary or uint8: imerode, imdilate, imclose and imopen.
A general morphological operator bwmorph is available for binary images.
Must consider behavior at the boundary.
The key to having effective morphological operations is picking a good structuring element.

Usually a small image that is used like a spatial filter.
Has 1's in positions corresponding to elements in the set. Has 0's elsewhere.
The locations of the 1's are called the neighborhood defined by the structuring element.
The location of the origin is important:

The origin isn't always in the center.
Two structuring elements which have the same bit pattern, but different origins behave differently.

To use a mask represented as an array with a Matlab morphological operation, use strel to convert it to the appropriate representation.

A eroded by B = {x : B_x is in A}
The symbol for erosion is a minus sign with a circle around it.
Erosion reduces the size of objects, eliminating features that are less than the scale of the neighborhood as defined by the structuring element.
Matlab definition of erosion (works for graylevel as well as binary images): A eroded by B = {x : x = min pixels in A in neighborhood B_x}
Matlab operation is imerode.
Matlab handles boundaries by assigning pixels beyond the boundary, the maximum value possible for data type (1 for binary, 255 for uint8).
Look at hand examples and Matlab script testerode

A dilated by B = {x : hat(B)_x is in A}.
The symbol for dilation is a plus sign with a circle around it.
Dilation expands the size of objects on the scale of the structuring element neighborhood.
Matlab definition of dilation (works for graylevel as well as binary images): A dilated by B = {x : x = max pixels in A in neighborhood B_x}
Matlab operation is imdilate.
Matlab handles boundaries by assigning pixels beyond the boundary, the minimum value possible for data type (1 for binary, 255 for uint8).
Look at hand examples and Matlab script testdilate.
Note: The Matlab version appears to follow Gonzales and Woods and reflects the structuring element before applying the mask operation. This doesn't appear to be documented. There is some inconsistency about the definition of dilation and hence the operations that depend on it. For example, Fundamentals of Digital Image Processing by Jain defines dilate without reflecting the structuring element B. This distinction is important if the structuring element is not symmetric.

A opened by B is an erosion of A by B followed by a dilation of A by B.
The symbol for the open operation is a small open circle.
Open smooths contours, breaks narrow isthmuses and eliminates little knobs.
Matlab defines open in terms of erosion and dilation. The definition works on both grayscale and binary images.
Matlab operation is imopen.
Look at examples in the Matlab script testopen.

A closed by B is a dilation of A by B followed by an erosion of A by B.
The symbol for the open operation is a small closed circle.
Close fuses narrow breaks, eliminates small holes and fuses gaps.
Matlab defines close in terms of erosion and dilation. The definition works on both grayscale and binary images.
Matlab operation is imclose.
Look at examples in the Matlab script testclose.

Objective: Explore the basic operations of morphology.

Last revision: November 13, 2001 at 11:45 am