Introduction to Morphological Operators 02 Nov20 1 About

Introduction to Morphological Operators 02 -Nov-20 1

About this lecture • In this lecture we introduce INFORMALLY the most important operations based on morphology, just to give you the intuitive feeling. • In next lectures we will introduce more formalism and more examples. 11/2/2020 2

EROSION 11/2/2020 3

What We Do Today. nd 2 Part • Introduction to Morphological Operators – Used generally on binary images, e. g. , background subtraction results! – Used on gray value images, if viewed as a stack to binary images. • Good for, e. g. , – Noise removal in background – Removal of holes in foreground / background • Check: www. cee. hw. ac. uk/hipr

A first Example: Erosion • Erosion is an important morphological operation • Applied Structuring Element: 02 -Nov-20 5

Example for Erosion Input image 1 0 0 Structuring Element 1 1 1 Output Image 02 -Nov-20 0 1 1 1 0 6

Example for Erosion Input image 0 0 0 Structuring Element 1 1 1 Output Image 0 0 02 -Nov-20 1 1 7

Example for Erosion Input image 1 0 Structuring Element Output Image 02 -Nov-20 0 1 1 8

Example for Erosion Input image 1 0 0 Structuring Element Output Image 02 -Nov-20 0 1 1 1 0 0 1 1 9

Example for Erosion Input image 1 0 0 0 Structuring Element Output Image 02 -Nov-20 0 1 1 10

Example for Erosion Input image 1 0 0 0 1 Structuring Element Output Image 02 -Nov-20 0 0 1 1 1 1 0 1 1 11

Example for Erosion Input image 1 0 0 0 1 1 Structuring Element Output Image 02 -Nov-20 0 0 1 1 1 1 0 0 1 12

Example for Erosion Input image 1 0 0 0 1 1 1 Structuring Element Output Image 02 -Nov-20 0 0 1 1 1 0 0 13

Introduction • • • Structuring Element Erosion Dilation Opening Closing Outlook: Hit-and-miss Operation, Thinning, Thickening 02 -Nov-20 14

Structuring Element (Kernel) • • • Structuring Elements can have varying sizes Usually, element values are 0, 1 and none(!) Structural Elements have an origin For thinning, other values are possible Empty spots in the Structuring Elements are don’t care’s! Box Disc Examples of stucturing elements 02 -Nov-20 15

Dilation & Erosion • Basic operations • Are dual to each other: – Erosion shrinks foreground, enlarges Background – Dilation enlarges foreground, shrinks background 02 -Nov-20 16

Erosion • Erosion is the set of all points in the image, where the structuring element “fits into”. • Consider each foreground pixel in the input image – If the structuring element fits in, write a “ 1” at the origin of the structuring element! • Simple application of pattern matching • Input: – Binary Image (Gray value) – Structuring Element, containing only 1 s! 02 -Nov-20 17

Another example of erosion • White = 0, black = 1, dual property, image as a result of erosion gets darker 02 -Nov-20 18

Erosion on Gray Value Images • View gray value images as a stack of binary images! 02 -Nov-20 19

Erosion on Gray Value Images • Images get darker! 02 -Nov-20 20

Counting Coins • Counting coins is difficult because they touch each other! • Solution: Binarization and Erosion separates them! 02 -Nov-20 21

DILATION 11/2/2020 22

Example: Dilation • Dilation is an important morphological operation • Applied Structuring Element: 02 -Nov-20 23

Dilation • Dilation is the set of all points in the image, where the structuring element “touches” the foreground. • Consider each pixel in the input image – If the structuring element touches the foreground image, write a “ 1” at the origin of the structuring element! • Input: – Binary Image – Structuring Element, containing only 1 s!! 02 -Nov-20 24

Example for Dilation Input image 1 0 0 Structuring Element 1 1 1 Output Image 02 -Nov-20 0 1 1 1 25

Example for Dilation Input image 0 0 0 Structuring Element 1 1 1 Output Image 1 0 02 -Nov-20 1 1 26

Example for Dilation Input image 1 0 Structuring Element Output Image 02 -Nov-20 1 0 0 1 1 1 0 1 1 27

Example for Dilation Input image 1 0 0 Structuring Element Output Image 02 -Nov-20 1 0 0 1 1 1 1 0 1 1 28

Example for Dilation Input image 1 0 0 0 Structuring Element Output Image 02 -Nov-20 1 1 1 1 1 0 1 1 29

Example for Dilation Input image 1 0 0 0 1 Structuring Element Output Image 02 -Nov-20 1 1 1 1 30

Example for Dilation Input image 1 0 0 0 1 1 Structuring Element Output Image 02 -Nov-20 1 1 1 1 31

Example for Dilation Input image 1 0 0 0 1 1 1 Structuring Element Output Image 02 -Nov-20 1 1 1 1 32

Another Dilation Example • Image get lighter, more uniform intensity 02 -Nov-20 33

Dilation on Gray Value Images • View gray value images as a stack of binary images! 02 -Nov-20 34

Dilation on Gray Value Images • More uniform intensity 02 -Nov-20 35

Edge Detection • 1. 2. 3. Edge Detection Dilate input image Subtract input image from dilated image Edges remain! 02 -Nov-20 36

