ISSN:
1573-7683
Keywords:
B-spline representations
;
subdivision schemes
;
continuous scale
;
affine invariant
;
progressive smoothing
;
computer implementation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Multiscale representations and progressive smoothing constitutean important topic in different fields as computer vision, CAGD,and image processing. In this work, a multiscale representationof planar shapes is first described. The approach is based oncomputing classical B-splines of increasing orders, andtherefore is automatically affine invariant. The resultingrepresentation satisfies basic scale-space properties at least ina qualitative form, and is simple to implement. The representation obtained in this way is discrete in scale,since classical B-splines are functions in $$C^{k - 2}$$ , where k isan integer bigger or equal than two. We present a subdivisionscheme for the computation of B-splines of finite support atcontinuous scales. With this scheme, B-splines representationsin $$C^r$$ are obtained for any real r in [0, ∞), andthe multiscale representation is extended to continuous scale. The proposed progressive smoothing receives a discrete set ofpoints as initial shape, while the smoothed curves arerepresented by continuous (analytical) functions, allowing astraightforward computation of geometric characteristics of theshape.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008261923192
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