LINEAR AND NONLINEAR FILTER FOR IMAGE PROCESSING USING MATLAB S IMAGE PROCESSING TOOLBOX

Transcription

1 LINEAR AND NONLINEAR FILTER FOR IMAGE PROCESSING USING MATLAB S IMAGE PROCESSING TOOLBOX This report is submitted to the School of Engineering and Information Technology, Murdoch University as a partial fulfilment of the requirement for the Bachelor of Engineering (Honours) FATIHAH MOHD PADZIL PROJECT SUPERVISOR: DR. GREGORY CREBBIN JANUARY, 2016

2 ACKNOWLEDGEMENT Firstly, I would like to take this opportunity to express my sincere gratitude to my supervisor, Dr. Gregory Crebbin, who was always there to listen and give advice with patience and a smile on his face, despite his busy schedule. His valuable comments, guidance and constant encouragement gave me motivation to finish this project. Also, I cannot forget to thank Dr. Linh Vu, as my second supervisor, and the School of Engineering and Information Technology for their support throughout this project. Finally, to all my family and friends, I would like to send my deep appreciation and respect for their continuous support and encouragement throughout my thesis and entire degree. i

3 ABSTRACT The proposal of the thesis is basically to study techniques in digital image processing. This thesis will cover two image processing areas, which are image restoration and image enhancement. More specifically, image restoration will involve the removal of noise and image enhancement will look into technique for edge enhancement. In this project, two classes of filter will be introduced, which are linear and nonlinear filters. Two type of noise source will be used which are Gaussian noise and salt and pepper noise. For noise removal, the mean filter is used as example of a linear filter and the median filter is used as an example of a nonlinear filter. For edge enhancement, only a linear filter is used, which is the unsharp mask filter. The simulation programs are written using the Image Processing Toolbox in MATLAB (MATrix LABoratory). Test images that corrupted by noise will be used in investigations to assess the strength and weakness for each type of filter. ii

4 TABLE OF CONTENTS ACKNOWLEDGEMENT... ABSTRACT... ii TABLE OF CONTENTS... iii 1. Introduction Problem scope Thesis Objective Report Outline Technical Review of Image Processing Overview of Digital Image Processing Image Processing System Digital Image Representation Image Processing Operations Noise Neighborhood Operations Image Restoration Linear Filter Nonlinear Filter Image Enhancement Unsharp mask filter MATLAB Image Processing Toolbox Methodology Image Input Noise Removal Process plan Mean Filter Median Filter Edge Enhancement Process Plan Results Mathematical rules iii

5 4.2 Mean Filter Result Result of 3 by 3 filtered image Result of 5 by 5 filtered image Median Filter Result Result of 3 by 3 filtered image Result of 5 by 5 filtered image Result of 11-by-11 window filter Unsharp Mask Filter Result Result Summary Problem Encountered and Countermeasures Conclusion and Recommendations Conclusion Recommendations References Appendix Appendix A Result for a 11 by 11 mean filter Result for a 11 by 11 median filter Appendix B Appendix C Appendix D Appendix E iv

6 LIST OF FIGURES Figure 1: Typical overall image processing system... 6 Figure 2: An image and the conversion used to represent rows (m) and columns (n) of the image Figure 3: Different type of noise Figure 4: A 3x3 window that centered over the picture element Figure 5: Illustration of Median filter operates Figure 6: Different between ideal edges and ramp edge Figure 7: Illustartion of Unsharp mask filter operates Figure 8: 8-bit image Figure 9: Program simulation process for noise removal Figure 10: Pixel value before filter take place Figure 11: Pixel value after filter take place Figure 12: original pixel value Figure 13: After median filtering Figure 14: Process flow of image sharpening by unsharp mask filter Figure 15: 3-by-3 Mean filter with salt and pepper noise Figure 16: 3-by-3 Mean Filter with Gaussian Noise Figure 17: 5-by-5 mean filter with salt and pepper noise Figure 18: 5-by-5 mean filter wit Gaussian noise Figure 19: 3-by-3 median filtered image with salt & pepper noise Figure 20: 3-by-3 median filtered image with Gaussian noise Figure 21: 5-by-5 median filtered image with salt & pepper noise Figure 22: 5-by-5 median filtered image with Gaussian noise Figure 23: Result of blurring with mean filter Figure 24: The edge image Figure 25: Image edge enhancement with different scaling constant k LIST OF TABLES Table 1: Image file formats Table 2: MSE value for mean filter Table 3: MSE value for 5-by-5 mean filter Table 4: MSE value for median filter Table 5: MSE value for 5 by 5 median filter v

7 1. INTRODUCTION 1.1 PROBLEM SCOPE In the modern world, digital images are necessary for a broad field of human activities. Image processing is rapidly evolving field with growing application in science and engineering. An image is a visual representation of an object or a scene produced by an optical device such as mirror or lens (Marques 2011). Digital images are pictures that have been transformed into a computer readable binary format consisting of logical 0s and 1s. They are widely used in medical applications such as digital radiography and MRI (Magnetic Resonance Imaging), in industrial applications such as safety system and quality control in manufacturing process, and in law enforcement and security system applications such as biometric techniques used in face, hand and fingerprint recognition (Solomon 2010) (Marques 2011). Image processing begins with the capture of an analog image by suitable devices, which is then converted to digital image before the image is processed by computer for better visual appearance to a human viewer (Marques 2011). Image processing covers a wide range of techniques and algorithms. Digital image processing can be separated into four categories, which are restoration, enhancement, coding and understanding (Lim 1990). In image restoration, the objective is to reduce or remove the noise in an image. Two type of filter will be designed, which are the mean filter, which is an example of a linear filter, and the median filter, which is an example of a nonlinear filter (Lim 1990). Two type of noise source are added to the image before filtering by both types of filter. 1

