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Fast and exact method for computing a stack of images at various focuses from a four-dimensional light field

[+] Author Affiliations
Ziv Mhabary

Ben-Gurion University of the Negev, The Faculty of Engineering Sciences, Department of Industrial Engineering and Management, Professor Khayim Khanani Street, Be’er Sheva 8410501, Israel

Ofer Levi

The Open University of Israel, Department of Mathematics and Computer Science, University Road 1, Ra’anana 4353701, Israel

Eran Small

Weizmann Institute of Science, Department of Physics of Complex Systems, Herzl Street 234, Rehovot 7610001, Israel

Adrian Stern

Ben-Gurion University of the Negev, The Faculty of Engineering Sciences, Department of Electro-Optical Engineering, Professor Khayim Khanani Street, Be’er Sheva 8410501, Israel

J. Electron. Imaging. 25(4), 043002 (Jul 11, 2016). doi:10.1117/1.JEI.25.4.043002
History: Received March 8, 2016; Accepted June 16, 2016
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Abstract.  This paper presents an efficient method for computing a stack of images digitally focused at various lengths from a four-dimensional light field (LF). The main contribution of this work is a fast and algebraically exact method that does not require interpolation in the frequency or spatial domains as alternative methods do. The proposed imaging operator combines two-dimensional (2-D) fast Fourier transform with 2-D fractional Fourier transform and has computational complexity of O(NlogN), where N is the number of pixels in the LF tesseract of dimension N=nx×ny×nu×nv. The whole method consists of unitary vector-based operations; therefore, parallel implementation is easy and can contribute additional speed up. While current state of the art methods suffer from inherent tradeoff between the reconstruction quality and computational complexity, the proposed method benefits of both low-computational complexity and high-reconstruction quality. We also offer a solution for refocusing at distances that are not included in the reconstructed images stack. For such a case, we provide a modified version of our method, which is also algebraically exact and has lower computational complexity than other exact methods.

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Citation

Ziv Mhabary ; Ofer Levi ; Eran Small and Adrian Stern
"Fast and exact method for computing a stack of images at various focuses from a four-dimensional light field", J. Electron. Imaging. 25(4), 043002 (Jul 11, 2016). ; http://dx.doi.org/10.1117/1.JEI.25.4.043002


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