Activity 4 - Enhancement by Histogram Manipulation

I wanted to apply what I learned during the class about improving the contrast so I used an image of a sample seen under a microscope. The image above is the original image.

Max grayscale pixel value = 103

Min grayscale pixel value = 17

Above is the histogram of the original image. We can see that it has only a limited range of grayscale values which means the image is of poor contrast.

The Cumulative Distribution Function (CDF) is shown above. The CDF is not linear and has a point of saturation where the value becomes 1 which is the highest value of the CDF

We backproject the image pixel values by finding its corresponding y-value in the CDF. That is, replace the pixel value by the values on the y-axis of the pixel value from the CDF. The resulting image is called the histogram equalized image. The histogram equalized image is shown below.

We could see visually that the contrast was improved. We verify this by looking at its histogram. The histogram is shown below.

The histogram is well spread which means that the image has good contrast. Comparing it to the original image, the contrast of the histogram equalized image is far much better. The CDf is shown below and it can be seen that it is linear.

I used another method to improve the contrast of my image. I stretched my CDF and in the process also stretched the range of grayscale values that are present. The resulting image, its histogram and CDF is shown below.

At the last part of the activity we transformed the image to have a desired CDF. The desired CDF equation has the equation G=tanh(16*(z-128)/255). But since the values must be from zero to one then we normalize the equation by adding one then dividing it by the maximum value. I did that on scilab and I get the CDF below.

Now we use the algorithm

1. From the pixel grayscale, find CDF value.

2.Trace this value in the desired CDF.

3.Replace pixel value by grayscale value having this CDF value in desired CDF.

The resulting image is shown below.

The CDF of this new image is shown below.

I could say it almost fits perfectly to the desired CDF. The histogram of this new image is shown below.

As we could see, the histogram shows that it has a poor contrast which is evident in the image seen. And also, some details are not conducive for human eyes

These are all the images in the following order: original, histogram equalized, stretched histogram, desired cdf)

I also used an image from mathworks.com

I would like to thank Eduardo David for the faster way of getting the histogram and cumulative some. Also for Rafael Jaculbia for some help in the understanding of CDF. I would rate my self 10 out 10 for this activity since I have successfully transformed my image to match the CDF that we want. I want to still try many other CDF but it would take so much of time and space.

image source:http://www.mathworks.com/access/helpdesk/help/toolbox/images/index.html?/access/helpdesk/help/toolbox/images/imadjust.html

Activity 3 – Image types and basic image enhancement

These are the information of the images above given by the command imfinfo in scilab.

Binary Image	Grayscale Image
FileName: binary.png	FileName: grayscale.png
FileSize: 2660	FileSize: 90505
Format: PNG	Format: PNG
Width: 200	Width: 420
Height: 140	Height: 320
Depth: 8	Depth: 8
StorageType: indexed	StorageType: indexed
NumberOfColors: 2	NumberOfColors: 256
ResolutionUnit: centimeter	ResolutionUnit: centimeter
XResolution: 72.000000	XResolution: 72.000000
YResolution: 72.000000	YResolution: 72.000000

Indexed Image	Truecolor Image
FileName: indexed.png	FileName: truecolor.jpg
FileSize: 25576	FileSize: 4812
Format: PNG	Format: JPEG
Width: 150	Width: 104
Height: 200	Height: 145
Depth: 8	Depth: 8
StorageType: indexed	StorageType: truecolor
NumberOfColors: 256	NumberOfColors: 0
ResolutionUnit: centimeter	ResolutionUnit: centimeter
XResolution: 72.000000	XResolution: 72.000000
YResolution: 72.000000	YResolution: 72.000000

FileSize: 46050

Format: JPEG

Width: 179

Height: 274

Depth: 8

StorageType: indexed

NumberOfColors: 256

ResolutionUnit: inch

XResolution: 96.000000

YResolution: 96.000000

The histogram of my scanned image is shown below. It can be seen that the histogram is quite spread meaning that the image has a good contrast. Also, we see that the image is well separated from the background because we could see a valley. Thank you for Jeric Pineda and Eduardo David for the help with the scilab code.

The scanned image is converted to a binary image by the command im2bw in scilab. We used the program we made in the previous activity and calculate the area of our scanned image. I also used paint to estimate the area of my scanned image.

