CME429 Introduction to Image Processing

Assist. Prof. Dr. Caner ÖZCAN

Part 11 Image Segmentation

The whole is equal to the sum of its parts. ~Euclid The whole is greater than the sum of its parts. ~Max Wertheimer

Outline

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10. Image Segmentation ►Fundamentals

►Point, Line, and Edge Detection

►Thresholding

►Region-Based Segmentation

►Segmentation Using Morphological Watersheds

►The Use of Motion in Segmentation

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Background

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►First-order derivative

►Second-order derivative

'( ) ( 1) ( )f

f x f x f xx

2

2( 1) ( 1) 2 ( )

ff x f x f x

x

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Detection of Isolated Points

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►The Laplacian

2 2

2

2 2( , )

( 1, ) ( 1, ) ( , 1) ( , 1)

4 ( , )

f ff x y

x y

f x y f x y f x y f x y

f x y

1 if | ( , ) |( , )

0 otherwise

R x y Tg x y

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1

k k

k

R w z

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Line Detection

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►Second derivatives to result in a stronger response and to produce thinner lines than first derivatives

►Double-line effect of the second derivative must be handled properly

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Detecting Line in Specified Directions

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Edge Detection

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►Edges are pixels where the brightness function changes abruptly

►Edge models

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Basic Edge Detection by Using First-Order Derivative

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2 2

1

( )

The magnitude of

( , ) mag( )

The direction of

( , ) tan

The direction of the edge

- 90

x

y

x y

x

y

f

g xf grad f

fg

y

f

M x y f g g

f

gx y

g

Basic Edge Detection by Using First-Order Derivative

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Edge normal: ( )

Edge unit normal: / mag( )

x

y

f

g xf grad f

fg

y

f f

In practice,sometimes the magnitude is approximated by

mag( )= + or mag( )=max | |,| |f f f f

f fx y x y

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The Canny Edge Detector

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►Optimal for step edges corrupted by white noise.

►The Objective

1.Low error rate The edges detected must be as close as possible to the true edge

2.Edge points should be well localized The edges located must be as close as possible to the true edges

3.Single edge point response The number of local maxima around the true edge should be minimum

The Canny Edge Detection: Summary

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►Smooth the input image with a Gaussian filter

►Compute the gradient magnitude and angle images

►Apply nonmaxima suppression to the gradient magnitude image

►Use double thresholding and connectivity analysis to detect and link edges

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0.04; 0.10; 4 and a mask of size 25 25L HT T

28 0.05; 0.15; 2 and a mask of size 13 13L HT T

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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Segmentation with Matlab

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References

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►Sayısal Görüntü İşleme, Palme Publishing, Third Press Trans. (Orj: R.C. Gonzalez and R.E. Woods: "Digital Image Processing", Prentice Hall, 3rd edition, 2008).

►“Digital Image Processing Using Matlab”, Gonzalez & Richard E. Woods, Steven L. Eddins, Gatesmark Publishing, 2009

►Lecture Notes, CS589-04 Digital Image Processing, Frank (Qingzhong) Liu, http://www.cs.nmt.edu/~ip

►Lecture Notes, BIL717-Image Processing, Erkut Erdem ►Lecture Notes, EBM537-Image Processing, F.Karabiber ► Image Processing Made Easy,

https://www.youtube.com/watch?v=1-jURfDzP1s