8 In image enhancement, the objective is to improve the pictorial appearance for human viewers and to prepare an image for storage and representation for machine perception. An unsharp mask filter is an example of an edge enhancement filter (Solomon 2010). 2

9 1.2 THESIS OBJECTIVE The aim of the project is designing the two classes of filter in image processing for noise removal and edge enhancement. The investigations that will be carried out in this project are motivated by the following scenario: An image is read using a special Matlab toolbox. For noise removal, noise is added to the image. After that, different filters will be applied to the noisy image. The strengths and weaknesses of each class of filter will be investigated and compared. For edge enhancement, different scale degree of enhancement are used to the one type of blurred picture. The main technical objectives of the thesis are: To identify the requirements of filters for specified image processing applications. These applications will include the removal of unwanted artefacts, such as noise, and the enhancement of critical features, such as the edges of objects. To develop a simulation program in Matlab, using the image processing toolbox. To design both linear and nonlinear filters for specific image processing tasks, and to compare the results of these two classes of filter. To design and implement image filters using MATLAB. To brief an introduction to the vast field of image processing. The main personal development objectives of the thesis are: To apply the theoretical and practical knowledge gained from 3 years of study at Murdoch University. To develop skills in programming, troubleshooting and system design. To develop project and time management skills. 3

10 1.3 REPORT OUTLINE The remaining chapters of this thesis will describe to the works undertaken in the project. The thesis is outlined as follows: Chapter 2: Will present a literature review and provide a background of image processing that covers the overview, techniques, and operations including edge enhancement. Chapter 3: Will describe the methodology and implementation of the simulation program. The linear and nonlinear filters for noise removal and image edge enhancement will be described. A process flow of the simulation program for both types of noise removal filter and edge enhancement filter will be described clearly. Chapter 4: Will investigate the findings of each type of image filtering technique. The strengths and weaknesses of each filter will be discuss in this chapter. Chapter 5: Will describe the problems that were encountered and the countermeasures that were taken to finish the thesis project. Chapter 6: Will conclude of the thesis report. This will also include recommendation for future research based on the findings of this thesis. 4

11 2 TECHNICAL REVIEW OF IMAGE PROCESSING The aim of this chapter is to conduct a literature review on digital image processing. This will include the basics of two image processing methods, which are image filtering and image edge enhancement. It will end by introducing MATLAB functions for reading, writing, querying, converting and displaying images. To conduct the review, books, journals, websites and the online resources were consulted so that more could be learnt about image processing. 2.1 OVERVIEW OF DIGITAL IMAGE PROCESSING The field of digital imaging has grown rapidly in recent years. Humans are exposed to the images on a daily basis in print, photographs and computer displays, where the images are still pictures that do not change with time. An image is a representation of an object or a view that is produced by an optical device such as camera or mirrors. A digital image represents an image by a two dimensional array of numbers, where each element of the array is a sampled value of the original image within a small square segment of space. These picture elements are called pixels. Each pixels is addressed by its rows and columns position in the array (Marques 2011). Digital image processing refers to the processing of a digital image by digital computers. The processing serves two main purposes, which are to improve the pictorial appearance of the original image for human viewers (Lim 1990) and to prepare the image for storage, transmission and representation for autonomous machine perception (Lim 1990) (Russ 2007). Digital image processing is widely used in various fields of application such as 5

12 industrial inspection, meteorology, astronomy, ultrasonic imaging, radiology, satellite imaging, remote sensing, and law enforcement (Bovik 2009). Digital image processing can be divided into three levels of processing which are low, mid and high. Low level processes involve basic operations such as noise reduction, contrast enhancement and image sharpening. The input and output at this level are both images. Midlevel processes result in attributes being extracted from an image, such as edges, contours, and the identity of individual objects. Lastly, higher level processes involves the analysis of images and interpretation of the contents of a scene (Marques 2011). 2.2 IMAGE PROCESSING SYSTEM A typical image processing system is built around a computer that performs digital signal processing, as shown in Figure 1 (Marques 2011). The input source is usually an object or a natural scene which is digitized and stored as a matrix of binary digits inside the computer. The digitized image is then processed using either a general purpose computer, a microprocessor or special purpose hardware. The result of processing is then displayed for human viewing or is used as an input to another system. The display could be a monitor, a photograph or it could be just a printer (Lim 1990). object (input) imaging system (observer) sample and quantitize (digitize) digital storage (store) digital computer (process) display (output) Figure 1: Typical overall image processing system 6

13 2.3 DIGITAL IMAGE REPRESENTATION A digital image, I (m, n) is a representation of an image as a two-dimensional array of picture elements or pixels where the indicator m is represent the row of image and the indicator n represents the column of the image. The number of column times the number of rows gives the total number of pixels in the image. Figure 2 shows an image and the conversion used to represent rows, m and column, n of an image. Each pixel is represents an as intensity value of the image, with intensity values typically ranging from 0 to 255. For grayscale images, a pixel is usually encoded as a value between 0 and 255, where black corresponds to pixel value 0 and white corresponds to pixel value 255. Intermediate values represent the various shades of grey (Marques 2011). For color images, each pixel is encoded with red, green, and blue (RGB) components, where each component value usually encoded in 8-bits, so that the combination these three elements is 24 bits in total (Tan 2007). Figure 2: An image and the conversion used to represent rows (m) and columns (n) of the image. The size of an image is a measure of its resolution. The resolution is related to image quality. Most image are not square but also in rectangular form with a width up to 4000pixels. In image processing the standard image sizes are used 256 x 256, 512 x 512 and 1024 x 1024 (Lim 1990). 7

