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## PowerPoint Slideshow about 'CIS 350 3 Image ENHANCEMENT in the SPATIAL DOMAIN' - jocelyn

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- 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

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 !)

- 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,…

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Spatial Domain

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

(Operator: sum)

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Operation on a set of images f1,f2,…

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(Operator: sum)

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- 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

- 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]

Log Transformations

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

- Used for gamma-correction

- Used for general purpose contrast manipulation

Piecewise Linear Transformations

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

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’)

Piecewise Linear Transformations

Gray Level Slicing

Piecewise Linear Transformations

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

- 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’

Equalized Histogram:

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

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.

(explanations on whiteboard)

- 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 !

Operation on a set of images f1,f2,…

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(Operator: sum)

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The operators AND,OR,NOT are functionally complete:

Any logic operator can be implemented using only these 3 operators

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

Op=

NOT(A) AND NOT(B)

OR

NOT(A) AND B

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

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(Operator: OR)

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(Matlab Examples)

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