Programming golden formula

"Make It Work, Make It Right, Make It Fast"

More is here.

PSNR (Peak Signal-to-Noise Ratio)

From http://www.debugmode.com/imagecmp/:

Compressing an image is significantly different than compressing raw binary data. Of course, general purpose compression programs can be used to compress images, but the result is less than optimal. This is because images have certain statistical properties which can be exploited by encoders specifically designed for them. Also, some of the finer details in the image can be sacrificed for the sake of saving a little more bandwidth or storage space. This also means that lossy compression techniques can be used in this area.

Lossless compression involves with compressing data which, when decompressed, will be an exact replica of the original data. This is the case when binary data such as executables, documents etc. are compressed. They need to be exactly reproduced when decompressed. On the other hand, images (and music too) need not be reproduced 'exactly'. An approximation of the original image is enough for most purposes, as long as the error between the original and the compressed image is tolerable.

Error Metrics

Two of the error metrics used to compare the various image compression techniques are the Mean Square Error (MSE) and the Peak Signal to Noise Ratio (PSNR). The MSE is the cumulative squared error between the compressed and the original image, whereas PSNR is a measure of the peak error. The mathematical formulas for the two are

MSE =

PSNR = 20 * log10 (255 / sqrt(MSE))

where I(x,y) is the original image, I'(x,y) is the approximated version (which is actually the decompressed image) and M,N are the dimensions of the images. A lower value for MSE means lesser error, and as seen from the inverse relation between the MSE and PSNR, this translates to a high value of PSNR. Logically, a higher value of PSNR is good because it means that the ratio of Signal to Noise is higher. Here, the 'signal' is the original image, and the 'noise' is the error in reconstruction. So, if you find a compression scheme having a lower MSE (and a high PSNR), you can recognize that it is a better one.

Matlab: Mandelbrot set

Recently I read article on Free Software Magazine titled Generating cool fractals. I was very pleased to find source code for generation of Mandelbrot set.
function mandelFrac
% MATLAB and Octave code to generate
%a Mandelbrot fractal

% Number of points in side of image and
% number of iterations in the Mandelbrot
% fractal calculation
npts=1000;
niter=51;
% Generating z = 0 (real and
% imaginary part)
zRe=zeros(npts,npts);
zIm=zeros(npts,npts);
% Generating the constant k (real and
% imaginary part)
kRe=repmat(linspace(-1.5,0.5,npts),npts,1);
kIm=repmat(linspace(-1,1,npts)',1,npts);

% Iterating
for j=1:niter
% Calculating q = z*z + k in complex space
% q is a temporary variable to store the result
qRe=zRe.*zRe-zIm.*zIm+kRe;
qIm=2.*zRe.*zIm+kIm;
% Assigning the q values to z constraining between
% -5 and 5 to avoid numerical divergences
zRe=qRe;
qgtfive= find(qRe > 5.);
zRe(qgtfive)=5.;
qltmfive=find(qRe<-5.);
zRe(qltmfive)=-5.;
zIm=qIm;
hgtfive=find(qIm>5.);
zIm(hgtfive)=5.;
hltmfive=find(qIm<-5.);
zIm(hltmfive)=-5.;
end

% Lines below this one are commented out when making
% the benchmark.

% Generating plot
% Generating the image to plot
ima=log( sqrt(zRe.*zRe+zIm.*zIm) + 1);
% Plotting the image
imagesc(ima);


Lenne picture

The original photo of famous Lenna picture which is found in many papers and books conserning image processing:-)

Ruby: Tk, select directory

Just quick code for selecting input/output directory#!/usr/bin/env ruby
require 'tk'
bdir=Tk.chooseDirectory('initialdir'=>'./')
puts bdir

Below an example that takes a directory and lists all txt files that contain string '_data' in their name. Than contents of each such file is copied to one output file ('allData.txt'):#!/usr/bin/env ruby
require 'tk'

bdir=Tk.chooseDirectory('initialdir'=>'./')

fout= open('allData.txt', 'w')

Dir.foreach(bdir) { |x|
next if x !~ /_data/
fpath=bdir+'/'+x
File.open(fpath).each_line {|l| fout << l}
}
fout.close


Excel: Visual Basic; mean value

Simple code in Microsoft VBA as a function in Excel. This function takes a range (x) and calculates mean value of the number lower than 0.
Function mymeanLr(x)
n = x.Count
ReDim xx(n + 1)
Dim ind As Integer
ind = 0
For i = 1 To n
If x(i) < 0 Then
xx(i - 1) = x(i)
ind = ind + 1
End If
Next i
mymeanLr = WorksheetFunction.Average(xx)
End Function


