
Digital Library of the
European Council for Modelling and Simulation 
Title: 
Exact Fast Algorithm For Optimal Linear Separation Of 2D Distribution 
Authors: 
Egor I. Ershov, Vassili
V. Postnikov, Arseniy
P. Terekhin,
Dmitry P. Nikolaev 
Published in: 
(2015).ECMS 2015 Proceedings edited
by: Valeri M. Mladenov, Grisha Spasov, Petia Georgieva, Galidiya Petrova, European
Council for Modeling and Simulation. doi:10.7148/2015 ISBN:
9780993244001 29^{th}
European Conference on Modelling and Simulation, Albena (Varna), Bulgaria,
May 26^{th} – 29^{th},
2015 
Citation
format: 
Egor I. Ershov, Vassili V. Postnikov, Arseniy P. Terekhin,
Dmitry P. Nikolaev (2015). Exact Fast Algorithm For Optimal Linear Separation Of 2D Distribution, ECMS
2015 Proceedings edited by: Valeri M. Mladenov, Petia Georgieva, Grisha Spasov, Galidiya Petrova
European Council for Modeling and Simulation. doi:10.7148/20150469 
DOI: 
http://dx.doi.org/10.7148/20150469 
Abstract: 
The paper presents a new fast
computation scheme for linear separation in twodimensional feature space. This
scheme is based on a combination of several image processing
techniques: fast Hough transform, cumulative sum computation and expression
of optimized criterion as a function of additive statistics. It is shown that
complexity of the scheme is O(n2 log n) for chosen
set of criteria. Two appropriate criteria are discussed, both being a 2D
extension of wellknown Otsu’s criterion: standard one considering covariance
trace and one considering covariance second eigenvalues.
Applicability of the latter criterion for the color segmentation problem is
discussed. 
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