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Design and recovery of 2-D and 3-D shapes using rational Gaussian curves and surfaces

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Abstract

A new representation for parametric curves and surfaces is introduced here. It is in rational form and uses rational Gaussian bases. This representation allows design of 2-D and 3-D shapes, and makes recovery of shapes from noisy image data possible. The standard deviations of Gaussians in a curve or surface control the smoothness of a recovered shape. The control points of a surface in this representation are not required to form a regular grid and a scattered set of control points is sufficient to reconstruct a surface. Examples of shape design, shape recovery, and image segmentation using the proposed representation are given.

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  1. Department of Electrical Engineering and Computer Science, University of Illinois at Chicago, 60680-4348, Chicago, IL

    Ardeshir Goshtasby

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Goshtasby, A. Design and recovery of 2-D and 3-D shapes using rational Gaussian curves and surfaces. Int J Comput 11263on 10, 233–256 (1993). https://doi.org/10.1007/BF01539537

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