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Carsten Killer

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University of Greifswald

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PhD student in the field of colloidal (dusty) plasmas

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18 Feb 2014 Screenshot Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer image processing, signal processing, physics 63 29
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08 Jul 2014 Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer

@Adnan: I don't see any way in which Abel inversion would be related to your problem. You might want to consider some edge detection algorithm (Matlab offers plenty of them) to find the shape of the person in each frame.

07 Jul 2014 Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer

@Adnan: I am not sure what you mean with "finding changes". Of course, in different measurement images, the Abel inversion results of these images will probably differ as well. But please consider that the Abel inversion is only suited for a special situation, i.e. the investigation of symmetrical objects. Of course you can apply the Abel inversion code individually for each row or column, if your data is some kind of line-of-sight integrated measurement of a symmetrical object/system.
If the axis of symmetry is vertical, you have to consider the rows of your images. Please keep in mind that the axis of symmetry is at the start of your input vector (row) , i.e. the first element of the row vector corresponds to the center of your system r=0 and the last element corresponds the the edge, r=R.

07 Jul 2014 Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer

@Adnan Farooq: Could you maybe pose a more specific question? To summarize, this code takes your input F(y) and calculates the inverse Abel transform, resulting in the corresponding f(r). (using the standard notation, e.g. used in http://en.wikipedia.org/wiki/Abel_transform ).

Please note that this code only performs the calculation for one vector, i.e. one row (or column, depending on your systems's geometry) of your image. If you want to transform a complete 2D image, every row (or column...) has to be processed individually.

10 Jun 2014 Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer

@surya Narayan:
1) In your case, only half of the data has to be used, i.e. the symmentry axis is at the beginning of your data vector. From the geometrical point of view, both halves (left and right) are independent. For perfect symmetry, they will of course yield identical results. Therefore, the difference between the left and right half isa good indicator for the quality of symmetry in your system.

2) The radius is important for the scaling of the results. For any arbitrary value of R you will get a qualitatively correct result from the Abel inversion (except for very low values of R << 1 , which should be avoided). But, if you need a quantitatively correct result, you have to use the (outer) radius of your object. (e.g. if you investigated some glowing or light absorbing stuff in a glass cylinder which has a radius of 50 mm , just use R=50 and your result will be scaled to mm units)

22 May 2014 Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer

Hi Sina,
about the data range: If you use the plot option of my code, both your original data and the calculated radial profile will be plotted normalized to 1 (to make it easer to visually compare the profiles). If you are interested in the correctly scaled data, please use the output (f_rec=abel_inversion(...) ) and plot it manually. (of course, the code uses your original data for the calculations and not the normalized data shown in the figure).

About your data: I am not sure what you mean with an "arrow". However, the boundary value of your data vector (i.e. the last value) should ideally be zero (or something close). This condition is crucial for the algorithm and is imposed by the basic geometry of the situation. If there is some kind of constant background information behind your data, you might want to consider substracting 0.5 in order to create a data vector from 0 to 0.1 (it depends on your specific situation whether this is legitimate).
I hope this helps a bit. Feel free to ask further questions if anything remains unclear.
Carsten

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08 Jul 2014 Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer Killer, Carsten

@Adnan: I don't see any way in which Abel inversion would be related to your problem. You might want to consider some edge detection algorithm (Matlab offers plenty of them) to find the shape of the person in each frame.

08 Jul 2014 Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer Farooq, Adnan

@Carsten. In my case i have video of a person who is walking in front of camera (we can see the side view of person) and there is nothing at the background. so all the frames consist of each step he took for walking. so i want to apply Abel inversion projection on each frames (similar like making features vector)

07 Jul 2014 Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer Killer, Carsten

@Adnan: I am not sure what you mean with "finding changes". Of course, in different measurement images, the Abel inversion results of these images will probably differ as well. But please consider that the Abel inversion is only suited for a special situation, i.e. the investigation of symmetrical objects. Of course you can apply the Abel inversion code individually for each row or column, if your data is some kind of line-of-sight integrated measurement of a symmetrical object/system.
If the axis of symmetry is vertical, you have to consider the rows of your images. Please keep in mind that the axis of symmetry is at the start of your input vector (row) , i.e. the first element of the row vector corresponds to the center of your system r=0 and the last element corresponds the the edge, r=R.

07 Jul 2014 Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer Farooq, Adnan

@ Carsten and Borek, Thanks for your answers. Actually i want to use Abel transform on sequence of images i have to find the changes in that ... so i want to in that case is it possible to apply Abel inversion directly on 2D row wise and column wise..??

07 Jul 2014 Abel Inversion Algorithm Fourier-based reconstruction of an unknown radial distribution assuming cylindrical symmetry. Author: Carsten Killer Borek

@Adnan Farooq

As Carsten wrote, result is a distribution
f(r), where r is the diameter of a symetric circle. It means, the distribution is same for angle phi from 0 to 2pi. To plot f(r,phi) in 2D, the same parametrization can be used. If you need something more sofisticated, see assymetric abel inversion, which can be used for assymetric signals for example for simple plot of irradiation profile of plasma in tokamaks.

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