Curvature Interpolation Method for the Recovery of Scattered Image Data

Hakran Kim, Velinda R. Calvert, Jin Ha Hwang, and Seongjai Kim


Nonuniform sampling theory, scattered data, surface reconstruction, curvature interpolation method (CIM), partial differential equation (PDE)


This article presents a novel approach for the recovery of scattered (nonuniformly sampled) image data. This problem is often appeared in digital image processing applications. Interesting applications can be found in e.g. computer graphics and the earth surface construction from light-detection-and-ranging data. We propose a new method called the recursive curvature interpolation method (R-CIM) for the recovery of scattered image data. The new algorithm constructs a reliable image surface recursively, for which each iteration produces a smooth correction term that is generated utilizing a generalized curvature source estimated from the last residual. The R-CIM employs an effective 9-point scheme for the curvature evaluation which in turn makes the image correction terms smooth and involve no ringing artifacts. It has been experimentally verified that the new method results in a satisfactory image of clear and reliable edges, starting from scattered image data of 5-6% sampling rate.

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