# Representation of frame image pixels

In paper Human identification using gaits Section 3.2, the authors explain how to represent a 3D image (x,y,t) into 2D image with (x,t) ; (y,t) denoted 1D signals. I have a conceptual doubt which is in my case I have a matrix (x,y) represent the centroid of the motion- a pixel point from one frame to the next. So, if we want to do some kind of processing like finding the fourier transform, then is it theoretically correct to treat x- coordinate and y coordinate separately?Do we need to perform some trasnformations?I did not understand how the authors are representing an image pixel as 1D signal.Questions are :

1. It is not clear how the authors have converted to four 1D signals. How to use/represent the image pixel coordinates as 1D signals as done in the paper for further analysis?Should I perform autocorrelation between x and y to get 1D vector?
2. Phase space plot = it is plot of 2 variables. So, in this case, will it be a plot of x(t) vs y(t) or x(t-1) vs x(t) or the future_predicted_values for x cordinate vs the current measured values of x coordinate?Or the plot of features?
3. Do I need to smooth the data?If so then how to use bsplines as I found that this is popularly used for smoothening.

Example data points representing pixels (x,y) are

x      y
160    210
160    230
160    250
170    83


and so on for 1000 frames.

Can somebody please help in explaining the concept and the way to proceed with image signals so that a phase space plot can be created.

The paper that you are quoting assumes that the motions along the different coordinates are independant functions, i.e., $$P(t) = \left(x(t),y(t)\right) = (f_1(t),f_2(t)) \neq f(x,y)(t),$$ where $P$ stand for position. The various 1D functions are obtained in this way.