Bioelectronics Project

Medical Image Processing

May 27th, 2015

Objectives

To introduce the concept of thresholding and the effects of edge detecting, mean

and median filters on an image.

Background

A common method of storing a digital image is as a set of two 2-dimensional

matrices. The first matrix is the color/gray-scale map matrix which may have any

number of rows but must have exactly 3 columns. Each row is interpreted as a color,

with the first column specifying the intensity of red light, the second green, and the

third blue. In the event that the three elements have the same value the row is

interpreted as a gray level rather than a color. Color intensity is normally specified on

the interval 0.0 to 1.0, for example [0 0 0] is black, [1 1 1] is white, [0.5 0.5 0.5] is

gray and [1 0 0] is pure red. The number of rows (R) in the color/gray-scale map

matrix defines the number of different colors/gray-scale levels that may be

represented in the image.

The second matrix is a direct representation of the image itself, where each

element of the matrix (or known as image matrix) corresponds to the color/gray-scale

level of the corresponding pixel selected from the image matrix. A common

configuration is to use 256 color/gray-scale levels so that each pixel can be

represented by a single byte (1 byte = 8bits => 28 or 256 levels).

The image used in this project represents the abdominal section an aorta cut in

half longitudinally. The vessel is first stained so that diseased tissue appears darker,

then mounted flat and scanned into a 65 by 339 image with 256 gray-levels. We will

apply a number of different image processing techniques to the original image and to

two versions of the image which have been contaminated respectively by white noise

and by salt and pepper noise.

The following is a brief background on each of the image processing techniques:

Thresholding

A threshold (T) is used to transform a multiple-level image into a binary image.

The operation is described by the following statement:

p(x,y) = g1 if p(x,y)T

p(x,y) = g2 if p(x,y) > T

where p(x,y) and p(x,y) are the pixel intensities of the original and thresholded

images respectively at the location (x,y), and g1 and g2 are two gray levels chosen to

represent the thresholded image.

Edge Detection

We will consider three types of edge detectors: a horizontal edge detector, a

vertical edge detector and a Laplacian filter. The three types of filtering involve the

discrete convolution of N by N sub-arrays of an image with a filter kernel (or mask).

For an N by N kernel (N is odd), this operation is carried out by the equation:

where p(x,y) and p(x,y) are the pixel intensities of the original and thresholded

images respectively at the location (x,y), and M(m,n) is the filter kernel. Thus the

kernel is slid over the image point by point and at each location the intensity value of

the new image is calculated based on the intensity of the corresponding pixel in the

original image and its surrounding pixels.

In this project we will be dealing with exclusively with 3 by 3 kernels. The

kernels corresponding to the three edge detectors used in this project are:

Mean (Arithmetic/Average) Filtering

The mean filter is applied in a way identical to the edge detectors described

above in that it also involves the discrete convolution of an N by N sub-array of an

image with a filter kernel. The only difference lies in the values of the elements

comprising the kernel, which are as shown below:

Convolution of this kernel with an image results in a new value for each pixel which

is equal to the mean of the original pixel value and its surrounding pixels. This results

in a smoothing out effect on the image.

Median Filtering

The median filter works in a way similar to the mean filter except that the value

of each new pixel is equal to the median of the original pixel value and its

surrounding pixels rather than the mean. The median filtering of an image using a 3

by 3 kernel may be represented by the following equation:

where the function median{ } determines the median of the numbers within the

parenthesis. The median filter is especially suited to eliminate spikes, such as those

found in salt and pepper noise, since the new pixel value is independent of

abnormally high or low values within corresponding sub-array.

Project Procedure and Questions

1. You will receive a copy of the following image files:

orig.bmp contains the original aorta image

rand.bmp contains the image contaminated by Gaussian white noise

s_p.bmp contains the image contaminated by salt and pepper noise

The following Matlab m-files will be also sent to you:

threshold.m performs thresholding

mask_filter.m performs edge detection or other filtering process

median_filter.m performs median filtering

h_gram.m calculates a histogram of pixel values in an image

org_gaus.m for your convenience

org_s_p.m for your convenience

avf_gaus.m for your convenience

mdf_gaus.m for your convenience

avf_s_p.m for your convenience

mdf_s_p.m for your convenience

2. Start Matlab

3. Read in, display and print the three images by executing the following commands:

4. Find the size of the original image matrix (imgo) and the map matrix (map) using

the size command. Answer the questions: size(imgo) = ? size(map) = ? How

many pixels does the image consist of? What is the maximum number of gray

levels possible in the image? List the map matrix simply by typing: map. Why are

the values of the elements in each row of the matrix the same?

