How can lower approximations and upper approximations be computed in an image ?
In order to compute the roughness in images you may extract texture features and evalaute them. There are some texture features that can be used to evalaute image rougnhenss. Some features may also suggest smooth surface, echogenicity, and a homogenous texture. This can be for example characteristics of asymptomatic carotid plaques of the common carotid artery, whereas irregular surface, echolucency and a heterogeneous texture are characteristics of potentially symptomatic plaques.
We have also a set of matlab function available with which you may extract texture features from images. See our publications on reserachgate amd also our website http://www.medinfo.cs.ucy.ac.cy/.
see also:
C.P. Loizou, C. Theofanous, M. Pantziaris, T. Kasparis, “Despeckle filtering software toolbox for ultrasound imaging of the common carotid artery”, Comput. Meth. & Progr. Biomed., vol. 114, pp. 109-124, 2014. Best paper, editor’s choice.
C.P. Loizou, M. Pantziaris, M.S. Pattichis, E. Kyriakou, C.S. Pattichis, “Ultrasound image texture analysis of the intima and media layers of the common carotid artery and its correlation with age and gender,” Comput. Med. Imag. Graph., vol. 33, no.4, pp. 317-324, 2009.
Deer Sheema, sometimes it can be helpful to compute the fractal dimension of images or image segments. The fractal dimension is a measure for image roughness and can be applied to regions, objects, background (enclosed is one of our publicationan). Nowadays, the wavelet transform can be successfully applied as well.
Good luck
Reiner Creutzburg
Thank you so much. Can all this discussion contribute to the rough entropy calculation ,is all this part of it in right direction?
I think that it can also be used towards this directions too. Entropy is a measure of signal complexity. Larger values are observed in heterogeneous and complex signals/images.
How about going through these also
(1) http://www.stat.ucla.edu/~sczhu/papers/IJCV_texton_reprint.pdf
(2) http://www.cs.berkeley.edu/~malik/papers/LM-3dtexton.pdf
(3) http://www.robots.ox.ac.uk/~vgg/research/texclass/with.html
(4) http://www.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/papers/mbls_ijcv01.pdf
hope it helps
Hello Sheema, you can check the types of functions called "envelope" and "correlation" for any 2D versions that can give the functionality you need. Even statististics functions and gaussian filters may be applicable if the pixel-to-pixel variations can be measured directly (greyscale images). These are good if the surfaces are unknown, random patterns like a beach with small and big grains of sand. I agree with Rainer that "wavelet" analysis can be an elegant and fast solution, especially if the image textures are made of many small identical patterns which can be easily recognized. Like the backgrounds and objects in 3D games for example.
Good luck!
Henrik
Thank you Mr.Henrik.I actually need to compute rough entropy thats why i needed to do so.I still am looking for the solution to compute rough set out of image.
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