Methods and applications of irregular sampling and scattered data interpolation of digital images

Shahidi, Reza (2003) Methods and applications of irregular sampling and scattered data interpolation of digital images. Masters thesis, Memorial University of Newfoundland.

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. Download (5MB) [English] PDF - Accepted Version Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission. (Original Version)

Abstract

This thesis examines the problem of the irregular sampling of images and the scattered data interpolation or reconstruction of images from these irregular samples. Since in our tests only a small number of samples are taken, the entire process can be viewed as low bitrate image compression. We look at two different existing irregular sampling algorithms, Farthest Point Sampling (EPS) and skewness-based sampling. We then propose two new progressive irregular sampling algorithms, gaps and Faster Farthest Point Sampling (FFPS). FFPS is, as its name suggests, quicker than FPS, while gaps addresses concerns regarding the quality of reconstructions from irregular samples. -- Note that reconstruction is the flip side of sampling. One existing fast reconstruction algorithm called Multilevel B-Spline Approximation does not work well on irregular sampling techniques which take samples relatively far away from edges, so a new modification of this algorithm, called New Edge-Directed Multilevel B-Spline Approximation (NEDMBA), which uses image inpainting, is introduced. -- Finally, we apply Faster Farthest Point Sampling to digital image halftoning to create a new algorithm called Farthest Point Halftoning. This new dither array generation algorithm is compared to other existing standards, for example the Modified Blue Noise Mask and the Void and Cluster method, and is shown to perform favorably.

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