Exploiting redundancy to solve the Poisson equation using local information

Authors:
Firas Hassan;Lavanya Vytla;Joan E. Carletta
Affiliations:
Electrical & Computer Eng. and Comp. Sci. Dept., Ohio Northern University, Ada, Ohio;Dept. of Electrical and Computer Engineering, The University of Akron, Akron, Ohio;Dept. of Electrical and Computer Engineering, The University of Akron, Akron, Ohio
Venue:
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Year:
2009

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Abstract

This paper proposes a novel method of solving the Poisson equation used in image processing techniques that are based on computations in the gradient domain. The Poisson equation is used to perform an inverse gradient transform; it back-solves to find an image that is closest to having a particular gradient. The traditional methods for back-solving require access to the entire gradientdomain image; in a real-time embedded implementation, this implies high hardware complexity, large latency, and large memory buffers. We propose a method that produces high quality results visually and is based on a small sliding window with specially chosen boundary conditions. The method has been simulated as a proof of concept, and should result in much faster and smaller digital hardware than traditional approaches.