A Study of the Effects of Gaussian Noise on Image Features

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INTRODUCTION
Digital images are vulnerable to different types of noise which affects the quality of the images. Noise is any undesired information that contaminates an image. The main source of noise in digital images arises during image acquisition (digitization) or during image transmission. The performance of image sensor is affected by variety of reasons such as environmental condition during image acquisition or by the quality of the sensing element themselves [1].
The criteria of the noise removal problem depends on the noise type by which the image is corrupting .In the field of reducing the image noise several type of linear and non linear filtering techniques have been proposed . Different approaches for reduction of noise and image enhancement have been considered, each of which has their own limitation and advantages [1]. Image enhancement deals with processing the image so that the resulted image become more suitable for a particullar application. The main goal of image enhancement and de-noising is to remove the noise as far as possible while retrieving the important information and edges of the images [2,3].
The problem is that most techniques to reduce or remove noise always end up softening the image and affecting image features, therefore studying the effect of these techniques on image features is very important. In [4], the authors studied the effect of Salt and Pepper noise on two features of medical images (Mean and Variance) and compared it with these features after applying Median enhancement filter.
In this paper, the effect of noise and enhancement filters on image features were studied and compared. The Gaussian noise was considered since it appears commonly on images from natural sources, and different methods for reduction of noise and image enhancement have been considered. Then, features from 3 different categories, a total of 10 features, were selected to measure the effect of noise and these filters on image features. Finally, the Mean Square Error (MSE) between the original image, noisy image, and enhanced image features were compared. Based on this comparison, the effect of these techniques on image features was analyzed.

THE NOISE MODEL
Image noise is the random variation of brightness or color information in images produced by the sensor and circuitry of a scanner or digital camera. Noise produces undesirable effects such as artifacts, unrealistic edges, unseen lines, corners, blurred objects and disturbs background scenes. Noise is very difficult to remove it from the digital images without the prior knowledge of noise model. That is why, review of noise models are essential in the study of image de-noising techniques [5].
There are several types of noise that can affect images. Some of these noise models are Gaussian noise, White noise, Fractal noise, Salt & Pepper noise, Periodic noise, Quantization noise, Speckle noise, Poisson noise, Poisson-Gaussian noise, Structured noise, Gamma noise, and Rayleigh noise [6]. The three common types of image noise are: Gaussian noise, Salt & Pepper noise, and Speckle noise [7]. The Gaussian noise is tested in this paper for being the most common noises that affects images naturally.

The Gaussian Noise
The Gaussian noise, also called normal noise, is caused by natural sources such as thermal vibration of atoms and discrete nature of radiation of warm objects [6].Gaussian noise generally disturbs the gray values in digital images. That is why Gaussian noise model essentially designed and characteristics by its PDF (Probability Density Function) or normalizes histogram with respect to gray value [5]. This is given as: ..…………………………. (1) where z represents the intensity, is the mean (average) value of z, and σ is its standard deviation. The standard deviation squared is called the variance.
Generally Gaussian noise mathematical model represents the correct approximation of real world scenarios. In this noise model, the mean value is zero; variance is 0.1 and 256 gray levels in terms of its PDF (Probability Density Function), which is shown in Fig. (1) .

ENHANCEMENT FILTERS
Filtering in an image processing is a basis function that is used to achieve many tasks such as noise reduction, interpolation, and re-sampling. Filtering image data is a standard process used in almost all image processing systems. The choice of filter is determined by the nature of the task performed by filter and behavior and type of the data. Filters are used to remove noise from digital image while keeping the details of image preserved is a necessary part of image processing [1]. The applications of image enhancement are Aerial imaging, Satellite imaging, Medical imaging, Digital camera application, Remote sensing [8].
Linear filtering can be used to remove certain types of noise. Certain filters, such as averaging or Gaussian filters, are appropriate for this purpose. The Enhancement filters that were used are: the averaging enhancement filter, the Gaussian Low Pass Filter, the Circular Averaging Filter (Disk), and the Motion Filter.

Averaging Filter
The Averaging Filter is a simple linear filter which is easy to implement for smoothing images. It is often used to reduce noise in images. The Averaging Filter is a linear filter which uses a mask over each pixel in the signal. Each of the components of the pixels which fall under the mask are averaged together to form a single pixel. This filter is also called as mean filter. The Averaging Filter is poor in edge preserving [2]. The Averaging filter is defined by: .….……………………….. (2) ……………………………. (3) where i = 1 to 9, and , , .... , .