14 2.4 IMAGE PROCESSING OPERATIONS In this section, several fundamental techniques that are commonly used in image processing will be discussed. Digital image processing can be divided to four common application areas which are image enhancement, restoration, coding and understanding. This thesis will focus on image restoration (noise removal) and enhancement (edge enhancement). The usual objective of these techniques is to make the processed image look better than the unprocessed image (Lim 1990) Noise An important problem for image processing is noise removal. Noise is unwanted contamination of an image. In digital images, noise can come from a variety of sources including noise of capture noise that results of variations of lighting i.e. too much or too little light, and processing noise that results from limitations in numerical precision, and mathematical approximations (e.g. π = ). A digital image is a representation of an original scene but it is not always perfect because of limitations of resolution by sampling and noise contamination (Solomon 2010). Noise in images can be characterized in many ways. In image processing, two main type of noise are often used, which are salt and pepper noise and Gaussian noise (Ajay 2015). Salt-and-pepper noise, also known as an impulsive noise, is caused by the random introduction of pure white or pure black pixels into image. This noise is commonly caused by camera sensor faults. Meanwhile, Gaussian noise, is also known as additive noise is noise with random intensity levels that have a Gaussian or normal probability density function. Usually it is caused by random processes in electronic equipment. Gaussian noise is the most 8

15 commonly used noise model in image processing (Solomon 2010). Figure 3 shows an example of different types of noise at an image. (a): Original Image (b): Image with salt-andpepper noise 9

16 (b): Image with Gaussian noise Figure 3: Different type of noise 10

17 2.4.2 Neighborhood Operations Usually, in image processing it is impractical to work on the whole image at once. When processing an image, usually the only a reference pixel and nearby pixels are used. To apply this principle, a neighborhood technique (also known as windowing technique) is used. A window in image processing is usually a small square array centered on the reference pixel. The operation on a given pixel is called a neighborhood operation because it used only the original pixel value at the given point and the pixel values in a neighborhood around that point (Marques 2011). For example, a 3x3 window that is centered over the picture at location (i, j) is shown in Figure 4. Figure 4: A 3x3 window that centered over the picture element A windowing function starts by defining a reference point in the input array, and then it performs an operation that involves only pixels in the neighborhood surrounding that reference point. It could be any shape or size of window but usually it is a square array centered on the input pixel (e.g. 3 x 3 or 5 x 5 windows centered at the given input pixel) (Marques 2011). 11

18 The result of the operation becomes the pixel value at the same location in the output image. For the edge pixels, it also use same window size, but the pixels value for outside an image is set at 0. The process is repeated for every pixel in the input image. For example, the function that is applied might be an averaging operation; it will sum the values of the neighborhood pixel then divide the result by the number of pixels in the neighborhood, thereby replacing the centre pixel by the average values of pixels in the neighborhood (Jaehne 2005). 12

19 2.5 IMAGE RESTORATION Image restoration is used to carry out several useful tasks in image processing. One of the primary tasks is noise removal. A filter is used to reduce the amount of unwanted noise in the particular image. As mentioned early, a filter usually operates on a neighborhood of pixels in an image. In the spatial domain, image filtering is done by convolving the input with the filter function to obtain the filtered image, (Abdul Rasak Zubair 2014) where the convolution takes place over the neighborhood of each input pixel. A mean filter and a median filter are both types of filter that can be used for noise removal. Whereas the mean filter is an example of a linear filter, the median filter is an example of a nonlinear filter (Lim 1990) (Solomon 2010). The next section will discuss in more detail both types of filter Linear Filter Linear filtering is carried out by convolving the input with a filter function to obtain the filtered image. A linear filter can be written as follows (Marques 2011): f(x, y) = I (m, n) w(x m, y n) m,n Here, I is represents the original image, f is represents the filtered pixels value, and w is represents the filter coefficients. 13

20 The mean filter, also known as an averaging filter, is an example of a simple linear filter. It operates by assigning the average value of all pixels in the neighborhood of the input pixels to the corresponding pixel in the output image. The principle of this filter matches perfectly with it name, as each pixel in the targeted image is replaced with the mean value of pixels surrounding it. The mathematical formulation for the mean filter (Marques 2011) is given as follows: f(x, y) = 1 mn (m,n) W I(m, n) Where: I = the noisy image, f = the restored image and (m, n) = the row and column coordinate respectively, within a window W of size m x n where the operation take places centered on input pixels at (x, y) (Marques 2011). For example, if a 3 x 3 window is used, the averaging operation uses the following 3x3 mask, which is placed over at the input pixel and its eight neighborhoods: [ 1 1 1] Averaging has the effect of smoothing the noise, as along as the noise is addictive and not impulsive. This filter is effective in removing the noise, but at the same time it blurs the image. Despite this drawback, it is still a useful filtering technique. 14

21 2.5.2 Nonlinear Filter One type of nonlinear filter operates by ranking the pixels in the specified neighborhood. It replaces the target pixel by a value corresponding to the chosen rank. The rank could be maximum value, minimum value or middle value in the neighborhoods pixels (Marques 2011) (Solomon 2010). In this project, the median filter will be used as an example of nonlinear filter. It used the middle value in the neighborhood of the target pixel. The median filter is a popular example of a nonlinear filter that is used in image processing. The median filter overcomes one of the limitations of the mean filter, which is its inability to reduce impulsive noise. The median filters are also useful in preserving edges of an image while reducing the image noise (Marques 2011). The median filter operates by sorting the pixel values within a neighborhood, then finding the median value from that ordered list and the replacing the original pixel by this median value in output image (Marques 2011). The mathematical formulation for median filter is given as follows: f(x, y) = median {I (m, n) (m, n) W} Where, I = the noisy image, f = the restored image and (m, n) = the row and column coordinate respectively, within a window W of size m x n where the operation take places (Marques 2011). 15

