Math @ Duke

Publications [#264894] of Guillermo Sapiro
Papers Published
 Sapiro, G; Cohen, A; Bruckstein, AM, A Subdivision Scheme for ContinuousScale BSplines and AffineInvariant Progressive Smoothing,
Journal of Mathematical Imaging and Vision, vol. 7 no. 1
(1997),
pp. 2340, ISSN 09249907
(last updated on 2019/06/20)
Abstract: Multiscale representations and progressive smoothing constitute an important topic in different fields as computer vision, CAGD, and image processing. In this work, a multiscale representation of planar shapes is first described. The approach is based on computing classical Bsplines of increasing orders, and therefore is automatically affine invariant. The resulting representation satisfies basic scalespace properties at least in a qualitative form, and is simple to implement. The representation obtained in this way is discrete in scale, since classical Bsplines are functions in Ck2, where k is an integer bigger or equal than two. We present a subdivision scheme for the computation of Bsplines of finite support at continuous scales. With this scheme, Bsplines representations in Cr are obtained for any real r in [0, ∞), and the multiscale representation is extended to continuous scale. The proposed progressive smoothing receives a discrete set of points as initial shape, while the smoothed curves are represented by continuous (analytical) functions, allowing a straightforward computation of geometric characteristics of the shape.


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