数字图像处理ch5(英文版)

Chapter 5: Image Restoration

Lecturer: JianbingShen

Email : shenjianbing@

Office room : 212

/~shenjianbing

Things which we see are not by

themselves what we see…It remains completely unknown to us what the objects may be by themselves and

apart from the receptivity of our sense. We know nothing but our manner of perceiving them.

–Immanuel Kant

The distinction between image enhancement and restoration Image enhancement is a subjective process

(1) Heuristic procedures designed to manipulate an image in order to take advantage of the psychophysical aspects of the human vision system

(2) Contrast stretching

The distinction between image enhancement and restoration Image restoration is an objective process

(1) Recover the image using a priori knowledge of the degradation phenomenon

(2) To model the degradation and apply the inverse process to recover the original image

(3) Formulating a criterion of goodness that will yield an optimal estimate of the desired result

(4) Image deblurring

Image Restoration

Image restoration vs. image enhance

Enhancement:

largely a subjective processPriori knowledge about the degradation is not a must (sometimes no degradation is involved)Procedures are heuristic and take advantage of the psychophysical aspects of human visual system

more an objective process

Images are degraded

Tries to recover the images by using the knowledge about the degradation

Restoration:

An Image Degradation Model Two types of degradation

Additive noise

Spatial domain restoration (denoising) techniques are preferred

Image blur

Frequency domain methods are preferred

An Image Degradation Model We model the degradation process by a degradation function h(x,y), an additive noise term, η(x,y), as g(x,y)=h(x,y)*f(x,y)+ η(x,y) f(x,y) is the (input) image free from any degradation

g(x,y) is the degraded image

* is the convolution operator

The goal is to obtain an estimate of f(x,y) according to the knowledge about the degradation function h and the additive noise η In frequency domain: G(u,v)=H(u,v)F(u,v)+N(u,v)

An Image Degradation Model Three cases are considered in this Chapter

g(x,y)=f(x,y)+ η(x,y) (5-2~5-4) g(x,y)=h(x,y)*f(x,y) (5-5~5-6) g(x,y)=h(x,y)*f(x,y)+ η(x,y) (5-7~5-9)

A model of the image

degradation/restoration process

The purpose of image restoration is to restore a degraded/distorted image to its original content and quality.Distinctions to Image Enhancement

Image restoration assumes a degradation model that is known or can be estimated.

Original content and quality ≠Good looking

Image Degradation Model Spatial variant degradation model

g(x,y)=∑∑h(x,y,m,n)f(m,n)+η(x,y)

Spatial-invariant degradation model

g(x,y)=∑∑h(x m,y n)f(m,n)+η(x,y)

Frequency domain representation

G(u,v)=H(u,v)F(u,v)+N(u,v)

Noise Models

We first consider the degradation due to noise only

h is an impulse for now ( H is a constant)

Autocorrelation function is an impulse function multiplied by a constantN 1M 1

a(x,y)=∑∑η(s,t) η(s x,t y)=N0δ(x,y)

t=0s=0 White noise

It means there is no correlation between any two pixels in the noise imageThere is no way to predict the next noise value

The spectrum of the autocorrelation function is a constant(white) (the statement in page 222 about white noise is wrong)

Gaussian Noise

Noise (image) can be classified according the distribution of the values of pixels (of the noise image) or its (normalized) histogram Gaussian noise is characterized by two parameters,μ (mean) andσ2 (variance), by1 1( z μ ) 2/ 2σ 2 p( z )= e 2πσ

70% values of z fall in the range[(μ-σ),(μ+σ)] 95% values of z fall in the range[(μ-2σ),(μ+2σ)]12

Other Noise Models

Rayleigh noise 2 2 ( z a )e ( z a )/ b p( z )= b 0

for z≥ a for z< a

The mean and variance of this density are given by a and b can be obtained through mean and variance14

b( 4 π )μ= a+πb/ 4 andσ= 42

Other Noise Models

Erlang (Gamma) noise

a b z b 1 az e p ( z )= (b 1)! 0

for z≥ 0 for z< 0

The mean and variance of this density are given by bμ= b/ a andσ 2=

a and b can be obtained through mean and variance15

a2

Other Noise Models

Exponential noise

ae az p( z )= 0

for z≥ 0 for z< 0

The mean and variance of this density are given by 1 2μ= 1/ a andσ=a2

Special case pf Erlang PDF with b=1

Uniform noise

Other Noise Models 1 p( z )= b a 0 if a≤ z≤ b otherwise

The mean and variance of this density are given by2

(b a ) 2μ= (a+ b)/ 2 andσ= 12

Other Noise Models

Impuse(salt-and-pepper) noise

Pa for z=a p(z)= Pb for z=b

0 otherwise

If either Pa or Pbis zero, the impulse noise is called unipolara and b usually are extreme values because impulse corruption is usually large compared with the strength of

the image signal It is the only type of noise that can be distinguished from others visually

Periodic Noise

Arises typically from electrical or electromechanical interference during image acquisition It can be observed by visual inspection both in the spatial domain and frequency domainThe only spatially dependent noise will be considered

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