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CIS 350 – 3 Image ENHANCEMENT in the SPATIAL DOMAIN. Dr. Rolf Lakaemper. Most of these slides base on the textbook Digital Image Processing by Gonzales/Woods Chapter 3. Introduction. Image Enhancement ? enhance otherwise hidden information Filter important image features

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slide1

CIS 350 – 3

Image ENHANCEMENT

in the

SPATIAL DOMAIN

Dr. Rolf Lakaemper

slide2

Most of these slides base on the textbook

Digital Image Processing

by Gonzales/Woods

Chapter 3

slide3

Introduction

  • Image Enhancement ?
  • enhance otherwise hidden information
  • Filter important image features
  • Discard unimportant image features
  • Spatial Domain ?
  • Refers to the image plane (the ‘natural’ image)
  • Direct image manipulation
slide4

Remember ?

A 2D grayvalue - image is a 2D -> 1D function,

v = f(x,y)

slide5

Remember ?

As we have a function, we can apply operators to this function, e.g.

T(f(x,y)) = f(x,y) / 2

Operator

Image (= function !)

slide6

Remember ?

T transforms the given image f(x,y)

into another image g(x,y)

f(x,y)

g(x,y)

slide7

Spatial Domain

  • The operator T can be defined over
  • The set of pixels (x,y) of the image
  • The set of ‘neighborhoods’ N(x,y) of each pixel
  • A set of images f1,f2,f3,…
slide8

Spatial Domain

Operation on the set of image-pixels

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(Operator: Div. by 2)

slide9

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Spatial Domain

Operation on the set of ‘neighborhoods’ N(x,y) of each pixel

(Operator: sum)

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slide10

Spatial Domain

Operation on a set of images f1,f2,…

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(Operator: sum)

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slide11

Spatial Domain

  • Operation on the set of image-pixels
  • Remark: these operations can also be seen as operations on the neighborhood of a pixel (x,y), by defining the neighborhood as the pixel itself.
  • The easiest case of operators
  • g(x,y) = T(f(x,y)) depends only on the value of f at (x,y)
  • T is called a
  • gray-level or intensity transformation function
slide12

Transformations

  • Basic Gray Level Transformations
  • Image Negatives
  • Log Transformations
  • Power Law Transformations
  • Piecewise-Linear Transformation Functions
  • For the following slides L denotes the max. possible gray value of the image, i.e. f(x,y)  [0,L]
slide13

Transformations

Image Negatives: T(f)= L-f

T(f)=L-f

Output gray level

Input gray level

slide14

Transformations

Log Transformations:

T(f) = c * log (1+ f)

slide15

Transformations

Log Transformations

InvLog

Log

slide16

Transformations

Log Transformations

slide17

Transformations

Power Law Transformations

T(f) = c*f 

slide18

Transformations

  • varying gamma () obtains family of possible transformation curves
  •  > 0
    • Compresses dark values
    • Expands bright values
  •  < 0
    • Expands dark values
    • Compresses bright values
slide19

Transformations

  • Used for gamma-correction
slide20

Transformations

  • Used for general purpose contrast manipulation
slide21

Transformations

Piecewise Linear Transformations

slide22

Piecewise Linear Transformations

Thresholding Function

g(x,y) = L if f(x,y) > t,

0 else

t = ‘threshold level’

Output gray level

Input gray level

slide23

Piecewise Linear Transformations

  • Gray Level Slicing
  • Purpose: Highlight a specific range of grayvalues
  • Two approaches:
  • Display high value for range of interest, low value else (‘discard background’)
  • Display high value for range of interest, original value else (‘preserve background’)
slide25

Piecewise Linear Transformations

Bitplane Slicing

Extracts the information of a single bitplane

slide27

Piecewise Linear Transformations

  • Exercise:
  • How does the transformation function look like for bitplanes 0,1,… ?
  • What is the easiest way to express it ?
slide28

Histograms

Histogram Processing

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Number of Pixels

gray level

slide29

Histograms

  • Histogram Equalization:
  • Preprocessing technique to enhance contrast in ‘natural’ images
  • Target: find gray level transformation function T to transform image f such that the histogram of T(f) is ‘equalized’
slide30

Histogram Equalization

Equalized Histogram:

The image consists of an equal number of pixels for every gray-value, the histogram is constant !

slide31

Histogram Equalization

Example:

T

We are looking for

this transformation !

slide32

Histogram Equalization

Mathematically the transformation is deducted by theorems in continous (not discrete) spaces.

The results achieved do NOT hold for discrete spaces !

However, it’s visually close, so let’s have a look at the continous case.

slide33

Histogram Equalization

(explanations on whiteboard)

slide34

Histogram Equalization

  • Conclusion:
  • The transformation function that yields an image having an equalized histogram is the integral of the histogram of the source-image
  • In discrete the integral is given by the cumulative sum, MATLAB function: cumsum()
  • The function transforms an image into an image, NOT a histogram into a histogram ! The histogram is just a control tool !
  • In general the transformation does not create an image with an equalized histogram in the discrete case !
slide35

Operations on a set of images

Operation on a set of images f1,f2,…

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(Operator: sum)

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slide36

Operations on a set of images

Logic (Bitwise) Operations

AND

OR

NOT

slide37

Operations on a set of images

The operators AND,OR,NOT are functionally complete:

Any logic operator can be implemented using only these 3 operators

slide38

Operations on a set of images

Any logic operator can be implemented using only these 3 operators:

Op=

NOT(A) AND NOT(B)

OR

NOT(A) AND B

slide39

Operations on a set of images

Image 1 AND Image 2

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(Operator: AND)

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slide40

Operations on a set of images

Image 1 AND Image 2:

Used for Bitplane-Slicing and

Masking

slide41

Operations on a set of images

Exercise: Define the mask-image, that transforms image1 into image2 using the OR operand

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255

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(Operator: OR)

255

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255

slide42

Operations

Arithmetic Operations on a set of images

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(Operator: +)

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slide43

Operations

Exercise:

What could the operators + and – be used for ?

slide44

Operations

Example: Operator –

Foreground-Extraction

slide45

Operations

Example: Operator +

Image Averaging

slide46

End

(Matlab Examples)

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