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Coordinate Logic Order Statistics & Applications in Image Processing

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Abstract

A new approach regarding Low-Level Image & Signal processing is presented. This new approach deals with the philosophy of finding a method for designing and executing algorithms (filters), using the least possible complexity. The proposed method is based on Coordinate Logic Order Statistics filters (CL-OS) which are an extension of Coordinate Logic Filters and introduces a minimalistic approach in filter design followed by an satisfactory efficiency in terms of quality, speed, complexity, and energy consumption. CL-OS filters have similar functionality with OS filters, specifically the basis of OS filters is the sorting of the original signal values while the basis of CL-OS filters is the sorting of the binary levels of the original signal values. The intrinsic feature of CL-OS filters is their explicit low overall complexity which is \(\varvec{O}(n)\), on the other hand the general overall complexity of OS filters is \(\varvec{O}(n^{2})\); moreover, CL-OS filters are characterized by a naturally embedded parallelism which makes them absolutely appropriate for H/W implementation and real-time applications. Another characteristic property of CL-OS is that their field of definition includes the OS’s field of definition causing an increase of the signal energy and thus constituting them not only smoothers but enhancers too. The last property is of great importance since it reveals new signal information giving a different interpretation of the original signal.

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Acknowledgments

Special thanks to Dr. Savvas A. Chatzichristofis and Prof. Yiannis S. Boutalis, for their valuable advises. Konstantinos B. Tsirikolias, for his help in the English language of this paper.

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  1. R&D Department, Daedalus Ltd., 22 Ikarias Str, Glyfada, 16675, Athens, Greece

    Kostas D. Tsirikolias

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  1. Kostas D. Tsirikolias
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Correspondence to Kostas D. Tsirikolias.

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Tsirikolias, K.D. Coordinate Logic Order Statistics & Applications in Image Processing. Circuits Syst Signal Process 34, 901–929 (2015). https://doi.org/10.1007/s00034-014-9884-4

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