how to detemine this residual matrix ?

I calculate the cumulative sum of a matrix :Gm,n(i,j)

Now, the next step is '' we adopt the simplest function of a plane-fitting (i.e.Gm,n(i,j)=ai+bj+c ) to fit the trending for each surface Gm,n and determine the residual matrix ym,n(i,j).''

Please, can someone give me the code how to detemine this residual matrix, please ?

[Peng Li]

You question isn't clear enough for people to provide valuable comments honestly.

[Nadya]

It is explained like this in the paper.

To estimate the eq 2, I need to determine ''the residual matrix''.

Sincerely, I myself didn't understand, especially the fact that I'm not a mathematician, but I need to program this method.

Answer 1

[Peng Li]

Interesting. This is an application of the detrended fluctuation analysis (DFA) to a 2D image. Based on what your screenshot shows, it implements the algorithm similarly like being implemented to a time series -- cut into segments based on a time scale s (or here a time-spatial scale), integration (cumulative sum), linear fitting to get residual, and finally there should be a log-log fit between s and F(s).

To answer the specific question you asked, the residual is nothing but the point difference between G_{m,n} and \tilde{G}_{m,n}. This means, the y variable y_{m,n} = G_{m,n} - \tide{G}_{m,n}. F is simply the average of sum of squared y.

[Nadya]

Exactly ! this is what I'm trying to implement : 2D DFA.

and how determine tilde{G}_{m,n} ? !!

Please,can you help me to write the code Matlab ?

[Peng Li]

\tilde{G}_{m,n} is the linear 2D fitting ai+bj+c. Basically c is the intercept, a and b being the slope along i and j respectively. Could you try coding it by yourself first? It should be straightforward now if you understand the algorithm. It's a bit wierd I guess if I do that for you lol

[Nadya]

Sincerely, I have no idea, I have never programmed the equations in Matlab.

Thank you anyway.

[Peng Li]

understand and I would just like to encourage you to try it out and ask back here if you get any issues. That way you probably have higher chance to get a solution. I will see what I can do but honestly I have short of time this week and next to meet multiple deadlines, conferences ...