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Fuzzy Logic in Image Processing

Jibin Chacko Jose

M2 PS

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Contents

• Image Processing

•Contrast enhancement

•Demonstration

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Image Processing• Different types of images – binary, grayscale

and colour.

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Image Processing• Image processing generally refers to a set of

computational techniques used for analysing, enhancing, compressing, and reconstructing an image

• Methods for image processing – frequency domain and spatial domain.

• Image processing methods include –

1. Contrast stretching2. Image soothing 3. Image sharpening

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Image Processing

An image can be represented mathematically by a

spatial brightness function f (m,n) where (m, n)

denotes the spatial coordinate of a point in the

(flat) image. The value of f (m,n), 0 < f(m,n) < ∞, is

proportional to the brightness value or gray level of

the image at the point (m, n).

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Image Processing

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Image Processing

For computer processing, the continuous

function f (m,n) has been discretized both in

spatial coordinates and in brightness. Such an

approximated image X(digitized) can be

considered as an M × N array 11 12 1

21 2

2

2 2

1

...

...( , )

M

N

MN

N

M

x x x

x x xX f m n

x x x

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Image Processing

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Image ProcessingAn image X of M × N dimensions can be

considered as an array of fuzzy singletons, each

with a value of membership denoting the degree

of brightness level p, p = 0, 1, 2, . . ., P − 1 (e.g.,

a range of densities from p = 0 to p = 255), or

some relative pixel density. Using the notation of

fuzzy sets,

11 11 12 12 1

22 2

1

21 21

1 1

2 2 2

2 2

/ / /

/ / /

/ / /

N N

M M MN MN

N N

M M

x x x

x x xX

x x x

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Contrast enhancement

Contrast within an image is the measure of

difference between the gray levels in an image.

The greater the contrast, the greater is the

distinction between gray levels in the image.

Images of high contrast have either all black or all

white regions; there is very little gray in the image.

Low-contrast images have lots of similar gray levels

in the image, and very few black or white regions

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Contrast enhancement

The contrast intensification operation on a fuzzy set A

generates another fuzzy set, A’ = INT (A ), in which the

fuzziness is reduced by increasing the values of μA(x) that

are greater than 0.5 and by decreasing the values of μA(x)

that are less than 0.5

In general, each μmn in X may be modified to μmn’ to

enhance the image X in the property domain by a

transformation function, Tr, where

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Contrast enhancement

The transformation Tr is defined as successive

applications of T1 by the recursive relation,

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Demonstration

Light small square box inside a larger square

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DemonstrationGray-scale intensity values of pixels in a 10 × 10

pixel array of the image shown

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DemonstrationScaled matrix of the intensity values in Table 1

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DemonstrationIntensity values above and below 0.5 have been

suitably modified to increase the contrast between the intensities.

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Demonstration

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Demonstration

Intensity matrix after applying the enhancement algorithm

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THANK YOU