Using the program made during the previous activity that uses Green’s theorem we obtained an area of 40376 square pixels. Using paint I estimated the area to be 40320 square pixels. Since my image is almost a perfect rectangle I just multiplied the length (252 pixels) by the width (160 pixels) to approximate the area of the scanned image. We see that the calculated area’s are almost the same which means that our method for computing the area using Green’s theorem is applicable.

I rate myself 10 out of 10 since I have successfully plotted the histogram of my scanned grayscale image and I have shown that the calculated area using Green’s theorem is close, if not equal, to the actual pixel area of the scanned image.

Colaborators: Eduardo David, Jeric Pineda, Rafael Jaculbia\

Sources of Image:

binary:http://en.wikipedia.org/wiki/Binary_image

grayscale:http://weblogs.java.net/blog/kirillcool/archive/2007/04/non_photorealis_1.html

indexed:http://en.wikipedia.org/wiki/Indexed_color

Area Estimation

For this activity we used scilab with siptoolbox to read images we have drawn.
The dimensions of the drawn images are known.
I have drawn the following images which are shown above:
Square(side = 214 pixels)
Circle(diameter = 157 pixels)
Triangle(base = height = 214)
Rectangle(118 pixels * 158 pixels)

Using the imread function, an image is converted to a binary matrix. Then using the follow function, the coordinates of the borders were obtained. Using the green's formula we could approximate the area of the image. Green's formula is shown above.
The code in scilab is shown below.

------------------------------------------------------------------------------------------------
A=imread('name of file');
[x,y]=follow(A);
x1=x;
y1=y;
x1(1)=x(size(x,'r'));
x1(2:size(x,'r'))=x(1:(size(x,'r')-1));
y1(1)=y(size(y,'r'));
y1(2:size(y,'r'))=y(1:(size(y,'r')-1));
X=x.*y1;
Y=y.*x1;
Area=0.5*(sum(X)-sum(Y))
------------------------------------------------------------------------------------------------

Calculated by Green's equation Calculated Using Dimensions %error
(pixel*pixel) (pixel*pixel)
Square 45796 45796 0
Circle 19508 19359 0.769667855
Triangle 22684.5 22898 0.932395842
Rectangle 18644 18644 0


Collaborators: Rafael Jaculbia, Eduardo David

I rate myself 10 out of 10 since I have successfully used Green's formula to estimate the area of the images and compared it to the areas calculated using the formulas for area of basic shapes. It is seen that there are no error's in square and rectangle shapes. This is because the pixels fit perfectly to the shapes since they are squares. Perfect circles, on the other hand, cannot be created through pixels. This is also true for shapes with diagonals like the triangle.

Activity 1

These are the data that I have gathered in the activity. I would rate myself 10 in reconstructing the graph since I have successfully overlapped my graph to the scanned graph. Also, I have done the necessary steps in order to calculate the pixels per unit of both the x-axis and the y-axis. Using this conversion I can convert the number of units(pixels) by multiplying(dividing) the number of pixels(units) obtained.

x(pixel location)	y(pixel location)	y-axis	pixel between ticks
67	506	0
67	443	100	63
67	380	200	63
66	317	300	63
66	255	400	62
66	186	500	69
65	130	600	56
65	67	700	63
		average	62.71428571
		pixels per unit	0.627142857
x(pixel location)	y(pixel location)	x-axis	pixel between ticks
67	506	0
98	506	5	31
129	506	10	31
160	506	15	31
191	506	20	31
		average	31
		pixels per unit	6.2
Origin(pixel location)	67	506
x pixels per unit	6.2
y pixels per unit	0.627142857
x(pixel location)	y(pixel location)	x pixels from origin	y pixels from origin	x equivalent unit	y equivalent unit
93	406	26	100	4.193548387	159.453303
117	307	50	199	8.064516129	317.3120729
134	266	67	240	10.80645161	382.6879271
177	186	110	320	17.74193548	510.2505695
177	60	110	446	17.74193548	711.1617312
83	443	16	63	2.580645161	100.4555809
83	443	16	63	2.580645161	100.4555809
99	386	32	120	5.161290323	191.3439636
115	324	48	182	7.741935484	290.2050114
131	276	64	230	10.32258065	366.7425968
147	239	80	267	12.90322581	425.7403189
163	208	96	298	15.48387097	475.1708428
177	161	110	345	17.74193548	550.1138952
177	136	110	370	17.74193548	589.977221
177	111	110	395	17.74193548	629.8405467
177	86	110	420	17.74193548	669.7038724