We have some raster data in GIS representation. We average each pixel value applying a window of certain extent - i.e. modified pixel value would be the mean around 3X3 pixel neighbourhood. Can we tell that this pixel value is smoothed over 3X3 pixel neighbourhood? Does it mean, that smoothing and averaging is the same or there is some difference in the applied algorithms?
I got some feeling, that averaging is the particular case of smoothing. There is smoothing algorithm called as moving average - I guess, that this technique works exactly as above-described averaging aroung given neighbourhood. Am I right or not?
Yes, in my experience, averaging in this sort of situation is a special case of smoothing. In general smoothing of, say, a series of points, you apply weights to the points proportional to the distance from the center point. A running average would have all the weights equal to one.
Thank you Elliot!
Then I got an extended question. Is not it the case that smotthong always plays only with weighting, while averaging principle is applied in all smoothing algorithms? Then there can be proporional weighting (equal weights), distance-weighted averaging, etc.
In smoothing is there principle, which applies a procedure, which is fundamentally different for any averaging (proportional or weighted)?
I'm sorry, Almaz. I do not understand your extended question. It may simply be a matter of your words and my inability to comprehend them.
The Wikipedia article on Smoothing is very good, although it is a bit more complex that I would have liked to have seen. http://en.wikipedia.org/wiki/Smoothing
Hello Almaz,
weighted and non-weighted averaging is indeed a very common method for applying smoothing, and this is nothing else than a convolution. However, smoothing or flattening means roughly speaking to replace or change the value of a pixel, that it becomes less outlier-like. To achieve this, there exist also other methods, in particular border-preserving smoothing methods are non-linear.
Just to mention some:
1. You can interpolate the pixel with B-Splines,
2. you can apply a (weighted) median filter, that is a non-linear border preserving smoothing,
3. you can use gray-scale morphology, as e.g. mean of erosion and and dilation.
4. you can minimize the local energy with e.g. the Ising model.
Best Felix
I agree with the previous responses. Averaging is one possible form of smoothing when using window sizes greater than 1. In my experience, any type of operation where a neighborhood of pixels is used to change the value of its central pixel is a smoothing operation.
'Smoothing' is a very common practice in geophysical investigations. Earth models, particularly in sedimentary environments, run on certain simple assumptions. Say for example, the subsurface is constituted of horizontal layers which are homogeneous and isotropic. If we assume that under certain circumstances, these assumptions do not hold good locally; the field datasets, say the gravity data, will be 'smoothened' to isolate regional trend. Also, by this means, 'residual anomaly' (Local factors) can be filtered. In a similar way, for the electrical resistivity data, a 'smooth' curve will be generated from the raw data. This may happen in certain circumstances where say a broadly sand horizon having small size clay pockets may give rise to 'wiggle traces'. By, 'smoothing' we filter out practically the clay pockets. Thus, 'smoothing' is directly related to 'Trend analysis' which may sometimes be realized by 'averaging' but better if not treated as 'same'.
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