A10 - Morphological Operations

A9 - ColorImage Segmentation

A8 - Enhancement in the Frequency Domain

A7 - Fourier Transform Model of Image Formation

A6 - Enhancement by Histogram Manipulation

A5 - Area Estimation for Images with Defined Edges

    Green's Theorem is a very useful way to compute areas ( or perimeters) of regions if one or the other is known. Supposing we have region R similar to the one shown in the Figure below

If we  take the counterclockwise direction to be the positive one then Green's theorem is given by

If we take C to be the collection of points in the boundary of R , choosing F1 = 0 and F2 = x gives us the equation below each relating a closed line integral to the area of R

Adding the two equations and averaging, we get

Which written in summation form and setting Nb to be t he number of pixels in the boundary of R then we have

I first created a circle of radius 0.7 using a code similar to the one I used in the Activity Scilab basics

stacksize(100000000);
nx = 500; //defines the number of elements along x and \y
ny = 500;
x = linspace(-1,1,nx);//defines the range
y = linspace(-1,1,ny);
[X,Y] = ndgrid(x,y);//creates two 2-D arrays of xand y coordinates
r = sqrt(X.^2 + Y.^2);//note element-per-elementsquaring of X and Y
A = zeros(nx,ny);
A(find(r<0.701)) = 1;
imshow(A);

with theoretical area pi*.7^2 = 1.53938

using the code 

nx = 500; ny = 500; //defines the number of elements along x and y

x = linspace(-1,1,nx); //defines the range

y = linspace(-1,1,ny);

[X,Y] = ndgrid(x,y); //creates two 2-D arrays of xand y coordinates

r= 0.401; // side of the square

S = zeros (nx,ny);

S (find (abs(X)<r & abs (Y)<r))=1;

imshow(S);

to form a square of side .4 with theoretical area .16

A4 - Image Types and Formats

This activity entailed the familiarization of different image types and formats

A.) Image Types

1.) Binary Images

Binary Images are black and white images with pixel values 0 OR 1. This means that one pixel is one bit. Fonts/text, fingerprints, particle tracks and signatures are some images whose information can be adequately saved in binary form

Using the info = imfinfo(filename) function of Scilab I got the properties :

Filename: C:\Users\Vyke\Desktop\Activity 4\ablackandwhite.png  

FileSize:    19827. 

Width:    800. 

Height: 771. 

BitDepth   8         

ColorType:truecolor

2.) Grayscale Images

Grayscale images

Grayscale images are images that are black AND white with each pixel (picture element) having a value that ranges from 0 to 256 with 0 being pure black and 256 pure white. Different values correspond to different intensities of “grayness” A value of 256 corresponds to the data stored in 8 bits or 1 Byte (2⁸). Graytone information similar to the ones found in x-rays and microscopic slides benefit greatly from grayscale images.

Filename:   C:\Users\Vyke\Desktop\Activity 4\audreygray.jpg

FileSize: 121635. 

Width:   420. 

Height: 563. 

BitDepth: 8         

ColorType :grayscale

3.) Truecolor Images

Truecolor images have pixels with three channels each of an intensity (that ranges from 0 to 256) of red, blue or green light. These channels are composed together to create other colors. Each pixel has 256³ possible colors. A lot of images come in truecolor form with a 256x256 pixel image having a size of 256 x 256 x 3 because each pixel has 3 channels each with 1 BYTE of memory.

Filename: C:\Users\Vyke\Desktop\Activity 4\audreytruecolor.jpg  

FileSize:    65180. 

Width: 430.

Height: 500.

BitDepth   8 .     

ColorType :truecolor

4.) Indexed Images

Indexed images are used when images with lesser detailed is needed, but that compensate with less memory (smaller data or color information) needed for the image. These images have two sets of data, the image itself, and its index, which are numbers that refer to colors in a color map. 

Filename: C:\Users\Vyke\Desktop\Activity 4\clownindex.png  

FileSize: 64993. 

Width:    560. 

Height: 420.

BitDepth   8 .     

ColorType :truecolor

5.) High dynamic range (HDR) images

Images of digital x-rays, plasma, nuclear explosions require more that regular 8 bits. The images are instead stored in 10 bits or 16 bits to achieve more detailed images.

Filename: C:\Users\Vyke\Desktop\Activity 4\hdr.jpg  

FileSize:  1472750. 

Width: 1920. 

Height: 1200.

BitDepth   8 .     

ColorType :truecolor

6.) Multi or Hyperspectral

Satelite images are examples of images that make use of more the 3 channels that correspond to the primary colors and instead have up to 100 channels (in the case of hyperspectral images).

Filename C:\Users\Vyke\Desktop\Activity 4\hyperspectral.jpg  

FileSize: 93967. 