22 For example, the pixel values within a window are 9, 12, 0, 5, 5, 9, 8, 10 and 7, and they are processed and ranked in order to give 0, 5, 5, 7, 8, 9, 9, 10 and 12. The median values is 8, which is then used as the output pixel value (Marques 2011). Figure 5 shows an illustration of how the median filter works. Figure 5: Illustration of Median filter operates. Compared to the mean filtering technique, the median filter simply replaces each pixel with the middle value in the neighborhood of the pixel, instead of using an averaging operation. As the median is one of the pixel values in the input image, the median filter does not create a new pixel value. This helps in preserving edges and shows why these filters can be useful for image processing (Solomon 2010). 16

23 2.6 IMAGE ENHANCEMENT Instead of image smoothing for image restoration, there are techniques for image enhancement that are called edge enhancement or image sharpening. If noise removal is an application of low pass filtering, then the image sharpening is an example of high pass filtering. Image sharpening refers to any enhancement technique that highlights edges and fine details in an image. Because edges contain the high frequency components of an image, high pass filters are used to sharpen the images and increase the contrast. Image sharpening is widely used in printing and photography (Bovik 2009). An edge represents a discontinuity or change of intensity (e.g. brightness, contrast) or color (e.g. luminance, chrominance) in an image. Edges in grayscale images appear at transitions between dark and bright areas in an image such as the boundaries that separate foreground objects and background scene. Figure 6 illustrates the difference between an ideal edge which is a sharp transition, and a ramp edge, which is a gradual transition between dark and bright areas in an image (Marques 2011) (Abdul Rasak Zubair 2014). a) Ideal edge b) Ramp edge 17 Figure 6: Different between ideal edges and ramp edge

24 Edge detection is the extraction of edges of significant objects in an image. It is basically a method of segmenting an image into regions based on discontinuities between their regions. Detection of edges is very useful in many applications such as pattern recognition and fingerprint and iris biometric identification, space science and robot vision (Abdul Rasak Zubair 2014). Image edge enhancement enhances the edges, such that an image with highlighted edges is more attractive than the original image. The objective of image edge enhancement is to improve visual appeal of the processed image compared to the unprocessed image. An alternative to an image sharpening filter is the unsharp mask filter (Marques 2011). 18

25 Unsharp mask filter Unsharp mask filtering is method that boosts the high frequency edge information in images (Lim 1990). An unsharp mask filter operates by subtracting a blurred version of the image from the original image in order to highlight the edges in the image. An unsharp masking filter is described by the equations (Solomon 2010): I edge (m, n) = I original (m, n) I smoothed (m, n) I (sharp) (m, n) = I original (m, n) + k [I edge (m, n)] where k is a scaling constant. To use this approach, first the edge image, I edge must be produced by subtracting the smoothed image, I smoothed from the original image, I original, where the smoothed image, I smoothed is often obtained by filtering the original image with a low pass filter, of which mean filter is the simplest example. (Solomon 2010). Using a specified scaling constant k, the edge image is then added to the original image to obtain the sharpened image. As the scaling constant k is increased from 0 to k limit, the degree of enhancement is increased. Generally, values for k is between 0.2 and 0.7 are acceptable, depending on level of enhancement required (Solomon 2010) (Bovik 2009). Figure 7 illustrate the idea of unsharp mask filter works. 19

26 Figure 7: Illustartion of Unsharp mask filter operates 20

27 2.7 MATLAB MATLAB (MATrix LABoratory) is a high-level text language and interactive environment used for numeric computation and data analysis (The MathWorks Inc 2016). MATLAB is the software that is used to illustrate signal processing concepts in this project. It consists of a main engine to perform computations and also several toolboxes for special purpose applications. Some special code will clarify why these are used instead of the other code. MATLAB is an essential of learning for Industrial Computer Systems Engineering (ICSE) and Instrumentation & Control Engineering (ICE) students as it can be used to simulate process systems and analyze process data. This section will describe the Image Processing Toolbox (IPT) in MATLAB that is used in developing the simulation programs for this thesis Image Processing Toolbox The image processing toolbox is distributed by MathWorks is contains a collection of functions for performing different operations specifically for signal and image processing. The operations available in this toolbox are: image analysis, segmentation, morphology, image enhancement, noise removal, blurring, geometric transformation, image registration and others. Each of these operations is performed by using their own in-built functions and can operate on diverse image types and on different features of the images (MathWorks 2016). 21

28 In MATLAB s IPT, there are two basic built-in functions, imread and imshow, that are used to read and display the image respectively. The imread function allows users to read image files in any type of image format. While imshow is used to display an image and includes a number of optimization parameters for setting properties associated with image display. These functions support all prevalent image formats and create the image array for use by other MATLAB functions. A various type of image format can be used inside the MATLAB toolbox. Table 1 simplify the image formats that are supported by MATLAB (Solomon 2010). For this project, the TIFF format was chosen because it comes with compressed and uncompressed formats. Table 1: Image file formats 22

29 3 METHODOLOGY This section will discuss the approach that is used to develop the simulation program. Both of the core image processing operations, which are noise removal and edge enhancement, will be discussed here. 3.1 IMAGE INPUT The original images that is used in this thesis come from the Signal and Image Processing Institute (SIPI) at University of Southern California (USC). These images can be accessed in their webpage (SIPI 2015). The images in the USC-SIPI image database are provided for research purposes. SIPI provide image of various sizes in their database, the images are stored in TIFF format. Figure 8: 8-bit image Figure 8 show the original image clock is used throughout project. This grayscale image is 256 width x 256 height. This is an uncompressed version of the original image. 23

