Image Restoration Fasih ur Rehman

–Goal of restoration: improve image quality –Is an objective process compared to image enhancement –Restoration attempts to recover an image that has been degraded by using a priori knowledge –Contrast stretching is an enhancement technique while de-blurring function is considered a restoration –Only consider in this chapter a degraded digital image Preview

A Model of Image Degradation Spatial domain: additive noise Frequency domain : blurring The degraded image in spatial domain is g(x,y)=h(x,y)*f(x,y)+η(x,y) Restoration can be categorized as two groups : deterministic and stochastic –Deterministic methods are applicable to images with little noise and a known degradation –Stochastic methods try to find the best restoration according to a particular stochastic criterion, e.g., a least square method Frequency domain is G(u,v)=H(u,v)F(u,v)+N(u,v) Objective: obtain an estimate of f(x,y)

Degradation and Restoration Model

Types of Degradation Three types of degradation that can be easily expressed mathematically –(1) Relative motion of the camera and object –(2) Wrong lens focus –(3) Atmospheric turbulence

Noise arise during image acquisition –Environment conditions –Quality of sensing elements –For Ex. Two factors for CCD: light level and sensor temperature Spatial and frequency properties of noise –White noise: the Fourier spectrum of noise is constant –Noise is independent of spatial coordinates Noise probability density function –the statistical properties of the gray level of spatial noise can be considered random variables characterized by a PDF Noise Models

Gaussian noise –Are used frequently in practice –The PDF of a Gaussian random variable, Z, is given by Rayleigh noise –The PDF of Rayleigh noise Erlang (Gamma) noise –The PDF of Erlang noise Noise Models

Exponential noise –The PDF of exponential noise Uniform noise –The PDF of uniform noise is given by Impulse noise –The PDF of impulse noise is given by –If b>a gray level b will appear as a light dot; –If either P a or P b is zero, the impulse is called unipolar –If neither probability is zero (bipolar), and especially if they are approximately equal: salt and pepper noise Noise Models

Gaussian Noise –Electronic circuit noise –Sensors noise due to poor illumination and /or temperature Rayleigh Noise: –Helpful in characterizing noise phenomena in ranging image Exponential and Gamma Noise –Application in laser imaging Impulse Noise –Found in quick transient such as faulty-switching –The only one that is visually indicative Uniform Noise –Basis for random number generator Difficult to differentiate visually between the five image (Fi.g 5.4(a) ~Fig5.4(b)) Noise Factors

Periodic Noise (spatially periodic noise) –Caused by electrical or electromechanical interference during image acquisition –Can be reduced significantly via frequency domain filtering (e. g: Sinusoidal wave, the impulses appear in an approximate circle) –E.g. (Fi.g 5.5) :An image severely corrupted by sinusoidal noise of various frequency Noise Factors

Estimation of Noise Parameters The parameters of periodic noise are often estimated by inspection of the Fourier spectrum of the image Periodicity tends to produce frequency spikes that often can be detected even by visual analysis Attempt to infer the periodicity of noise components How to identify the noise model? –Calculate the mean and variance of the gray levels (illustrate with the image strips in Fig. 5.4) The shape of the histogram identifies the closet PDF match

Image Restoration

Chapter 5 Image Restoration Chapter 5 Image Restoration

Spatial Filtering –Apply when only additive noise is present Mean filter (noise reduction spatial filters) –Performance superior to the filters discussed in Section 3.6 Arithmetic Mean Filter –Computes the average value of the corrupted image g(x,y) –The value of the restored image f Restoration in Presence of Noise

Geometric Mean Filter: –Smooth comparable to the arithmetic mean filter, but it tends to loss less detail. Harmonic Mean Filter: –Work well for salt noise and Gaussian noise, but fails for pepper noise Restoration in Presence of Noise

Median Filters: –Are particularly effective in the presence of both bipolar and unipolar impulse noise Max and Min Filters (Fig. 5.8) –Max filter:reduce low values caused by pepper noise –Min filter: reduce high values caused by salt noise Midpoint Filter Combines order statistics and averaging Order-Statistics Filters

Image Restoration