Opening & Closing • Important operations • Derived from the fundamental operations – Dilatation – Erosion • Usually applied to binary images, but gray value images are also possible • Opening and closing are dual operations 02 -Nov-20 37

OPENING 11/2/2020 38

Opening • Similar to Erosion – Spot and noise removal – Less destructive • Erosion next dilation • the same structuring element for both operations. • Input: – Binary Image – Structuring Element, containing only 1 s! 02 -Nov-20 39

Opening • Take the structuring element (SE) and slide it around inside each foreground region. – All pixels which can be covered by the SE with the SE being entirely within the foreground region will be preserved. – All foreground pixels which can not be reached by the structuring element without lapping over the edge of the foreground object will be eroded away! • Opening is idempotent: Repeated application has no further effects! 02 -Nov-20 40

Opening • Structuring element: 3 x 3 square 02 -Nov-20 41

Opening Example • Opening with a 11 pixel diameter disc 02 -Nov-20 42

Opening Example • 3 x 9 and 9 x 3 Structuring Element 3*9 9*3 02 -Nov-20 43

Opening on Gray Value Images • 5 x 5 square structuring element 02 -Nov-20 44

Use Opening for Separating Blobs • Use large structuring element that fits into the big blobs • Structuring Element: 11 pixel disc 02 -Nov-20 45

CLOSING 11/2/2020 46

Closing • Similar to Dilation – Removal of holes – Tends to enlarge regions, shrink background • Closing is defined as a Dilatation, followed by an Erosion using the same structuring element for both operations. • Dilation next erosion! • Input: – Binary Image – Structuring Element, containing only 1 s! 02 -Nov-20 47

Closing • Take the structuring element (SE) and slide it around outside each foreground region. – All background pixels which can be covered by the SE with the SE being entirely within the background region will be preserved. – All background pixels which can not be reached by the structuring element without lapping over the edge of the foreground object will be turned into a foreground. • Opening is idempotent: Repeated application has no further effects! 02 -Nov-20 48

Closing • Structuring element: 3 x 3 square 02 -Nov-20 49

Closing Example • Closing operation with a 22 pixel disc • Closes small holes in the foreground 02 -Nov-20 50

Closing Example 1 1. Threshold 2. Closing with disc of size 20 02 -Nov-20 Thresholded closed 51

Closing Example 2 • Good for further processing: E. g. Skeleton operation looks better for closed image! skeleton of Thresholded and next closed 52

Closing Gray Value Images • 5 x 5 square structuring element 02 -Nov-20 53

Opening & Closing • Opening is the dual of closing • i. e. opening the foreground pixels with a particular structuring element • is equivalent to closing the background pixels with the same element. 02 -Nov-20 54

HIT and MISS 11/2/2020 55

Hit-and-miss Transform • Used to look for particular patterns of foreground and background pixels • Very simple object recognition • All other morphological operations can be derived from it!! • Input: – Binary Image – Structuring Element, containing 0 s and 1 s!! 02 -Nov-20 56

Hit-and-miss Transform • Example for a Hit-and-miss Structuring Element • Contains 0 s, 1 s and don’t care’s. • Usually a “ 1” at the origin! 02 -Nov-20 57

Hit-and-miss Transform • Similar to Pattern Matching: • If foreground and background pixels in the structuring element exactly match foreground and background pixels in the image, then the pixel underneath the origin of the structuring element is set to the foreground color. 02 -Nov-20 58

Corner Detection with Hit-andmiss Transform • Structuring Elements representing four corners 02 -Nov-20 59

Corner Detection with Hit-andmiss Transform • Apply each Structuring Element • Use OR operation to combine the four results 02 -Nov-20 60

Basic THINNING 11/2/2020 61

Thinning 1. Used to remove selected foreground pixels from binary images 2. After edge detection, lines are often thicker than one pixel. 3. Thinning can be used to thin those line to one pixel width. 02 -Nov-20 62

Definition of Thinning • Let K be a kernel and I be an image with 0 -1=0!! • If foreground and background fit the structuring element exactly, then the pixel at the origin of the SE is set to 0 • Note that the value of the SE at the origin is 1 or don’t care! 02 -Nov-20 63

Example Thinning We use two Hit-andmiss Transforms 02 -Nov-20 64

Basic THICKENING 11/2/2020 65

Thickening • Used to grow selected regions of foreground pixels • E. g. applications like approximation of convex hull 02 -Nov-20 66

Definition Thickening • Let K be a kernel and I be an image with 1+1=1 • If foreground and background match exactly the SE, then set the pixel at its origin to 1! • Note that the value of the SE at the origin is 0 or don’t care! 02 -Nov-20 67

Example Thickening 02 -Nov-20 68

PROBLEMS 11/2/2020 69

Problems 1. Consider the images on slide 17! Why are the images getting darker under erosion? Explain! 2. Consider the images on slide 31! Why are the intensities becoming more uniform? Explain! 3. Compare Dilatation and Erosion! How are they related? Verify your answers with Matlab! 4. Apply Erosion and Dilatation for noise removal! 5. Consider slide 38: Remove the artefacts remaining with the horizontal lines. 02 -Nov-20 70

Problems 6. Derive dilatation and erosion from the Hitand-miss transformation 02 -Nov-20 71

Sources Used Volker Krüger & Rune Andersen University of Aalborg, Esbjerg 02 -Nov-20 72