bash: use sed and awk to calculate an awarage value in the file

#!/bin/bash
FD=`cat $1 | sed -e 's/^[0-9.]*//g' -e 's/^\t//g' -e 's/^M$//g' \
| awk '{for (i=1; i<=NF; i++) s=s+$i}; END{print s/9/12}'`
echo $1 $FD
The script calculates avarage of values in a txt without values from the first column.
Example txt file:0 2.7792 2.7876 2.8023 2.8248 2.8413 2.8551 2.8679 2.8593 2.8537
18.281 2.7619 2.7723 2.7864 2.7888 2.8105 2.8314 2.8697 2.8695 2.8615
26.719 2.749 2.7464 2.7622 2.7811 2.8145 2.8276 2.8359 2.8438 2.8482
45 2.7596 2.7601 2.7614 2.779 2.803 2.803 2.8207 2.8391 2.8374
63.281 2.778 2.7809 2.8013 2.8071 2.8408 2.8423 2.8478 2.8514 2.826
71.719 2.7871 2.7927 2.8171 2.819 2.8366 2.8581 2.876 2.8826 2.8648
90 2.8007 2.8038 2.8219 2.8371 2.851 2.8628 2.8683 2.879 2.8719
108.28 2.781 2.7835 2.7901 2.7982 2.8214 2.8314 2.8488 2.852 2.8416
116.72 2.7731 2.7749 2.7784 2.7852 2.8077 2.8155 2.8226 2.8274 2.832
135 2.7744 2.7826 2.7854 2.7998 2.8153 2.8154 2.8358 2.8627 2.8775
153.28 2.7866 2.8011 2.8079 2.8253 2.8517 2.862 2.8727 2.8728 2.8644
161.72 2.7906 2.8071 2.8278 2.8424 2.8674 2.8679 2.8709 2.8716 2.8635


Ruby: reading Microsoft/OpenOffice spreadsheets

Reading of Excel files (*.xls) can be done using roo package for Ruby.One function that I write for myself was function that reads Excel file (fragment seen on the below picture) to a Hash table, where first column (image file name) is a key. Moreover, a key is only base name of the file,i.e., no extension. The line #(1) is very interesting, as I found out that roo reads x-rays in a way that each character is separated by '0'. Thus, to get correct String, it is necessary to remove zeros from the string. This is I think due to encoding shame. Excel uses Unicode 16, instead of ASCI; hence, each character is represented by two bites: firt byte is a character, and the second byte is '0'. Hence, to read the file name to ASCI, it is necessary to skip ever second byte. It must be done, because otherwise gsub does not want to work.


def readExcelToHash f
oo = Excel.new(f)
oo.default_sheet = 1
xcl=Hash.new
0.upto(oo.last_row) { |line|
r=oo.row(line)
next if r[0].to_s.length==0
rs= String.new r[0].to_s
a=String.new
rs.each_byte{|x| a+= x.chr if x!=0} #(1)
next if rs =~ /^#/
xcl[a.gsub(/\.tif+$/,'')]=r
}
xcl
end
As far as creating spreadsheets is concerned, roo does not provide this functionality.

Noise and blur effect on the image

Adding noise to an image adds hight frequency components to it. High frequency components are those that are responsible for image sharpness, i.e., pixel to pixel distances. In other words, the smallest components of the image like edges. On the other hand, blur removes high frequency components from the image. Bellow, the picture presents image (left column) and its Fourier transforms (right column).



P.S
Above Fourier transforms were calculated using free ImageJ software.

Ruby: Plotting with gnuplot in Mac X

To plot in Ruby, one can use rgplot interface to gnuplot. To install it, just download gnuplot-gem and install bysudo gem install ./gnuplot-2.2.gem
If you have gnuplot already installed it is good, if not install it bysudo port install gnuplot.
Assuming that everything went well, one can now plot and save figures using Ruby.
Simple example of Ruby code that plots simple data and saves (do not display) it to png file.
#!/usr/bin/env ruby
#testGnuplot.rb
require 'rubygems'
require 'gnuplot'



outFname='graph.png'
xData=[1, 2, 3, 4,5]
yData=[2, 3 ,4, 2,3]

#xData=(0..10).collect { |v| v.to_f }
#yData= xData.collect { |v| v ** 2 }



Gnuplot.open do |gp|
Gnuplot::Plot.new( gp ) do |plot|
plot.output outFname
plot.terminal 'png'
plot.title "Array Plot Example"
plot.ylabel "y"
plot.xlabel "x"

x= xData
y= yData

plot.data << Gnuplot::DataSet.new( [x, y] ) do |ds|
ds.with = "linespoints"
ds.notitle
end

end
end

This is especially useful when one want to plot a lot of figures contained in a data file. Of corese, this is the simples example, and more complicated things require to do some experimenting before desired plots are obtained. Nonetheless, this is good start.


To plot two data on one graph and to save it as png one can do as below:

#!/usr/bin/env ruby
#test.rb
require 'rubygems'
require 'gnuplot'
outFname='graph.png'
xData=[1, 2, 3, 4,5]
yData=[2, 3 ,4, 2,3]
yData2=[1, 2 ,3, 3,4]

Gnuplot.open do |gp|
Gnuplot::Plot.new( gp ) do |plot|
plot.output outFname
plot.terminal 'png'
plot.title "Array Plot Example"
plot.ylabel "y"
plot.xlabel "x"

x= xData
y= yData

plot.data =[ Gnuplot::DataSet.new( [x, y] ) do |ds|
ds.with = "linespoints"
ds.notitle
end,
Gnuplot::DataSet.new( [xData, yData2] ) do |ds|
ds.with = "linespoints"
ds.notitle
end
]

end

end

Results is (graph.png):