Dear Xiaofeng,

You have stumbled with the problem of deciding the "length of the ruler" you require for your analysis. On my experience, there is no one single answer, and depends very much on what you are trying to achieve. I see 3 potential steps forward:

1.- How does your window size relates to the physics you are trying to measure? A small relative size will not allow you to see major trends while a relative large size will hide details you might me interested in. i.e. if you are trying to measure surface roughness related to the activity of landslides along slope cuts in transportation corridors, you might want a relatively small window size, however if you are trying to evaluate surface roughness related to deep rotational failures along a river valley, you might want to increase the window size.

2.- Is there a standard window size for your particular analysis? There might be a well established procedure for your analysis that requires a particular window size or a tendency for a particular size in previous studies. If you intend to compare your findings with others previously published, at least part of your study should use the same window size as previous publications.

3.- You could take a "fractal" approach. Here, you calculate your variables based on different window sizes. Then you plot the size (horizontal axis) Vs. your calculated result (vertical axis) in a log-log space. The slope of the linear fit has been interpreted as a measure of the variable that is independent of the size of the ruler your might choose. This a fractal analysis in a nutshell of course.

I hope this thoughts might be of some help.

Cheers,

Renato

Thank you Macciotta, your advices are useful. Maybe there is not an universal window size. "Fractal approach" is actually a good method. However the key point for this method is to find a useful mathematical index to evaluate the result. But sometimes it is difficult. For example we just want to evaluate some spatial metrics by the moving window method(i.e. density)then each pixcel will get an density value calculated . Of course, we shoule try many times with different window size. Then the question is that how can we choose a useful mathematical index to evaluate the window size series  in this circumstance? In other words, who can be chosen as the vertical axis? Is there theory about how to evaluate these results on choosing window size?

Thanks again!

     Thanks Ferrarini, yes your sugestion is useful. Different researcher may use different to obtain the rules underlying these data. Maybe the suitable window size is an range, for example from to 3*3 to 9*9.  However if the window size is over large, the rules meybe concealed. In other words, if we use a over large window size we may not discover the rules which we expect to find.

    Will you please introcude some relational papers or  literaturel about how to decide the window size?

Thanks so much!

Hi,

Start with auto-correlation analysis of your samples using variogram method. Based on the range you get from the variogram analysis you define your window size equal to the size of the range. Hope that helps.

Concur with the others, there is really no universal optimal window size. Really depends on what your object size is, the imagery you are using, and the image characteristics you are aiming to capture. In the paper noted below, we tried to use variograms to provide for customization of the windows and the information generated (Wulder et al. 1998, RSE). Pretty old, so am sure more and better has been done since. In general, IMHO for characterizing local variance conditions fancier methods have not really outperformed simpler and more transparent approaches (e.g., variance within a fixed window).  If you have your objects via other means (say segmentation), within object texture is also a useful option. 

Best of luck with your research. 

Article Aerial Image Texture Information in the Estimation of Northe...

Take a look at this paper (on the old side and I am sure more up to date papers have been published):

An automatic Optimum kernel-size selection technique for edge enhancement

Pat Chavez

Brian Bauer

Remote Sensing of Environment (REMOTE SENS ENVIRON)

1982

 Edit ABSTRACT Edge enhancement is a technique that can be considered, to a first order, a correction for the modulation transfer function of an imaging system. Digital imaging systems sample a continuous function at discrete intervals so that high-frequency information cannot be recorded at the same precision as lower frequency data. Because of this, fine detail or edge information in digital images is lost. Spatial filtering techniques can be used to enhance the fine detail information that does exist in the digital image, but the filter size is dependent on the type of area being processed. A technique has been developed by the authors that uses the horizontal first difference to automatically select the optimum kernel-size that should be used to enhance the edges that are contained in the image.

Perhaps there are some ideas that may be useful for your applications.

Pat

I m also facing the same issue. I developed an algorithm for same and compared that with brute force technique. However , I need to know the benchmark techniques for deciding the window size for time series analysis using weighted moving average

Hello People!

How do you pose the moving window, when you are at a corner of a map (virtual), if you kep the moving window size same then robot might not be on the center anymore and in that case, I am getting issue with polar histogram?

Is any of you got similar issue?