Publications [#264894] of Guillermo Sapiro

Papers Published

1. Sapiro, G; Cohen, A; Bruckstein, AM, A Subdivision Scheme for Continuous-Scale B-Splines and Affine-Invariant Progressive Smoothing, Journal of Mathematical Imaging and Vision, vol. 7 no. 1 (January, 1997), pp. 23-40, ISSN 0924-9907 [doi]
   (last updated on 2025/02/02)

   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 B-splines of increasing orders, and therefore is automatically affine invariant. The resulting representation satisfies basic scale-space properties at least in a qualitative form, and is simple to implement. The representation obtained in this way is discrete in scale, since classical B-splines are functions in Ck-2, where k is an integer bigger or equal than two. We present a subdivision scheme for the computation of B-splines of finite support at continuous scales. With this scheme, B-splines 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.