Maria V. Storozhilova, Dmitry V. Yurin
Rank algorithms are wellknown approach to image enhancement, denoising, and some other applications. Whereas there is known a wide class of rank algorithms, only a small set of them such as min, max and median filters are frequently used in practice. More complex algorithms as mean by epsilonV neighbourhood or mean by KNV neighbourhood are used very rare, probably due to their computation complexity. On the other hand, there are known fast median filtering algorithms.
The target of our research is to develop fast rank algorithms. Based on multiscale histograms and using lazy histogram updating technique we developed fast calculation scheme for finding
 Arbitrary rank element by neighbourhood
 Mean by epsilonV neighbourhood
 Mean by KNV neighbourhood
 Sliding equalization
Download source code (MS Visual Studio 2008 project)
Fast rank algorithms in use, image size 250x250 pixels:



Source image 

Image with added Gaussian noise 
Easiest noise removal algorithms:



r = 1, median filtering 

r = 1, mean by square neighborhood 
EpsilonV filtering:



epsilon = 10 (too small), r = 2,
Gaussian noise was not suppressed 

epsilon = 15 (good), r = 2,
Most of Gaussian noise was suppressed, leaf boundaries remained sharp 



epsilon = 15 (good), r = 7,
Most of Gaussian noise was suppressed, leaf boundaries remained sharp 

epsilon = 30 (too large), r = 7,
Gaussian noise was suppressed, leaf boundaries remained sharp, but micro relief was eliminated 
KNV filtering:



Image with added Gaussian noise 

K = 1/8N, r = 7,
Gaussian noise was not suppressed 



K = 1/4N, r = 7,
Gaussian noise was partially suppressed, sharp corners of the leaf (≤90°) were “rounded” 

K = 1/3N, r = 7,
Gaussian noise was suppressed, sharp corners of the leaf (≤120°) were “rounded” 
Publications
2013
M. V. Storozhilova, D. V. Yurin. “Fast Rank Algorithms Based on Multiscale Histograms and Lazy Calculations” // Pattern Recognition and Image Analysis, Vol. 23, No. 3, Pleiades Publishing, Ltd., 2013, p. 367–374. Springer.
2011
M. V. Storozhilova, D. V. Yurin. “Fast rank algorithms based on multiscale histograms” // In: 21th International Conference on Computer Graphics GraphiCon'2011. Moscow, Russia, 2011, pp. 132−135. PDF.
M. Storozhilova, D. Yurin. “Fast Rank Algorithms with Multiscale Histograms Lazy Updating” // In: 8th Open GermanRussian Workshop “Pattern Recognition and Image Understanding” (OGRW82011). Lobachevsky State University of Nizhny Novgorod, November 2126, 2011, 2011, pp. 280−283. PDF.