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Paper describes that a 2D signal(say video) can be projected to 1D for time series analysis by using a transformation function fx=Ax+constant and fy=Ay+constant where Ax , Ay represents the (x,y) coordinates of a single trajectory A. Then,these fx vs t can be plotted and various analysis can be performed. Going by their justification,is it logical to think that a coordinate position of an object can only be described by a single coordinate when doing time series analysis and signal compression?

Also,they mention about taking cartesian product.Why is that?

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  • $\begingroup$ You can look for cartesian product directly on Wikipedia, they have an entry for that. $\endgroup$ – heltonbiker Jul 26 '12 at 20:27
  • $\begingroup$ Thank you for the reply. I went through that earlier but do not understand what is the need of doing that?Do we have to do cartesian product since we are projecting 2D into 1D? $\endgroup$ – Priya M Jul 26 '12 at 20:36
  • $\begingroup$ From what I understood, the paper tries to do a lot of complex things, and many of them are not related to your specific question. Actually, it seems you are still trying to get the motivation of the authors instead of needing help to answer a specific question. $\endgroup$ – heltonbiker Jul 26 '12 at 21:00
  • $\begingroup$ Well, the authors claim that(through lemma),Fig2 and in page5 that 2D can be reduced/converted to 1D. So I wanted to confirm is it really this process if we want to perform time series analysis on multidimensional signals say video we convert from n dimensions to 1D dimension or is there any other way as I do not know.Also, I fail to understand why cartesian product is required in this case. $\endgroup$ – Priya M Jul 26 '12 at 21:06
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Yes you can re-represent the 2d signal as a 1-d signal and use signal processing algorithms on it. In doing this you can lose some of benefits of representing the data this way.

Eg. If you were looking at compression of a mostly continuous 2-d dataset you may get benefits by treating the data as 2-dimensional and compressing in each dimension. Representing the data as concatenated rows or columns introduces discontinuities that the compression won't handle as well.

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  • $\begingroup$ What if the data is an image(2D gray or RGB) then if i want to do time analysis or any other process,would this still be applicable?Is there a book or concept which mentions that its legal to convert a 2D coordinate system to 1D?Further,is there a role of the cartesian product in this conversion? $\endgroup$ – Priya M Jul 26 '12 at 21:12

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