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IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point A digital image is a 2D representation of a continuous image by a 2D array of discrete

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Page 1: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

IMAGE 1

An image is a two dimensionalFunction f(x,y) where x and y are spatial coordinatesAnd f at any x,y is related to the brightness at that point

A digital image is a 2D representation of a continuous image by a 2D array of discrete samples

Each element of the 2D array is a pixel.

Page 2: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Definition

Histograms count the number of occurrences of each possible value

H D( )

Count Grey level

Page 3: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Properties

• Sum of all values in the histogram equals the total number of pixels

H D( )dD0

∞

∫ =imagearea

Page 4: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Properties

• Sum of all values between a and b equals the area of all objects in that range

H D( )dDa

b

∫ =areaofall partsa≤I ≤b

Page 5: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Properties

• Integrated optical density

• Mean greylevel

IOD= DH D( )dD0

∞

∫

MGL=IOD area

Page 6: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Application: Adjusting Camera Parameters

• Too bright - lots of pixels at 255 (or max)

• Too dark - lots of pixels at 0

• Gain too low - not enough of the range used

Page 7: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Application: Segmentation

• Can be used to separate bright objects from dark background (or vice versa)

Page 8: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Normalizing Histograms

• Probability density function = histogram normalized by area

p D( )=1AH D( )

Page 9: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Cumulative Histograms

• Counts pixels with values up to and including the specified value

C a( ) = H D( )dD0

a

∫

Page 10: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Cumulative Density Functions

• Normalized cumulative histograms

P a( )= p D( )dD0

a

∫ =1AC a( )

Page 11: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

IMAGE 1

Page 12: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Image 1: Bright

Page 13: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Image 1: Dark

Page 14: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Image 1: Low contrast

Page 15: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

Image 1: High contrast

Page 16: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

RESOLUTION

Page 17: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

INTERPOLATION

Page 18: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

HISTOGRAM EQUALIZATION

Page 19: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point

THRESHOLDING

104

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199

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Inverted

Page 24: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 25: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 26: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 27: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 28: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 29: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 30: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 31: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 32: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 33: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 34: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 35: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 36: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 37: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 38: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 39: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 40: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 41: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 42: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 43: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 44: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 45: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 46: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 47: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 48: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 49: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 50: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 51: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 52: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 53: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 54: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 55: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
Page 56: IMAGE 1 An image is a two dimensional Function f(x,y) where x and y are spatial coordinates And f at any x,y is related to the brightness at that point
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SMOOTH 3

MEDIAN 3

SMOOTH 7

MEDIAN 5


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