30 3.2 NOISE REMOVAL The purpose of this section is to describe the methods that are used to complete the simulation program to filter images for noise removal. As discussed in Section 2.5, two types of filter are used for noise removal: mean filter and median filter Process plan In this thesis project, the image database was simulated in MATLAB s IPT by following the flow diagram given in Figure 9. Read Input image Convert Indexed image Double precision classes Choose Window size for mean Filter and median Filter Add Salt and Pepper Noise Gaussian Noise Display Original image Noisy Image Filtered image Compare Mean- square value Figure 9: Program simulation process for noise removal 24

31 First, when the simulation program is run the image input is read using imread function. The input image is a grayscale image with 256 x 256 pixels with 1 byte per pixel that stored an intensity value from 0 to 255. This image is indexed image in uint8 (unsigned 8-bit integer) data classes. To make the input image suitable for image processing that performs a numbers of an arithmetic operations, the image input is changed from uint8 to double (double precision floating point) class to allow for more precision. This class increases storage from 1 byte per pixel to 8 bytes per pixel, with pixels value that range from 0.0 to 1.0, with no negative numbers. This format is more useful when arithmetic operations are performed. Next is where the noise is added to the input image. Two types of noise were introduced in Chapter 2 Section which were salt and pepper noise and Gaussian noise. The imnoise function in IPT can set the type of noise along with intensity parameter value ranging from 0 to 1. The noise is added to the image. For salt and pepper noise, the noise density, which has a default value of 0.5 is the additional parameter. While, for Gaussian noise, mean and variance of Gaussian noise is needed in, this has default values of zero mean with 0.01 variance. Then the window operation size is chosen. In the simulation program the window size can be added manually. This makes it easier to change the size when the visual appearance of image is compared for different window sizes. Lastly, after filtering the original image, the noisy image and the filtered image are displayed. There will be two windows that will pop up for image display, where the Figure 1 window displays the original image and the Figure 2 window display the noise added image and the filtered image. 25

32 When the image displays, the image processing results can be see subjectively. But to confirm that a filter is good at reducing noise, the mean-square error between original and processed images is calculated. The smaller the error, the better the filtering performance Mean Filter The mean filter operates by replaces each pixel by the average value of the neighborhood. In this simulation a by 3 x 3 mean window filter is used. The method of mean filter works is illustrated in Figures 10 and 11: Figure 10: Pixel value before filter take place Figure 11: Pixel value after filter take place 26

33 Consider the pixels at the coordinate (2, 3), which has an original value of is as shown in Figure 10. The nine neighboring pixels value are summed and then divided by 9 to give the average value; 1 ( ) 9 = The output value is shown in Figure 11. The process is repeated at the next pixel until all pixels are processed. The same method could be apply to 5 x 5 mean filter but, this time a 25 neighborhood of pixels would be used in the averaging Median Filter The median filter operates by sorting the pixel values within the neighborhood, where the median value within the window replaces the original value. The simulation using a 3 by 3 median filter is shown in Figures 12 and 13. Figure 12: original pixel value 27

34 Figure 13: After median filtering Again, the pixels at coordinate (2, 3) with original pixel values of is , is shown in Figure 12. The nine neighboring pixels is arranged in ascending order as follows: , , , , , , , , The median value of replaces the original value, as shown in Figure 13. The process is repeated at the next pixel until all pixels are processed. The same method could be applied to a 5 x5 median filter but this time 25 neighborhood pixels would be sorted. 28

35 3.3 EDGE ENHANCEMENT The purpose of this section is to describe a method of operation that is used to complete the simulation program for image sharpening by using an unsharp mask filter. As discussed in Section 2.6.1, the unsharp mask filter is a technique that is used to increases the sharpness of the image by using a blurred image of the original input image Process Plan In this section, the image sharpening was simulated by following the flow diagram shown in Figure

36 Read Input image Convert Double precision Blur Using mean filter 3 by 3 window Subtract Original image with filtered image Choose Scaling constant, k Add Original image with blurry image Display Original image and sharpening image Figure 14: Process flow of image sharpening by unsharp mask filter 30

37 The simulation for edge enhancement is based on the unsharp masking theory (Solomon 2010) (Marques 2011). Firstly, the image was read by using the imread function. The image input values that range from 0 to 255 in the uint8 data class are converted to the double precision data class with values that range from 0.0 to 1.0. This allows for more precise calculation when the arithmetic operations of addition, and subtraction are done. Next, the input image is filtered with a 3 x 3 mean filter to obtain the blurred image from an original image. The blurred image is now subtracted from the original image to get an edge image. The edge detect image will be displayed together with the final result. Then, the scaling constant k is chosen. It can be varied manually in this simulation program. After the scaling constant k is chosen, each pixel in the edge images is scaled by k and then is added back into the original image to obtain the edge sharpened image. The image edge enhancement was tested using three different values of scaling constant. Lastly, the blurred image, the edge image and the enhanced image are displayed together in the Figure 1 window. 31

38 4 RESULTS In this section the results from this project are presented. The results are in the form of filtered images and mean square error measurements. For noise removal technique, two types of noise are added to the input image. The filtered image is then compared to the original noise-free image and noisy image. The results will show how effective the filters are at removing the different kinds of noise in the image. For edge enhancement, three different scaling factors are compared to find scaling factor that gives the best enhancement of the edges in the image. 4.1 MATHEMATICAL RULES The mean square error (MSE) is chosen as an objective metric for deciding which type of filter is best at removing the different types of noise. MSE is widely used in image processing (Kaiwen Zhang 2002). It measures overall gray-value difference between pixels of the reference image and the filtered image for the entire image without considering correlation between the neighborhood pixels. The MSE is defined as: MSE = 1 mn (x original(m, n) m n x filtered (m, n)) 2 Pixels are treated individually so all pixels in the image are equally important. As a human observer, some pixels errors may cause more significant visual effects than other pixels errors, but MSE would assign the same error value to both pixels. The greatest quality is when the MSE equal to zero. The smaller MSE, the better the filter for filtering that type of noise. 32

