1/02/2013

Matlab dimension change function -> reshape

Useful function ~ ^^

A = magic(3)

A =
     8     1     6
     3     5     7
     4     9     2

>> B = reshape(A, 1, 3*3)

B =
     8     3     4     1     5     9     6     7     2


Image Normalization using Standard deviation - example source code

You can understand Standard deviation normalization, referenced on this web page.
http://www.d.umn.edu/~deoka001/Normalization.html
This web page introduce that..(wrote by Siddharth Deokar)

-------------------------------------------------------------------------
Normalization by Standard Deviation
We normalize the attribute values by using standard deviation.

For Example:

Consider 5 instances which has attribute A with the follwing values: {-5, 6, 9, 2, 4}

First we calculate the mean as follows:

Mean = (-5+6+9+2+4) / 5 = 3.2

Second, we subtract the mean from all the values and square them:

(-5-3.2)^2 = 67.24
(6-3.2)^2 = 7.84
(9-3.2)^2 = 33.64
(2-3.2)^2 = 1.44
(4-3.2)^2 = 0.64

Then we find the deviation as follows:

Deviation = sqrt ((67.24 + 7.84 + 33.64 + 1.44 + 0.64) / 5) = 4.71

Now we normalize the attribute values:

x => (x - Mean) / Deviation

-5 => (-5 - 3.2) / 4.71 = -1.74
6 => (6 - 3.2) / 4.71 = 0.59
9 => (9 - 3.2) / 4.71 = 1.23
2 => (2 - 3.2) / 4.71 = -0.25
4 => (4 - 3.2) / 4.71 = 0.17

-------------------------------------------------------------------------



This is sample source code:

//

int i,j,z;
 double sum=0; 
 double Mean;
 
 //sum, mean
 for(j=0; j< Height; ++j)
 {
  for(i=0; i< Width; ++i)
  {
   sum = sum + Pdata[i][j];
  }
 }

 Mean = sum/(Height*Width);
 
 //Deviation
 double dSum=0;
 double deviation;
 double std_dev; 
 
 for(j=0; j< Height; ++j)
 {
  for(i=0; i< Width; ++i)
  {        
   Pdata[i][j] = (Pdata[i][j] - Mean);

   dSum = dSum + (Pdata[i][j]*Pdata[i][j]);
  }
 }
 
 deviation = dSum / (Width*Height);
 std_dev = sqrt(deviation);
 
 //Normalization
 for(j=0; j< Height; ++j)
 {
  for(i=0; i< Width; ++i)
  {        
   Pdata[i][j] = (Pdata[i][j] / std_dev);
  }
 }