Date of Award

1-1-2011

Document Type

Campus Access Thesis

Department

Mathematics

First Advisor

Peter G Binev

Abstract

Embark on an exploration of subdivision schemes and some heuristics for developing new schemes with applications to curves and surfaces, as well as, to image smoothing and analysis. An explanation of the planning and development stages of smoothing schemes is given. Steps are then taken to derive the rules for new schemes, which implement derivatives and gradients in order to improve the performance of specially localized schemes. Consideration is taken for one dimensional and two dimensional settings. These algorithms have applications such as smoothing the appearance of data sets represented by curves, contours, and surfaces. The algorithms discussed here result in a smooth curve without losing as much information as observed with some traditional algorithms.

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