39 4.2 MEAN FILTER RESULT Result of 3 by 3 filtered image The first result that is presented are for the 3-by-3 mean filter applied to images with both type of noise. From Figure 15 and Figure 16, the filtered image give evidence of less noise than the unfiltered noisy image. The noise tends to be removed but some details such as edges, becomes blurred so, while the mean filter can remove the noise, it tends to blur the image. Figure 15: 3-by-3 Mean filter with salt and pepper noise 33

40 Figure 16: 3-by-3 Mean Filter with Gaussian Noise The Gaussian noise is removed more effectively with the mean filter compared to salt and pepper noise. The salt and pepper noise becomes blurred but is not removed. The meansquare-errors support these observations. The MSE value is calculated for, the original to the noise added image, and the original image to the filtered image. The values are recorded in Table 2. Table 2: MSE value for mean filter Gaussian Salt and pepper Original image and noise added image Original image and filtered image From the table, the filtered Gaussian noise image has the smallest MSE value, which shows that the mean filter removes Gaussian noise better than it removes salt and pepper noise. 34

41 4.2.2 Result of 5 by 5 filtered image This is result that is presented are for the 5-by-5 mean filter applied to images with both type of noise. Figure 17 shows the 5 by 5 mean filter with salt and pepper noise and Figure 18 shows the 5-by-5 mean filter with Gaussian noise. From the image review, the both image became more blurred because the mean filter tends to blur the noise instead of reduce it. It shows that window 5-by-5 mean filter not really suitable to uses when to reduce the noise. Figure 17: 5-by-5 mean filter with salt and pepper noise 35 Figure 18: 5-by-5 mean filter wit Gaussian noise

42 Table 3: MSE value for 5-by-5 mean filter Gaussian Salt and pepper Original image and noise added image Original image and filtered image The MSE value for 5-by-5 mean filter is recorded in Table 3. From the table, with the almost same noise- added to the image, the Gaussian noise is seen to be more reduce from the image but the both image filtered look more blurred. 36

43 4.3 MEDIAN FILTER RESULT Result of 3 by 3 filtered image The median filter has uses in image processing because it is the simplest nonlinear filter that can produce interesting results. Figure 19 shows an image with salt and pepper noise that is filtered by 3 x 3 median filter, while Figure 20 shows Gaussian noise that is filtered by the same median filter. Both types of noise are reduced in the image, but by looking at Figure 19, it is clear that salt and pepper noise has being removed more effectively than the Gaussian noise. From these images, the median filter is not only good at removing the noise but also at preserving the edges of the image. It is clear that the median filter works better when removing the salt and pepper noise compared to removing Gaussian noise. Figure 19: 3-by-3 median filtered image with salt & pepper noise 37

44 Figure 20: 3-by-3 median filtered image with Gaussian noise The MSE value for the median filter is calculated between the original and the noiseadded image, and between the original image and the filtered image. The MSE for both types of noise are recorded in Table 4. From the table, the filtered salt and pepper noise image has the smallest MSE value, which is near to zero. By comparing Table 2 and Table 4, the median filter is considerably more effective than mean filter in removing salt and pepper noise. Table 4: MSE value for median filter Gaussian Salt and pepper Original image and noise added image Original image and filtered image

45 4.3.2 Result of 5 by 5 filtered image This is result that is presented are for the 5-by-5 median filter applied to images with both type of noise. Figure 21 shows the 5-by-5 median filter with salt and pepper noise and Figure 22 shows the 5-by-5 median filter with Gaussian noise. Figure 21: 5-by-5 median filtered image with salt & pepper noise 39 Figure 22: 5-by-5 median filtered image with Gaussian noise

46 From the image review, for salt and pepper noise clearly can see the noise is remove from the image and still have some edge is preserved. For Gaussian noise, the image become a bit blurred but still good when compare to the 5-by-5 mean filter. The mean-square-errors support these observations. The MSE value is calculated for, the original to the noise added image, and the original image to the filtered image. The values are recorded in Table 5. Table 5: MSE value for 5 by 5 median filter Gaussian Salt and pepper Original image and noise added image Original image and filtered image From the table, the salt and pepper noise is seen to work better than the Gaussian noise when to remove the noise using median filter. By comparing to window of median filter, 3- by-3 window is work better than the 5-by-5 window filter. 40

47 4.4 RESULT OF 11-BY-11 WINDOW FILTER The uses of larger windows for mean and median filter were also studied. A window of size 11-by-11 was chosen. The result are not included here because the larger windows caused the image to become more blurring, especially when using mean filter on salt and pepper noise which is not effective at all. The results for 11-by11 mean filter and 11-by- 11median filter are included in Appendix A of this thesis. 4.5 UNSHARP MASK FILTER RESULT The unsharp masking filter is one technique for edge enhancement. Figure 19 shows the blurred image resulting from the application of a 3 by 3 mean filter to the input image. The blurred image is then subtracted from the original image to obtain the edge difference image, as shown in Figure 23. The final enhancement images based on using different scaling constants is shown in Figure

48 Figure 23: Result of blurring with mean filter Figure 24: The edge image 42

49 k= 0.2 MSE = k= 0.5 MSE = K= 0.7 MSE = k= 0.8 MSE = k=7 MSE = K=11 MSE= Figure 25: Image edge enhancement with different scaling constant k The results in Figure 25 show that by increasing the parameter k, the degree of enhancement increases but the noise within the image becomes more apparent. The different values of k that were used are 0.2, 0.5, 0.7, 0.8, 1.0 and 11. A value of 0.8 is upper value for k, beyond which the noise effects become more severe. 43