Gaussian Low Pass Filter
The Gaussian filter is a nonlinear filter that has a bell shape, and the standard deviation controls the "tightness" of the bell [6]. The Gaussian function of two variables has the basic form : ……………………………. (4) Where σ is the standard deviation and the coordinates x and y are integers. To generate the mask from this function, we sample it about its center. Thus, , , .... , .

Circular Averaging Filter (Disk Filter)
The Circular averaging filter is a pillbox within the square matrix of size (2 x radius+1).
The radius used in this paper is 5. This filter has the same equation of the Averaging filter with different w values.

The Motion Filter
The Linear motion filter used to represent the linear motion of the camera during the acquisition of the image. The Linear motion can be modeled using the degradation function [6]: As seen from the equation, this function is in frequency domain. So, this filter considered one of the frequency domain filters. The output image from this filter can be computed using:  (6) Where F(u,v) is the Fourier Transform of the original image f(x,y), and is the inverse Fourier. Although this filter isn't used to remove Gaussian noise, it was interesting to see how this filter will affect image features compared to the previous filters.

THE PROPOSED ALGORITHM
Many techniques used to remove certain types of noise. The problem is that most techniques that reduce or remove noise always soften the image as well as affect the image features. The decision of the best filter for a certain type of noise should consider the affected feature in addition to the visual apperance.
In this paper, a new algorithm proposed to study the effect of different enhancement filters on image features. A data set of 100 images was used for this study. These images were taken from [6] being a dependable source of data set. The Gaussian noise first applied to each image, and then the four enhancement filter is applied to the noisy images. Some examples of applying Gaussian noise to an image and then the enhancement filters are shown in Fig. (2) and Fig. (3) .

Different Noise Parameters
Since this paper need to study the effect of Gaussian noise with varity range of paprameters, Nine different cases of noise parameters were used in this paper. The different cases of used mean and variance for Gaussian noise are shown in Fig. (4).

Fig. (4): Different mean and variance cases of the Gaussian noise
Next, various type of features extracted from all the images. The choice of features was very important task and different categories was considered which is described in the next section.

Image Features
In this paper, various types of features were developed and compared. The features that were tested and evaluated include the mean, variance, entropy, contrast, correlation, energy, homogeneity, haar diagonal, haar Vertical, and haar Horizontal. There are three main sources for the generation of these useful features: 1. Image-based Features: Features that can be calculated directly from the image data.

2.
Texture-based Features: Features that could be calculated indirectly using the cooccurrence matrix.

3.
Transform-based Features: Features that take advantage of a standard coordinate system.

Image-based Features [6]
Image-based features can be used to represent various properties of pixels and their neighborhoods. Mean and Variance features are extracted directly from the images, as below: …………………………… (7) ………………………… (8) Where z represents the intensity value, is the probability of these values, given

Texture-based Features [6]
The properties of an image texture are detected indirectly by using the co-occurrence matrix , Let be an operator that defines the position of two pixels relative to each other, and consider the image with L possible intensity levels. The matrix has elements is the number of times that pixel pairs with intensities and occur in in the position specified by , where .
The total number, n, of pixel pairs that satisfy is equal to the sum of the elements of .
Then the quantity is an estimate of the probability that a pair of points satisfying will have values .
Correlation is the measure of how a pixel correlated to its neighbors over the entire image.

…………………………… (16)
Energy is a measure of the number of repeated pairs. Contrast is a measure of intensity contrast between a pixel and its neighbors over the entire image.

Transform-based Features
Wavelet transform is an effective tool for feature extraction, because they allow analysis of  The following points should be noted:    (2) and (3) show the results for Case 3 and Case 7 respectively.  The results in Table (2) and (3) show that changing the mean or variance didn't have a major impcat on filters effect on the features. The overall average results for all the 9 cases summarized in Table (4). It is interesting to observe the following results from each group of features:   3-According to the Wavelet-based Features, the Motion filter came up with the best results.

4-Different Filter responses according to image features could be achieved after applying
Gaussian Noise with variable parameters.

5-Some
Filters, like disk enhanced filter, offended the features of an image more than the noise itself.

6-
Changing the Gaussian noise parameters (Mean and Variance) has no effect on filters and effects on image features, especially texture features.
For Future work, the other enhanced filters can be tested and more features can be included. For a general case, the other types of noise can be considered and an overall result of different filters affecting the features can be calculated and analyzed.