Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Representation of local geometry in the visual system
Biological Cybernetics
An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A Multiscanning Approach Based on Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Solid shape
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
Toward a computational theory of shape: an overview
ECCV 90 Proceedings of the first european conference on Computer vision
Two-scale difference equations I: existence and global regularity of solutions
SIAM Journal on Mathematical Analysis
Inflections on curves in two and three dimensions
Computer Aided Geometric Design
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Shape recognition under affine distortions
IAPR Proceedings of the international workshop on Visual form: analysis and recognition
Scale and the differential structure of images
Image and Vision Computing - Special issue: information processing in medical imaging 1991
A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
International Journal of Computer Vision
Stationary Subdivision
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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 {\bf 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 {\bf C}^r are obtained for any real r in [0, \infty), 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.