50 4.6 RESULT SUMMARY In this section the findings of this project are summarized here. For noise removal technique, two type of noise is added which is salt-and-pepper and Gaussian noise and two type of filter is apply to remove this noise. For linear filter example is mean filter, works better when removing the Gaussian noise compared to removing the salt and pepper noise. For nonlinear filter example is median filter. Median filter are introduced to overcome the limitation of mean filter so it works better when removing the salt and pepper noise comparing to removing Gaussian noise. But median filter not only remove the noise but also preserve the edges of image. For noise removal, only small size of window is consider to use for removing noise. This can see when the bigger size of window is applied the image tends to become more blurred when filtering job is done. For edge enhancement, three different scaling factors are compared to find scaling factor that gives the best enhancement of the edges in the image. The k value is measured from k = 0.2 to 11. Results from Figure 25 shows that the degree of enhancement, 0.8 is chosen because the edge is enhance nicely without amplify the false edge (noise). The false edge is amplify can clearly see on when k = 11 compared to the original image. 44

51 5 PROBLEM ENCOUNTERED AND COUNTERMEASURES During the progress plan stage of this project a few of problem were encountered. Corrective action was taken to ensure this project and thesis could be completed according to the plan and design. The first problem that was identified was that Murdoch University only has one license for the MATLAB Image Processing Toolbox. This license only could be accessed from a special server which is ENGEN2 and only one person can accessed the toolbox at the time. To solve this problem, a request was sent to the technician, Will Stirling, to open this server. The second problem was the limited resources in the library. There were only a limited number of book for image processing. A few useful books could not be found either in hardcopy or e-book format from library resources. There are also a lot of journal articles available but the books have more detail explanation about MATLAB code. The countermeasure for this problem was to borrow a book from the supervisor. 45

52 6 CONCLUSION AND RECOMMENDATIONS 6.1 CONCLUSION In conclusion, different filters have different strengths and weaknesses. So different types of filter are needed when solving image processing problems. Sometimes a nonlinear filter may work better than a linear filter. In image restoration, the nonlinear filter can do a better job that the linear filter. As seen in the results, while the linear filter can remove the noise, the nonlinear filter not only removes the noise but also can preserve edges. This is why, not just a single filter is needed to remove noise, but a range of filters are needed, depending on the situation encountered. In summary, this project had archieved its main objective to develop a simulation program in MATLAB using the Image Processing Toolbox. Basic knowledge about image processing was introduced in the literature review chapter. Both linear and nonlinear filters for specific image processing tasks were designed: the mean filter as a linear filter type and the median filter as a nonlinear filter type. The requirements of the filters to remove unwanted artefacts (noise) and to enhance edges were identified. Lastly, with this thesis, the main achievement when developing these programs, was that the theoretical and practical knowledge gained from three years study at Murdoch could be applied to a new problem. This is a significant achievement because it helped develop the skills in programming, troubleshooting and system design. 46

53 6.2 RECOMMENDATIONS Due to the time limitation, there is still a lot of works that could be done in this area. Following the investigations described in this thesis, a number of more advanced image processing tasks could be investigated: - The simulation programs were limited to basic applications of image processing; the existing program could be extended to other application such as object identification and image coding. - The simulations used only a gray-level image. The next step would be to upgrade to using color images. - Other enhancement methods can be applied to enhance the edges of images such as the Laplacian-based method (Solomon 2010). - The simulation program was built by using the MATLAB Image Processing Toolbox. It is possible to build simulators using other toolbox such as signal and processing toolbox and computer vision toolboxes. 47

54 7 REFERENCES Abdul Rasak Zubair, Olasebikan Alade Fakolujo. "International Journal of Computer and Information Technology." Image Edge Detection and Image Edge Enhancement: Numerical experiment on High Pass Spatial Filtering, 2014: Ajay Kumar Boyat, Brijendra Kumar Joshi. "A Review Paper." Noise Models in Digital Image Processing, April Bovik, Alan C. The Essential Guide to Image Processing 2nd Edition. London, UK: Academic Press, Jae S. Lim. Two- Dimensional Signal and Image Processing. Englewoods Cliff, NJ: Prentice Hall, Jaehne, Bernd. Digital Image Processing. Heidelberg, Germany: Springer-Verlag Berlin, Kaiwen Zhang, Shouzhong Wang, Xiepen Zhang. A New Metric for Quality Assesment of Digital Image Based on Weighed-Mean Square Error, Marques, Oge. Practical Image and Video Processing Using Matlab. Somerset, NJ, USA: John Wiley & Son, Russ, John C. The Image Processing Handbook 5th Edition. Raleigh, North Carolina: Taylor & Francis Group, SIPI. Signal and Image Processing Institute, University of Southern California (accessed September 2015, 1). Solomon Chris, Toby Brecken. In Fundamental of Digital Image Processing: A Practical Approach with Example in Matlab. Hoboken, NJ: John Wiley & Son, Tan, Li. Digital Signal Processing : Fundamentals and Applications. Burlington, MA, USA: Academic Press, The MathWorks Inc (accessed December 2015). Zubair, Abdul Rasak. "International Journal of Research in Commence, IT & Management." Comparison of Image Enhancement Techniques,

