Median Filter (5) sparsely populated 5x5 median filters effect on - - PDF document

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IIP 41

Median Filter (5)

Castleman, 1996

effect on white noise; std of output image vs. # pixels participating sparsely populated 5x5 median filters

IIP 42

Sharpening (1)

• Used to:

highlight fine detail Enhance detail that has been blurred (in error

• r part of the acquisition procedure)
• Sort of differentiation (1st and 2nd order) as
• pposed to “integration” for smoothing
• However, enhance other discontinuities

such as noise

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IIP 43

Sharpening (2)

2 2

1st order derivative of a 1D function ( 1) ( ) 2nd order derivative of a 1D function ( 1) ( 1) 2 ( ) and similarly for 2D f f x f x x f f x f x f x x ∂ = + − ∂ ∂ = + + − − ∂

IIP 44

1D Illustration

Gonzalez & Woods, 2002

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IIP 45

Laplacian (1)

• Rotation invariant (isotropic)
• Emphasize discontinuities and de-emphasize

regions of slowly varying gray levels

• Laplacian for image enhancement:

[ ]

2 2 2 2 2

( 1, ) ( 1, ) ( , 1) ( , 1) 4 ( , ) f f f x y f x y f x y f x y f x y f x y ∂ ∂ ∇ ≡ + ∂ ∂ = + + − + + + − −

2 2

( , ) ( , ) if center coefficient is negative ( , ) ( , ) ( , ) if center coefficient is positive f x y f x y g x y f x y f x y  −∇  =  +∇  

IIP 46

Laplacian (2)

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IIP 47

Laplacian (3)

Rosenfeld & Kak, 1976 image image minus Laplacian

IIP 48

Laplacian (4)

Gonzalez & Woods, 2002

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IIP 49

Laplacian (5)

Gonzalez & Woods, 2002

IIP 50

Sobel Operations (1)

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IIP 51

Sobel Operations (2)

Gonzalez & Woods, 2002

IIP 52

Laplacian + Sobel

Gonzalez & Woods, 2002

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IIP 53

Sharpening (4) – Gradient

binary image Gradient (using absolute values)

Gonzalez & Wintz, 1977

IIP 54

High Pass Filter

• Illustration

image + high-pass high frequency emphasis + histogram equalisation

Gonzalez & Wintz, 1977

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IIP 55

Image Enhancement – Summary

(a) A biological intensity image; (b), (c) and (d) the result of applying a median filter, a low-pass filter and two-level binarisation, respectively, to (a).