Assessed  Lab  2:  Image  analysis  Due:  5pm  Monday,  6  May  2013    In  many   fields   there   is   a  need   to   automate   the  often   tedious   task  of   extracting  information   from   images.   For   example,   counting   cells   on   a   microscope   image,  identifying  geological  features  in  geomagnetic  data  images.  Here  we  will  write  a  small  program  to  count  the  number  of  stars  in  a  light  telescope  image.  However,  before   we   get   going   we   will   do   some   practice   tasks   in   manipulating   and  interrogating   large  matrices,   as   image   files   are   really   just   data   stored   in   large  matrices.    Task  1:  Matrix  interrogation    Write  a  single  function  that  takes  in  a  square  integer  matrix  A  and  the  scalars  N  and  G,  as  well  as  a  2-­‐value  vector  R  indicating  the  inclusive  range  [R(1),  R(2)]  as  inputs.  The  function  should  return  as  an  output:  

A1:  the  value  of  the  largest  element  in  the  matrix  (1  mark)  A2:  the  average  of  the  elements  in  the  Nth  column    (2  mark)  A3:  the  value  of  the  most  frequently  occurring  number    (2  marks)  A4:  the  number  of  elements  within  a  specified  range  R,  inclusive  of  the  

edge  values    (3  marks)  A5:  a  Mx2  matrix,  with  each  row  containing  two  elements  to  represent  the  

indicial  position  (i.e.  row  number,  column  number)  of  each  appearance  of  the  number  G.    (4  marks)    function [A1,A2,A3,A4,A5] = LAB2_Task1(A, N, G, R)  Upload function file LAB2_Task1.m to cssubmit.  Note,  in  this  task  you  will  need  to  create  your  own  square  integer  matrix  to  test  your   code.   The   function   randi may be useful for this. For example, randi([5,30],5) will give a 5x5 matrix of uniformly distributed random integers between 5 and 30 (see below)   >>A=randi([5,30],5) A = 27 18 16 26 22 16 13 19 10 17 19 21 30 7 18 19 22 20 29 22 6 21 22 9 8              

Task  2:  Automate  star  count  through  image  processing  (8  marks)    

   The  main  idea  here  is  that  each  pixel  in  an  image  is  an  element  in  a  matrix.  In  a  greyscale  image  each  pixel  has  a  value  ranging  from  black  =0  to  white  =  255.  Here  we  count  a  pixel  as  being  a  star  if  its  value  exceeds  a  threshold  level  (as  there  is  always  background  noise  in  a  signal).  We  are  then  seeking  to  count  the  number  of  matrix  elements  with  a  value  exceeding  a  threshold  and  using  that  number  as  a  estimate  of  the  number  of  stars  in  the  image.  Depending  on  the  threshold  value  used  you  will  likely  get  a  different  estimate  for  the  number  of  stars.    Perform  the  following  steps  in  a  script  file:  

1. Import  the  RGB  image  file  ‘stars.png’  shown  above  using  the  Matlab  image  import  function  imread('image_name.ext') and assign the imported image to a variable name. Note this image file will need to be first saved in your Matlab directory.

2. Convert  the  image  from  a  RGB  image  to  greyscale  using  the  Matlab  function  rgb2gray() and again assign it to a variable name.

3. Show image using command: figure,imshow(‘greyscale_image_variable_name’)

4. Write a command to find the value of largest element in the data file and give it the variable name big

5. Choose a star detection threshold between 0 and 1 and call it threshold 6. Sort through the image data matrix and set values to 0 if they fall below

threshold*big and 1 if they are >=threshold*big. Save this ‘filtered’ black and white image data as a new matrix i.e. assign the filtered

image data to a new variable. 7. Use the imshow command again (as in step 3) to show the filtered image.

figure(2),imshow(‘filtered_image_variable_name’)

The human eye + brain is a very good image processor. Comparing the images in step 7 and step 3 try to estimate the value of threshold in which the filtered image best represents the original image in terms of detecting the right number of stars? For example, when threshold =1 the filtered image is black (no pixels are counted as stars), when threshold =0, the image is white (all pixels treated as stars), so your estimate should be between 0 and 1.

8. Copy and paste the Matlab commands relating to steps 5 and 6 to below the command in your script file used for step 7 (above).

9. Enclose these pasted commands within a for loop, and make the necessary changes so that you can then try (sweep) values of threshold from 0 to 1 in increments of 0.01, which we refer to as the threshold step.

10. For each value of threshold sum the number of data points (pixels) exceeding the detection threshold. This corresponds to a star count.

11. Plot threshold versus star count using Plot(x,y)  Does  the  number  of  stars  counted  surprise  you?    12. Write  a  function  file  called  Star_detection.m  to  carry  out  the  task  

described  in  steps  8  to  10  (do  not  include  the  plot  in  step  11  in  the  function  file).  Your  function  file  needs  to  be  written  so  that  it  can  take  an  image  filename  and  a  scalar  value  for  the  threshold  step  as  input,  convert  it  into  greyscale  image  and  returns  a  Mx2  matrix  as  an  output,  with  each  row  of  the  output  corresponding  to  a  [threshold,  star  count]  pair.    

 The  first  line  of  your  function  file  should  be  function [Count] = Star_detection(filename, step)  As  a  check,  you  should  be  able  to  call  this  function  file  in  Matlab  (i.e.  from  a  command  line  or  script  file)  to  get  the  same  output  as  step  11  e.g.      > count = Star_detection(‘stars.png’, 0.01) > plot(count(:,1), count(:,2))

Upload function file Star_detection.m to cssubmit.