55 8 APPENDIX 8.1 APPENDIX A Result for a 11 by 11 mean filter 49

56 50 LINEAR AND NONLINEAR IMAGE PROCESSING FILTER

57 Result for a 11 by 11 median filter. 51

58 52 LINEAR AND NONLINEAR IMAGE PROCESSING FILTER

59 8.2 APPENDIX B Appendix B shows the Matlab code for noise removal by a mean filter. clc; clear; % Read image. I = imread('c:\users\ \documents\matlab\thesis Ariesa\clock.tiff'); [r c]=size(i) %convert image to double precesion Id = im2double (I); % Apply salt and pepper noise to image using imnoise. Isp = imnoise(id,'salt & pepper',0.05); % Apply gaussian noise to image using imnoise. Ig = imnoise(id,'gaussian',0,0.02); %predefined filter NxN window (mean filter) n = input ('enter the window size of MEAN Filter, (n for NxN matrix):'); %specify window size mean = ones (n,n)/(n*n) %imfilter=computes each element of the output,using double-precision floating point. %for salt and pepper noise Ispf = imfilter (Isp,mean); %for gaussian noise Igf = imfilter (Ig,mean); % Display original image and noise image for comparison. figure (1) subplot (1,2,1), imshow(isp) title ('Image with Noise (Salt&Pepper)') subplot (1,2,2), imshow(ispf) title ('Filtered Image Using Mean Filter') % Display original image and noise image for comparison. figure (2) subplot (1,2,1), imshow(ig) title ('Image with Noise (Gaussian)') subplot (1,2,2), imshow(igf) title ('Filtered Image Using Mean Filter') 53

60 % MSE % 1st try % ORIGINAL - FILTERED IMAGE diffg = ( Id -Ispf).^2; MSE1= sum(sum(diffg))/ (r*c); fprintf('\n\noriginal IMAGE AND FILTERED IMAGE') fprintf('\nthe Mse value for Salt and pepper noise is: %.5f', MSE1); diffg = ( Id -Igf).^2; MSE2= sum(sum(diffg))/ (r*c); fprintf('\nthe Mse value for Gaussian noise is: %.5f', MSE2); % MSE % 2nd try % OORIGINAl - NOISY IMAGE diffg = ( Id -Isp).^2; MSe1= sum(sum(diffg))/ (r*c); fprintf('\n\noriginal IMAGE AND NOISE ADDED IMAGE'); fprintf('\nthe Mse value for salt and pepper noise is: %.5f', MSe1); diffg = ( Id -Ig).^2; MSe2= sum(sum(diffg))/ (r*c); fprintf('\nthe Mse value for Gaussian noise is: %.5f', MSe2); 54

61 8.3 APPENDIX C Appendix C shows the Matlab code for noise removal by a median filter. clc; clear; % Read image. I = imread('c:\users\ \documents\matlab\thesis Ariesa\clock.tiff'); %convert image to double precesion Id = im2double (I); [r c] = size (I) % Apply salt and pepper noise to image using imnoise. Isp = imnoise(id,'salt & pepper',0.05); % Apply gaussian noise to image using imnoise. Ig = imnoise(id,'gaussian',0,0.02); %predefined filter NxN window (mean filter) n = input ('enter the window size of MEDIAN Filter, (n for NxN matrix):'); %specify window size %B = medfilt2(a, [m n]) performs median filtering, where each output pixel % contains the median value in the m-by-n % neighborhood around the corresponding pixel in the % input image. %median = medfilt2 ((image_noise,[n n]); %median filter with NxN window % %for salt and pepper noise Ispf = medfilt2 (Isp,[n n]); %for gaussian noise Igf = medfilt2 (Ig, [n n]); % Display original image and noise image for comparison. figure (1) subplot (1,2,1), imshow(isp) title ('Image with Noise (Salt&Pepper)') subplot (1,2,2), imshow(ispf) title ('Filtered Image Using Median Filter') % Display original image and noise image for comparison. figure (2) subplot (1,2,1), imshow(ig) title ('Image with Noise (Gaussian)') subplot (1,2,2), imshow(igf) title ('Filtered Image Using Median Filter') % Mean Square Error %--- calculates the MSE. % calculates the "square error" image. % change to double so that we can get negative differences. % \ 55

62 % MSE % 1st try % ORIGINAL - FILTERED IMAGE diffg = ( Id -Ispf).^2; MSE1= sum(sum(diffg))/ (r*c); fprintf('\n\noriginal IMAGE AND FILTERED IMAGE') fprintf('\nthe Mse value for Salt and pepper noise is: %.5f', MSE1); diffg = ( Id -Igf).^2; MSE2= sum(sum(diffg))/ (r*c); fprintf('\nthe Mse value for Gaussian noise is: %.5f', MSE2); % MSE % 2nd try % OORIGINAl - NOISY IMAGE diffg = ( Id -Isp).^2; MSe1= sum(sum(diffg))/ (r*c); fprintf('\n\noriginal IMAGE AND NOISE ADDED IMAGE'); fprintf('\nthe Mse value for salt and pepper noise is: %.5f', MSe1); diffg = ( Id -Ig).^2; MSe2= sum(sum(diffg))/ (r*c); fprintf('\nthe Mse value for Gaussian noise is: %.5f\n\n', MSe2); 56

63 8.4 APPENDIX D Appendix C shows the Matlab code for an unsharp mask filter. clc; clear; % Read image. I = imread('c:\users\ \documents\matlab\thesis Ariesa\clock.tiff'); [r c] = size (I) %convert image to double precesion Id = im2double (I); % smoothes by 3x3 mean filter mean = ones (3,3)/(3*3) smooth = imfilter (Id,mean); edge= Id- smooth; k = input ('enter the scaling constant,k:'); sharp1 = Id + k*(edge); figure(1) imshow(smooth); title ('Blurred Image'); figure (2) subplot(1,2,1); imshow(edge); title('edge Detection'); subplot (1,2,2) imshow(sharp1); title('sharpened Image') % MSE % 1nd try % noisy image - filterd image % salt and pepper image diffs1 = ( Id- sharp1).^2; mse1= sum(sum(diffs1))/ (r*c); fprintf('\n\nsharpened Image without noise'); fprintf('\nthe Mse value is: %.5f', mse1); 57

64 8.5 APPENDIX E Result for an unsharp mask filter. 58

65 59 LINEAR AND NONLINEAR IMAGE PROCESSING FILTER