20151201MSciPhotometryAnalysisOb1part3 < Public < RHUL Physics Department TWiki

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:

Found an interesting structure:

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 and are the x and y coordinates of the individual pixels of the star and is the pixel value of the pixel, and is the total number of pixels of a given star.
An example of a found star center is shown below:

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:

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:

Below are more examples:

If one takes a single mode over the entire image:

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.

This shows an attempt at removing the background from the image.

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.

-- ElenaCukanovaite - 01 Dec 2015

Attachments

Topic attachments
I	Attachment	History	Action	Size	Date	Who
png	Floodfill_original.png	r1	manage	87.8 K	01 Dec 2015 - 11:47	DavidHadden
png	floodfill_imrpoved.png	r1	manage	37.8 K	01 Dec 2015 - 13:14	ElenaCukanovaite
png	center_improved.png	r1	manage	68.5 K	01 Dec 2015 - 13:34	ElenaCukanovaite
png	interesting_stars.png	r1	manage	62.2 K	01 Dec 2015 - 13:38	ElenaCukanovaite
png	FT_Loc1_nocut.png	r1	manage	1203.7 K	01 Dec 2015 - 16:33	DavidHadden
png	IFT_Loc1_bkgcut.png	r1	manage	49.6 K	01 Dec 2015 - 16:33	DavidHadden
png	IFT_Loc1_starcut.png	r1	manage	1317.4 K	01 Dec 2015 - 16:33	DavidHadden
png	Stacking_ap_6.png	r1	manage	42.2 K	01 Dec 2015 - 17:09	DavidHadden
png	l1_quadrants_copy.png	r1	manage	969.8 K	01 Dec 2015 - 22:42	ElenaCukanovaite
png	full.png	r1	manage	45.7 K	01 Dec 2015 - 22:43	ElenaCukanovaite
png	85_by_85.png	r1	manage	63.8 K	01 Dec 2015 - 22:44	ElenaCukanovaite
png	30_by_30.png	r1	manage	52.9 K	01 Dec 2015 - 22:45	ElenaCukanovaite
png	17_by_17.png	r1	manage	50.6 K	01 Dec 2015 - 22:46	ElenaCukanovaite
png	1_by_1.png	r1	manage	48.7 K	01 Dec 2015 - 22:47	ElenaCukanovaite

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Topic revision: r9 - 02 Dec 2015 - DavidHadden

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