In this paper we introduce how to handle different kinds of image formats in MATLAB 9.3 by using Matlab Workspace and its Various Commands. Also we illustrated example of processing the images. Shete S. G. | Ghadge Nagnath G. "Image Processing in MAT
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Noise Models in Image Processing Pi19404 February 3, 2013
Contents
Contents 0.1 Int Introd roduct uction ion . . . . . . . . 0.2 Gaussian Noise Model . . 0.3 Rayleigh Noise Model . . . 0.4 Uniform Noise Model . . . 0.5 Uniform Noise Model . . . 0.6 Exponential Noise Model 0.7 Sal Saltt and Pepper Pepper No Nois isee . . 0.8 Use of Noise Models . . . 0.9 Code . . . . . . . . . . . . . References . . . . . . . . . . . .
Noise Models in Image Processing 0.1 Introduction In Im Imag agin ingg sy syst stem emss ar aree co comm mmon only ly af affe fect cted ed by no nois isee du duri ring ng im imag agee aquisition and transmission. Consider the experiment of acquiring the image.Let us assume than we have a system than generates a ideal image.Let us perform the experiment N times and compare the noisy image with ideal image. If we compare the error during the N runs of experiment the noise encountered would not be the same.And it cannot be represented in terms of a simple mathematical expression. However if we observe than noise follows some statictical properities can be observed.we can construct a statical representation of noise. Such a representation is called as statical noise model.It is simply the process to model and describe noise using a mathematical way. Noise singal is commonly modelled as random variable which is char acterized by its Probability density function. And if we assume that statistical properties of noise do not change with time then noise can also be modelled as stationary random process . There are many Different commonly used noise models encoun tered in image processing. Some noise models have been observed in physical systems,while others provide a tool for simplified mathematical analysis.We may choose different models based on application at hand. we wi willll lo look ok at dif iffe ferren entt ty type pess of no nois isee mo mod del els, s,th thei eirr use sess an and d their effect on sample image.
Noise Models in Image Processing
0.2 Gaussian Noise Model The gaussian 1D-PDF is expressed in the form
where is mean and variable.
is va vari rian ance ce as asso soci ciat ated ed wi with th th thee ra rand ndom om
The PDF tells us probability of observing instance of random variable. If we were to compute the PDF/relative frequency plot of gaussian random variance we would observe than most of the values are centered about the mean.The relative frequency of values away from the mean are less. Such a model can be used in situations where each pixels is affected by no nois isee in inde depe pend nden entl tlyy of ot othe herr pi pixe xels ls an and d no nois isee PD PDF F fo follllow owss a gaussian distribution. Let us look at a sample test image and effect of gaussian noise on the PDF of such an image Condside the test image,Its pixels inte in tens nsit itie iess ta take ke 3 va valu lues es 0, 0,0. 0.55 an and d 0. 0.9. 9. Thu huss it itss hi hissto togr gram am is represented by 3 delta functions. Now we apply gaussian noise to the image and then observe the histogram of the image. In the corrupted image histogram we can see that histogram which originally consisted of 3 impulse functions ,gets spread out in accordance with Gasussian PDF. The gassusian function can be observed in the noisy image histogram. We can observe that the output image PDF is convolution of input image PDF and gaussian noise PDF. This is due to fact that PDF of sum of two random variable is convolution of PDF of two random variables involved. If we were only given the noisy image we may be abl blee to es esttimate the noise under the assumption that it is gaussian in nature.
Noise Models in Image Processing
(a) Gaussian Noise Model
Noise Models in Image Processing
0.3 Rayleigh Noise Model The PDF for Rayleigh random variable is given by
for
>0 and
The param paramete eterr co cont ntro rols ls th thee am ammo moun untt of sp spre read ad,hi ,high gher er th thee va valu luee higher the spread. As in the above case the PDF of output image is obtained by convolution of input image and rayleigh noise PDF.
(b) Rayleigh Noise Model
Noise Models in Image Processing
0.4 Uniform Noise Model The PDF for Uniform random variable is given by
The para pa rame mete ters rs co cont ntro rols ls th thee am ammo moun untt of sp spre read ad,h ,hig ighe herr th thee difference higher the spread. As in the above case the PDF of output image is obtained by convolution of input image and uniform noise PDF.
(c) Uniform Noise Model
Noise Models in Image Processing
0.5 Uniform Noise Model The PDF for Uniform random variable is given by
The para pa rame mete ters rs co cont ntro rols ls th thee am ammo moun untt of sp spre read ad,h ,hig ighe herr th thee difference higher the spread. As in the above case the PDF of output image is obtained by convolution of input image and uniform noise PDF.
(d) Uniform Noise Model
Noise Models in Image Processing
0.6 Exponential Noise Model The PDF for Uniform random variable is given by
The para pa rame mete ters rs co cont ntro rols ls th thee ammo ammoun untt of sp spre read ad.. Hi High gher er th thee value faster the function falls to zero from the maximum. As in the above case the PDF of output image is obtained by convolution of input image and uniform noise PDF.
(e) Exponential Noise Model
0.7 Salt and Pepper Noise The Salt and pepper noise takes values either 0 or 1. It represents itself as randomly occurring white and black pixel.
Noise Models in Image Processing
The PDF for Impulsive noise is given by
As in the above case the PDF of output image is obtained by convolution of input image and uniform noise PDF. The Salt and pepper noise has the effect of shifting the PDF of input histogram
(f) Salt and Pepper Noise Model
0.8 Use of Noise Models The histogram of above noise modesl can be used to estimate the type of noise and parameters of the noise model.
Noise Models in Image Processing
Depending on the noise detected in the image different type of filters or filters with varying parameters can be applied to the image. Median filter is very effective for salt and pepper noise while Gaussian filter can be applied in case of gaussian,uniform noise etc. Assuming or estimating noise from the image also helps in image denois den oising ing and res restor toratio ationn appl applicat ication ionss to dev develo elope pe opt optimu imum m fil filter terss for specific types of noise models. Thus noise models helps in selecting the filter or parameters of filters in image denoising and restoration applications. We will look these aspects in detail in later articles.
0.9 Code The code consits of two parts the host code and the device cod co de. Ho Host st si sid de co cod de use sess Ope penC nCvv API PI’s ’s to re read ad th thee im imag agee fr from om vid vi deo fililee an and d de demo mons nstr trat ates es th thee ca callllin ingg of th thee ke kerrne nell co cod de for Box filter,Gaussian Filter and Sobel with naive and optimized parallel version and host CPU version . Code is available in repository
