Digital Image Processing Morphological Image Processing

2 of 63 What Is Morphology?  Presented by J. Serra in  Morphological image processing (or morphology) describes a range of image processing techniques that deal with the shape (or morphology) of features in an image  The basic ideal of Morphology is to use a special structuring element to measure or extract the corresponding shape or characteristics in the input images for further image analysis and object recognition.  The mathematical foundation of morphology is the set theory.  In this chapter, the input images are binary images.

3 of 63 0, 1, Black, White?  Throughout all of the following slides whether 0 and 1 refer to white or black is a little interchangeable  All of the discussion that follows assumes that images are made up of 0s for background pixels (off pixels) and 1s for object pixels (foreground=on pixels)  After this it doesn’t matter if 0 is black, white, yellow, green…….

4 of 63 A is a set, if a=(a 1,a 2 ) is an element of A, then, a  A If not, then, a  A  : null (empty) set Typical set specification: C={w|w=-d, for d  D} Basic Concepts of Set Theory

5 of 63  A subset of B: A  B  Union of A and B: C=A  B  Intersection of A and B: D=A  B  Disjoint sets: A  B=   Complement of A: A c ={w|w  A}  Difference of A and B: A-B={w|w  A, w  B}=A  B c Basic Concepts of Set Theory

6 of 63 Basic Concepts of Set Theory

7 of 63 Logic Operations involving Binary Image The principal logic operations AND OR and NOT Perform on a pixel by pixel basis Basic Concepts of Set Theory

8 of 63 Basic Concepts of Set Theory

9 of 63 Structuring Elements, Hits, Fits, & Missing B A C Structuring Element Fit: All on pixels in the structuring element cover on pixels in the image Hit: Any on pixel in the structuring element covers an on pixel in the image Miss: no pixel in the structuring element covers an on pixel in the image All morphological processing operations are based on these simple ideas

10 of 63 Structuring Elements Structuring elements can be any size and make any shape However, for simplicity we will use rectangular structuring elements with their origin at the middle pixel

11 of 63 Fitting, Hitting, &Missing B C A Structuring Element Structuring Element 2

12 of 63 Fundamental Operations  Fundamentally morphological image processing is very like spatial filtering  The structuring element is moved across every pixel in the original image to give a pixel in a new processed image  The value of this new pixel depends on the operation performed  There are two basic morphological operations: erosion and dilation

13 of 63 Dilation Dilation of image f by structuring element s is given by f s The structuring element s is positioned with its origin at (x, y) and the new pixel value is determined using the rule:

14 of 63 Dilation Example Structuring Element Original Image Processed Image

15 of 63 Dilation Example Structuring Element Original Image Processed Image With Dilated Pixels

16 of 63 B is the structuring element in dilation. Dilation Dilation:  B is often called the “structuring element”  Process consists of obtaining the reflection of B, about its origin  Then shifting this reflection, B, by x  The dilation of A by B is the set of all x, displacements such that B and A overlap by at least one element

17 of 63 Dilation Example Structuring Element Original Image Processed Image

18 of 63 Dilation Example

19 of 63 What Is Dilation For? Dilation can repair breaks Dilation can repair intrusions Watch out: Dilation enlarges objects