CME429 Introduction to Image Processing

Assist. Prof. Dr. Dr. Caner ÖZCAN

Week 11 Image Compression

But life is short and information endless ... Abbreviation is a necessary evil and the abbreviator's business is to make the best of a job which, although

intrinsically bad, is still better than nothing. ~Aldous Huxley

Outline

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8. Image Compression ►Fundamentals

►Some Basic Compression Methods

►Digital Image Watermarking

Relative Data Redundancy

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►Let b and b’ denote the number of bits in two representations of the same information, the relative data redundancy R is

R = 1-1/C C is called the compression ratio, defined as

C = b/b’

e.g., C = 10, the corresponding relative data redundancy of the larger representation is 0.9, indicating that 90% of its data is redundant

Why do we need compression?

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►Data storage

►Data transmission

How can we implement compression?

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►Coding redundancy Most 2-D intensity arrays contain more bits than are needed to represent the intensities

►Spatial and temporal redundancy Pixels of most 2-D intensity arrays are correlated spatially and video sequences are temporally correlated

►Irrelevant information Most 2-D intensity arrays contain information that is ignored by the human visual system

Examples of Redundancy

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Image Compression Standards

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Some Basic Compression Methods: Huffman Coding

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Some Basic Compression Methods: Huffman Coding

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The average length of this code is

0.4*1 0.3*2 0.1*3 0.1*4 0.06*5 0.04*5

= 2.2 bits/pixel

avgL

CME429 Introduction to Image Processing

Assist. Prof. Dr. Dr. Caner ÖZCAN

Week 13 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

40 0.05; 0.15; 2 and a mask of size 13 13L HT T

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