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

Castleman, 1996 Median Filter (5) sparsely populated 5x5 median filters effect on white noise; std of output image vs. # pixels participating 41 IIP Sharpening (1) • Used to: � highlight fine detail � Enhance detail that has been blurred (in error or part of the acquisition procedure) • Sort of differentiation (1 st and 2 nd order) as opposed to “integration” for smoothing • However, enhance other discontinuities such as noise 42 IIP 1

Sharpening (2) 1st order derivative of a 1D function ∂ f = + − f x ( 1) f x ( ) ∂ x 2nd order derivative of a 1D function ∂ 2 f = + + − − f x ( 1) f x ( 1) 2 ( ) f x ∂ 2 x and similarly for 2D 43 IIP Gonzalez & Woods, 2002 1D Illustration 44 IIP 2

Laplacian (1) ∂ ∂ 2 2 f f ∇ ≡ + 2 f ∂ ∂ 2 2 x y [ ] = + + − + + + − − f x ( 1, ) y f x ( 1, ) y f x y ( , 1) f x y ( , 1) 4 ( , ) f x y • Rotation invariant (isotropic) • Emphasize discontinuities and de-emphasize regions of slowly varying gray levels • Laplacian for image enhancement:  −∇  2 f x y ( , ) f x y ( , ) if center coefficient is negative =  g x y ( , ) +∇  2  f x y ( , ) f x y ( , ) if center coefficient is positive 45 IIP Laplacian (2) 46 IIP 3

Rosenfeld & Kak, 1976 Laplacian (3) image image minus Laplacian 47 IIP Gonzalez & Woods, 2002 Laplacian (4) 48 IIP 4

Gonzalez & Woods, 2002 Laplacian (5) 49 IIP Sobel Operations (1) 50 IIP 5

Gonzalez & Woods, 2002 Sobel Operations (2) 51 IIP Gonzalez & Woods, 2002 Laplacian + Sobel 52 IIP 6

Gonzalez & Wintz, 1977 Sharpening (4) – Gradient binary image Gradient (using absolute values) 53 IIP Gonzalez & Wintz, 1977 High Pass Filter • Illustration + high-pass image + histogram high frequency equalisation emphasis 54 IIP 7

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). 55 IIP 8