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

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

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PNGpng FT_Loc1_nocut.png r1 manage 1203.7 K 01 Dec 2015 - 16:33 DavidHadden  
PNGpng Floodfill_original.png r1 manage 87.8 K 01 Dec 2015 - 11:47 DavidHadden  
PNGpng IFT_Loc1_bkgcut.png r1 manage 49.6 K 01 Dec 2015 - 16:33 DavidHadden  
PNGpng IFT_Loc1_starcut.png r1 manage 1317.4 K 01 Dec 2015 - 16:33 DavidHadden  
PNGpng center_improved.png r1 manage 68.5 K 01 Dec 2015 - 13:34 ElenaCukanovaite  
PNGpng floodfill_imrpoved.png r1 manage 37.8 K 01 Dec 2015 - 13:14 ElenaCukanovaite  
PNGpng interesting_stars.png r1 manage 62.2 K 01 Dec 2015 - 13:38 ElenaCukanovaite  
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Topic revision: r6 - 01 Dec 2015 - ElenaCukanovaite

 
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