Smoothing data on segmented regions independently from other segments

I have a set of measured data on a rectangular area (let's say the surface of a material) for which I have a binary image indicating the regions corresponding to two different constituent phases of the surface. Priori to differentiation, I need to perform data smoothing on the segmented areas separately so as not to lose the a priori known spatial heterogeneity of the differentiated data at the boundary edges between segments.

I have been thinking of smoothing using Finite Elements with different smoothing parameters for each of the segments, but I don't know how to efficiently do it.

I have also tried using thin plate smoothing spline tpaps of MATLAB for each segment, but it was extremely slow for large data and hence being practically impossible.

I highly appreciate if any one shares their experiences related to my problem.

Thanks

Farhad

Answer 1

[Image Analyst]

How about if you just made each binary region the mean gray level for that region. That would be the ultimate smoothing. Do you want to do that?

Or would you consider a general method like non-local means or the sigma filter or the k-nearest neighbors filter? http://www.mathworks.com/matlabcentral/fileexchange/?term=non-local+means

[Farhad M]

Thanks for the reply and sorry if the problem was not clearly explained. My data is NOT the gray-scale image, it is full-field displacement measurements at pixels obtained using image correlation technique. I need to differentiate the data to obtain strain field. However, noisy data on the displacements have detrimental effects on the strain. On the other hand, if I use regular data smoothing techniques, I will lose real details in the strain field, particularly at the interfacial boundaries (between regions). I know that losing details is almost an inevitable outcome of filtering. However, I have a priori knowledge about the specific locations of these details, i.e. the interfacial boundaries given I have access to the binary image which segments these regions. Therefore, the idea is to perform smoothing on each region separately and leave the edges kind of non-smooth.

Thanks again and hope I have well explained this time.

[Farhad M]

Your first suggestion would not work at all since I don't want to do ultimate smoothing. As for the second suggestion, I did not find k-nearest neighbors filter from the link. Do you think it might be helpful given my update on the problem?

[Image Analyst]

The methods I described will work with any 2D array, regardless of whether it is an actual "image" or not. You can Google other noise reduction methods such as k-Nearest Negihbors, K-SVD, K-LLD, BM3D, etc. and find links such as these:

http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MANDUCHI1/Bilateral_Filtering.html

http://www.cs.tut.fi/~foi/GCF-BM3D/

http://users.soe.ucsc.edu/~milanfar/talks/

Not all of them are available via the File Exchange.

[Farhad M]

Thanks a lot!