Width: 432 

Height: 341

BitDepth   8 .     

ColorType :truecolor

7.) 3D Image

3D images are produced by either using: point clouds ( x,y,z) to store spatial data  or even several 2D cross sections piled on top of each other forming image stacks as in medical scans. These all generate the spatial properties integral to 3d images.

Filename : C:\Users\Vyke\Desktop\Activity 4\3d.jpg  

FileSize: 489617. 

Width: 800

Height: 548

BitDepth   8 .     

ColorType :truecolor

8.) Temporal images or Videos

These are images the move with time. 

B. Image Formats

Images can be saved under different formats to suite your needs. Images can be significantly reduced in size to cater to storage limits or can be saved to preserve quality.

Images in different file formats will have different properties. There are two ways images can be saved: lossy and lossless. Lossy compression techniques create very compressed files with some loss in image data. These create images that aren’t as detailed as the original ones but the changes are ignorable or irrelevant. Lossless compression maintains the original image data with no loss of data for every pixel. These are very important when even minute details of an image are important.

JPEG

JPEG stands for Joint Photographic Experts Group and are used particularly for photographic pictures. This is the standard format for images taken with digital cameras and for photographic images in general. JPEG formats utilize the lossy compression meaning that some of the original image information is not retained but are highly compact. This makes it very easy to edit and makes JPEG files extremely flexible. JPEG compresses files by retaining elements in an image that matter the most and capitalizes on image contrast to decide what details to keep. This therefore makes noisier images harder to compress that less noisier ones

TIFF

TIFF stands for Tagged Image File Format and is widely used in printing and publishing. There make use of lossless compression techniques keeping images more detailed but at the same time making them bigger in size. Multiply layered images can easily stored in one TIFF. They are excellent for images that need to be kept first and archived.

GIF

GIF stands for Graphics Interchange Format and are images that can produce moving images by displaying images sequentially. GIF images produce images that are not as detailed as original ones because 256 colors are maintained from an image with originally a lot more. GIF images load segment-by-segment using interlacing. Images stored in GIF are optimal for logos graphs and other images where color detail in unimportant but transparency is. GIF supports transparency.

PNG

PNG stands for Portable Network Graphics and are an excellent substitute to GIF images. PNG can compress images 5% to 25% more than in GIFs and support variable transparency. This means users can decide on how transparent an image can be but whose drawback are inconsistencies in displaying transparency depending on the browser. PNG utilizes 2D interlacing making them load twice as fast as GIF images.

SVG

SVG or Scalable Vector graphics allows very good quality graphics and animation that retain detail even when increasing the size of the image. This can create images that looks the same whether it’s the size of a small icon or scaled to fit a huge monitor. SVG can be applied to still images and moving ones.

C.

Choosing the image I used as an example for a truecolor image, A truecolor picture of Audrey Hepburn, I will demonstrate the SIVP functions by turning it to a grayscale image and to a black and white image.

Using the code

im = imread('C:\Users\Vyke\Desktop\Activity 4\audreytruecolor.jpg');
gim= rgb2gray(im);
imshow(gim)

I successfully turned into a grayscale image

using the code snippet shown below:

im = imread('C:\Users\Vyke\Desktop\Activity 4\audreytruecolor.jpg');
bim= im2bw(im,0.4);
imshow(bim)

I turned it into a black and white image

References:

[1] "Activity 3: Image Types and Formats 2010", Dr. Maricor Soriano

[2]http://www.cambridgeincolour.com/tutorials/imagetypes.htm

[3] http://www.practicalecommerce.com/articles/1821-Image-Formats-What-s-the-Difference-Between-JPG-GIF-PNG-

A3 - Scilab Basics

This activity capitalizes on Scilab's relative ease in operating with matrices.

Using the code :

nx = 100; ny = 100; //defines the number ofelements along x and y

x = linspace(-1,1,nx); //defines the range
y = linspace(-1,1,ny);
[X,Y] = ndgrid(x,y); //creates two 2-D arrays of xand y coordinates
r= sqrt(X.^2 + Y.^2); //note element-per-elementsquaring of X and Y
A = zeros (nx,ny);
A (find(r<0.7) ) = 1;
f = scf();
grayplot(x,y,A);
f.color_map = graycolormap(32);

given by Ma'm Jing to create a circular aperture we were tasked to study it and use it to create 

different images. 