5. Create three new maps using the following commands:

6. Enter the following commands to display the image imgo using each of the three

new maps:

[imgo,map]=imread('orig.bmp');

[imgn,map]=imread('rand.bmp');

[imgs,map]=imread('s_p.bmp');

Answer the questions: How do these three renderings of the image differ from the

original rendering? Why are the renderings different even though they use the

same image matrix? Why is the background for all three of the new renderings

still back?

7. The following Matlab function is to perform thresholding on the image:

0)

pct100 = ? pct175 = ? pct245 = ? Why is the value obtained for pct100 smaller

then that obtained for pct245? How is this apparent when comparing the plots of

imgt100 and imgt245?

When we threshold the image to separate the healthy from the diseased tissue we

are assuming that the pixels corresponding to each group belong to different

populations and that a fixed threshold may distinguish one from the other. To test

whether this is true for our image we will calculate a histogram which has

gray-scale level as the x-axis and for which each column represents the number of

image

matrix

threshold hi value lo value thresholded

image

percent

diseased

imgo 100 1 0 imgt100 pct100

imgo 175 2 0 imgt175 pct175

imgo 245 3 0 imgt245 pct245

[imgt100,pct100]=threshold(imgo,100,1,0);

pixels having the corresponding gray-scale level. If our assumption regarding the

two populations is true we should see two peaks in the histogram, one

corresponding to the healthy tissue and the other to the diseased tissue. The

following function has been written to do this:

Type in the following commands to plot the histogram for the original image (We

use lo=2 to ignore the background and hi=255 because this gives a nicer

histogram. If you dont believe try 256 instead!).

By looking at the histogram which of the three thresholds best separates the two

populations of tissue (100, 175, or 245)? Could you have chosen a better threshold

than this? If so what value would you have used and why?

8. Combine the three threshold images to form the image matrix imgtcmb and plot

and print this image using the following commands:

How does this combined image differ from the original image? How many bits

would be necessary to represent one pixel in this image? In what way does this

remind you of the quantization error discussed before in our class?

image = single(image);

9. The following Matlab function has been written to perform the discrete

convolution of a 3 by 3 filter kernel with an image matrix.

Use this function to apply horizontal and vertical edge detectors and a Laplacian

filter to the imgt175 thresholded image we obtained in Step 8 as follows:

Do all the above edge detectors work (Yes/No)? What are their effects on the

image?

Before going to the next step, convert the matrices into the double format using

the commands:

imgtbin = min(1,imgtbin);

imgtbin = double(imgtbin);

imgo = double(imgo);

imgn = double(imgn);

imgs = double(imgs);

10. Use the mask_filter function to apply a mean filter to the original image:

With reference to the values of the mean filter kernel, describe and explain the

effect the filter had on the image?

11. Use the median_filter function to apply a median filter to the original image and

plot it below the mean filtered image on Figure 9:

Describe and explain the effect the Median filter had on the image? Compare and

contrast the effects of the mean and median filters on the original image with

special reference to shifts in the edges of the image outline and the image features

(i.e., the box and the two notches). In conclusion specify which of the two filters

introduces least distortion of the image.

12. In this last step we will examine the effect of mean and median filtering on

Gaussian white noise and salt and pepper noise. We will create six figures

which will enable comparison of corresponding images. To facilitate this job and

save you a lot of boring typing you have six Matlab m-files which will do the

work. These files are all similar to org_gaus.m, as given below:

By comparing Figure 10 to Figure 11, what is the main difference between the

Gaussian white noise and salt and pepper noise in terms of the noise pixel

intensity? Explain this in terms of the definition of the two types of noise.

Now, enter the following commands:

The commands should plot the original image contaminated by Gaussian noise at

the top, the same image after mean and median filtering respectively in the middle,

and the absolute difference between the two corresponding images at the bottom.

Compare these two figures together and with Figure 10 and answer the following

questions: Which of the two filters seems to have reduced the Gaussian noise

better? Explain what made you reach this conclusion. Also, by comparing the

unfiltered noise image to the mean filtered noise image describe the effect that the

filter had on the Gaussian noise and explain how this came about; repeat the above

question for the median filter.

Then, enter the following commands:

The commands should plot the original image contaminated by salt and pepper

noise at the top, the same image after mean and median filtering respectively in

the middle, and the absolute difference between the two corresponding images at

the bottom. Compare these two figures together and with Figure 11 and answer

the following questions: Which of the two filters seems to have reduced the salt

and pepper noise better? Explain what made you reach this conclusion. Also, by

comparing the unfiltered noise image to the mean filtered noise image describe the

effect that the filter had on the salt and pepper noise and explain how this came

about; repeat the above question for the median filter.

Project Requirements (Due on 6/3):

You should submit a copy of your answers to the questions raised by this project

with all the printouts (Figures 1, 5, 7, 8) requested in the project.