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## Image Processing

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**Image Processing**Image Restoration Part 1**What is Image Restoration?**• Image restoration attempts to restore images that have been degraded by using a prior knowledge of the degradation phenomenon. • Identify the degradation process and attempt to reverse it • Similar to image enhancement, but more objective**Noise Model**• We can consider a noisy image to be modelled as follows: • where f(x, y) is the original image pixel, η(x, y) is the noise term and g(x, y) is the resulting noisy pixel • If we can estimate the model the noise in an image is based on this will help us to figure out how to restore the image**Degradation/restoration process model**• Degradation model • A degradation function and additive noise that operate on an input image f(x, y) to produce a degraded image g(x, y):**Degradation/restoration process model**• Restoration model • Given g(x, y) and some knowledge about the degradation function H and the noise η, obtain an estimate fˆ(x, y) of the original image • If H is a linear spatially invariant process: • In spatial domain: • h(x, y): spatial representation of the degradation function • In an equivalent frequency domain**Sources of noise**• Arise during image acquisition (digitization) and/or transmission • Environmental conditions: light, temperature, humidity, atmospheric disturbance... • Quality of sensing elements and transmission media • Human interference • Assumptions of noise • Independent of spatial coordinates • Uncorrelated with respect to the image**Noise Model**• Spatial noise • Considered as random variables, characterized by a probability density function (PDF) • Noise models • Simulate the behavior and effect of noise • There are many different models for the image noise term η(x, y) • Gaussian • Most common model • Rayleigh • Erlang • Exponential • Uniform • Impulse • Salt and pepper noise**Noise Model**• Gaussian (normal) noise, PDF: * z: gray level, μ: mean value, σ: standard deviation,σ2: variance**Histogram to go here**Noise Example • The test pattern to the right is ideal for demonstrating the addition of noise • Consists of constant areas that span the gray scale from black to near white. Image Histogram**Periodic Noise**• Typically arises from electrical or electromechanical interference during image acquisition. • FT of a pure sinusoid is a pair of conjugate impulses located at the conjugate frequencies of sine wave. • More in section 5.4**Estimation of Noise Parameters**• The parameters of noise PDFs may be known partially from sensor specifications • But its necessary to estimate them form images. • Capture a set of images of flat environment. • In the case of optical sensors, this is simple as imaging a solid board that is illuminated uniformly. • The resulting images are good indicators of system noise.**Estimation of Noise Parameters**• Use data from image strip to calculate the mean and variance of the gray levels. • If the strip is denoted by S, then**Restoration in the Presence of Noise Only-Spatial Filtering**• When the only degradation present in an image is noise, • and • The noise terms are unknown, so subtracting them from g(x,y) or G(u,v) is not realistic option. • In periodic noise, it is possible to estimate N(u,v) from the spectrum of G(u,v). • So subtraction can be done to obtain an estimate of the original image • This is an exception rather than a rule • Spatial filtering is the method of choice in situations when only additive noise is present.**** Impulsive (Salt & Pepper) Noise**• Definition • Each pixel in an image has a probability pa or pb of being contaminated by a white dot (salt) or a black dot (pepper) X: noise-free image, Y: noisy image with probability pa noisy pixels with probability pb clean pixels with probability 1 - pa - pb add salt & pepper noise