                                                            Fig 1. Centered circular aperture

The first image that was easiest to recreate was the annulus which is like two 

concentric circles centered at the middle. I merely gave the region, with radii between 0.4 and 0.7,  in    the range [-1,1] in both axes, a value of 1 using the code shown below.

nx = 100; ny = 100; //defines the number ofelements along x and y
x = linspace(-1,1,nx); //defines the range
y = linspace(-1,1,ny);
[X,Y] = ndgrid(x,y); //creates two 2-D arrays of xand y coordinates
r= sqrt(X.^2 + Y.^2); //note element-per-elementsquaring of X and Y
A = zeros (nx,ny);
A (find(r<0.7 &  r >0.4) ) = 1;// portion between circles of radii 0.4 and 0.7 is given a value of 1
f = scf();
grayplot(x,y,A);
f.color_map = graycolormap(32);
this results in the image shown below. 



Fig 2. Annulus with black center

Another annulus can be created by switching the values of A making the default value 1 instead of  an array of 0's using the below code,
nx = 100 ; ny =1 00; //defines the number of elements along x and y
x = linspace(-1,1,nx);//defines the range
y = linspace(-1,1,ny);
[X,Y] = ndgrid(x,y);//creates two 2-D arrays of x and y coordinates
r= sqrt(X.^2 + Y.^2)//note element-per-elementsquaring of X and Y
A = ones (nx,ny);// made 1
A (find(r< 0.7 & r >0.4)) = 0;// portion between circles of radii 0.4 and 0.7 is gibven a value of 0
f = scf ();
grayplot(x,y,A);
f.color_map = graycolormap(32);


This gives an aperture with a white center as shown below. 
                                    

    Fig 3. Annulus with white center

The next image that was easiest to create is the square centered at the middle. Using the code shown below where I defined the side of the square to be r with a length of 0.4 I was able to accurately derive such a square.

nx = 100; ny = 100; //defines the number of elements along x and y
x = linspace(-1,1,nx); //defines the range
y = linspace(-1,1,ny);
[X,Y] = ndgrid(x,y); //creates two 2-D arrays of xand y coordinates
r= 0.4; // side of the square
A = zeros (nx,ny);
A (find (abs(X)<r & abs (Y)<r))=1;
f = scf();
grayplot(x,y,A);
f.color_map = graycolormap(32);

                                                Fig 4. White square aperture centered in the middle

The corrugated roof or the sinusoid along the x axis was the next image I created. I used the 

da = gda() default function and x_label.text  to label the x  in order to show that the sinusoid is indeed oriented along the x-axis. I also made the x-axis range from -1 to 2.

nx = 100 ; ny =100; //defines the number of elements along x and y
x = linspace(-1,2,nx);//defines the range. Note that x ranges from -1 to 2 and y ranges from -1 to 1
y = linspace(-1,1,ny);
[X,Y] = ndgrid(x,y);//creates two 2-D arrays of x and y coordinates

da=gda()
da.x_label.text="x";// label for x axis

A = sin(X.*%pi*7);
f = scf ();
grayplot(x,y,A);
f.color_map = graycolormap(32);

The image is shown here, 


                                         Fig 5. Sinusoid along the x-axis forming a corrugated roof

The next image I created was the circular aperture with graded transparency (gaussian transparency). Using the definition of the Gaussian

nx = 100; ny = 100; //defines the number ofelements along x and y
x = linspace(-1,1,nx); //defines the range
y = linspace(-1,1,ny);
[X,Y] = ndgrid(x,y); //creates two 2-D arrays of xand y coordinates
r= sqrt(X.^2 + Y.^2); //note element-per-elementsquaring of X and Y
A = zeros (nx,ny);
A = (exp(-r) ) ;// using definition of Guassian 
f = scf();
grayplot(x,y,A);
f.color_map = graycolormap(32);


                                                 Fig 6.  Gaussian transparent circular aperture
The last image I was able to create was the grating along the x-axis. I used the for loop to set all 
columns of A which are multiples of 10 to have a value of 1 yielding 10 gratings for the 100 elements in the x axis. 

nx = 100; ny = 100; //defines the number ofelements along x and y
x = linspace(-1,2,nx); //defines the range
y = linspace(-1,1,ny);
[X,Y] = ndgrid(x,y); //creates two 2-D arrays of xand y coordinates



da=gda()
da.x_label.text="x";// label for x axis

; // for x and y axes labels
A = zeros (nx,ny);
for r = 1:10:nx
    A(:,r)= 1
    end

f = scf();
grayplot(x,y,A);
f.color_map = graycolormap(32);

This gave me the image with 10 gray gratings across the x-axis. I used the x.label.text 
to properly identify the x from the y axis. I also made the range of x from -1 to 2 to differentiate it from
 the y axis.  This is seen in the image below 

                                                                      Fig 6. Gratings across the x-axis

Honestly, I think I deserve a perfect 10/10 because  I did everything that was asked and I properly labelled all pictures ( they can stand alone) and adequately explained my rationale.