Floodfill algorithm improvements

  • To improve our algorithm we defined a star to be anything above 5 pixels in size.
  • It seems that all hot pixels were removed:
Floodfill_original.png

floodfill_imrpoved.png

  • Found an interesting structure:
interesting_stars.png
  • To improve center founding, we found x and y weighted averages, such that:
 \begin{equation} x_{\rm center} = \frac{\sum_{i = 1}^N x_i p_i}{\sum_{i=1}^N p_i}\end{equation}  \begin{equation} y_{\rm center} = \frac{\sum_{i = 1}^N y_i p_i}{\sum_{i=1}^N p_i}\end{equation}
  • where $x_{\rm center}$ and $y_{\rm center}$ are the x,y centers and $x_i$ and $y_i$ are the x and y coordinates of the individual pixels of the star and $p_i$ is the pixel value of the pixel, and $N$ is the total number of pixels of a given star.
  • An example of a found star center is shown below:
center_improved.png
  • The standard deviations were found using the following equations:
 \begin{equation} \sigma_x = \sqrt{\frac{\sum_{i = 1}^N (x_i - x_{\rm center})^2 p_i}{\sum_{i=1}^N p_i}}\end{equation}  \begin{equation} \sigma_y = \sqrt{\frac{\sum_{i = 1}^N (y_i - y_{\rm center})^2p_i}{\sum_{i=1}^N p_i}}\end{equation}  <br />

  • where $\sigma_x$ and $\sigma_y$ are the standard deviations in x and y.
  • Some information about found sigmas for all stars in this image:
  Minimum value Maximum Value Average Value
$\sigma_x$ 0.58 4.96 2.42
$\sigma_y$ 0.44 4.34 2.24

A different way to estimate the mode

  • Building on what we did last week, instead of just splitting the image array into 4 separate arrays and finding the mode in each new array, we allowed for an arbitrary number of arrays that the main array can be split into.
  • A 2 by 2 splitting would be the following:
l1_quadrants_copy.png
  • If one splits the main image into as many arrays as there are elements in the original image, one would expect to get the original image back. This can be seen below:
full.png
  • Below are more examples:
85_by_85.png

30_by_30.png

17_by_17.png

  • If one takes a single mode over the entire image:
1_by_1.png

2D Fourier Transforms

  • Fourier transforms of such a star field will give regions in k space for both background and stars.
  • One of these can then be removed, leaving just stars or the background upon inverse Fourier transforming.
  • Initial attempts of this can be seen below.

  • This shows a location 1 image, with its background now clustered around the edges.
FT_Loc1_nocut.png
  • This shows an attempt at removing the background from the image.
IFT_Loc1_bkgcut.png
  • This shows an attempt at removing the stars from the image. Note the image is logged, in order to better see the remnants of the stars.

IFT_Loc1_starcut.png

-- ElenaCukanovaite - 01 Dec 2015

Topic attachments
I Attachment Action Size Date Who Comment
PNGpng 17_by_17.png manage 50.6 K 01 Dec 2015 - 22:46 ElenaCukanovaite  
PNGpng 1_by_1.png manage 48.7 K 01 Dec 2015 - 22:47 ElenaCukanovaite  
PNGpng 30_by_30.png manage 52.9 K 01 Dec 2015 - 22:45 ElenaCukanovaite  
PNGpng 85_by_85.png manage 63.8 K 01 Dec 2015 - 22:44 ElenaCukanovaite  
PNGpng FT_Loc1_nocut.png manage 1203.7 K 01 Dec 2015 - 16:33 DavidHadden  
PNGpng Floodfill_original.png manage 87.8 K 01 Dec 2015 - 11:47 DavidHadden  
PNGpng IFT_Loc1_bkgcut.png manage 49.6 K 01 Dec 2015 - 16:33 DavidHadden  
PNGpng IFT_Loc1_starcut.png manage 1317.4 K 01 Dec 2015 - 16:33 DavidHadden  
PNGpng Stacking_ap_6.png manage 42.2 K 01 Dec 2015 - 17:09 DavidHadden  
PNGpng center_improved.png manage 68.5 K 01 Dec 2015 - 13:34 ElenaCukanovaite  
PNGpng floodfill_imrpoved.png manage 37.8 K 01 Dec 2015 - 13:14 ElenaCukanovaite  
PNGpng full.png manage 45.7 K 01 Dec 2015 - 22:43 ElenaCukanovaite  
PNGpng interesting_stars.png manage 62.2 K 01 Dec 2015 - 13:38 ElenaCukanovaite  
PNGpng l1_quadrants_copy.png manage 969.8 K 01 Dec 2015 - 22:42 ElenaCukanovaite  

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Topic revision: r9 - 02 Dec 2015 - DavidHadden

 
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