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Shape Design, Representation, and Restoration with Splines

  • Y. Ikebe
  • S. Miyamoto
Part of the Springer Series in Information Sciences book series (SSINF, volume 6)

Abstract

The purpose of the present paper is to demonstrate several applications of interpolation and approximation methods such as splines to picture engineering In particular, three types of applications, i.e., shape design, shape representation, and shape restoration are discussed. Shape design is concerned with construction of visually beautiful curves and interactive modification of the curves. The method of B-splines gives a physically natural (minimum curvature] curve which is locally modifiable, since it is a linear combination of basis functions (B-splines) having local support. Bezier’s method generates a smooth curve (polynomial) by means of Bezier polygon and is appropriate for interactive use, although a local modification may propagate throughut the whole interval. Shape representation approximates a given irregular shape, where a method suitable for use depends on a particular way in which data are given. For surface approximation Coons methods are used as a standard tool, where an entire surface is subdivided into pieses whose boundary data are used to construct an approximating surface for the corresponding piece. When the boundary data are given at a selected set of points, tensor product of splines has been known to be usable. For surfaces which can be adequately described in terms of one-parameter family of curves, the technique known as lofting is applicable. If two families of parametric curves must be mixed to define a given surface, one may effectively use boolean sum approximation. Shape restoration is an approximation of an existing object, where the data are noisy or incomplete. In this case an approximation will depend on smoothing property and the nature of data given. Moreover, in some cases, irregularly distributed data points must be incorporated. In the image restoration the convolution property of B-splines is useful for the restoration of space- invariant degradations. As an additional example, we mention the pattern generation of air pollution, where spline under tension is prefered to the ordinary cubic spline in view of the accuracy of the approximation.

Keywords

Tensor Product Point Spread Function Image Restoration Shape Design Smoothing Spline 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Y. Ikebe
    • 1
  • S. Miyamoto
    • 1
  1. 1.University of TsukabaIbaraki 305Japan

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