Image interpolation as a boundary value problem

Hei Tao Fung; Kevin J. Parker

doi:10.1117/12.233195

27 February 1996 Image interpolation as a boundary value problem

Hei Tao Fung, Kevin J. Parker

Author Affiliations +

Proceedings Volume 2727, Visual Communications and Image Processing '96; (1996) https://doi.org/10.1117/12.233195
Event: Visual Communications and Image Processing '96, 1996, Orlando, FL, United States

Abstract

Image interpolation is the determination of unknown pixels based on some known pixels. The conventional interpolation methods such as pixel replication, bilinear interpolation, and cubic spline interpolation, assume that the known pixels are located regularly on a Cartesian mesh. They cannot be easily extended to other cases where the configurations of the known pixels are different. We propose a novel formulation of the image interpolation problem to deal with the more general cases, such as the case where a region of image is missing and the case where the known pixels are irregularly placed. The interpolation problem is formulated into a boundary value problem involving the Laplacian equation and the known pixels as the boundary conditions. The matrix equation resulting from the formulation has a unique solution. It can be solved efficiently by the successive over-relaxation (SOR) iteration. The advantage of the proposed interpolation method lies in its flexibility in handling the general cases of interpolation.

Citation Download Citation

Hei Tao Fung and Kevin J. Parker "Image interpolation as a boundary value problem", Proc. SPIE 2727, Visual Communications and Image Processing '96, (27 February 1996); https://doi.org/10.1117/12.233195

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