Now showing items 1-9 of 9

• #### A Hermite interpolatory subdivision scheme for C2-quintics on the Powell-Sabin 12-split ﻿

(Journal article; Peer reviewed, 2014)
In order to construct a C1C1-quadratic spline over an arbitrary triangulation, one can split each triangle into 12 subtriangles, resulting in a finer triangulation known as the Powell–Sabin 12-split. It has been shown ...
• #### Binary segmentation of medical images using implicit spline representations and deep learning ﻿

(Peer reviewed; Journal article, 2021)
We propose a novel approach to image segmentation based on combining implicit spline representations with deep convolutional neural networks. This is done by predicting the control points of a bivariate spline function ...
• #### Detecting similarity of rational plane curves ﻿

(Journal article; Peer reviewed, 2014)
A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such ...
• #### Detecting symmetries of rational plane and space curves ﻿

(Journal article; Peer reviewed, 2014)
This paper addresses the problem of determining the symmetries of a plane or space curve defined by a rational parametrization. We provide effective methods to compute the involution and rotation symmetries for the planar ...
• #### Similarity detection of rational space curves ﻿

(Journal article; Peer reviewed, 2017)
We provide an algorithm to check whether two rational space curves are related by a similarity. The algorithm exploits the relationship between the curvatures and torsions of two similar curves, which is formulated in a ...
• #### Stable Simplex Spline Bases for C3 Quintics on the Powell–Sabin 12-Split ﻿

(Journal article; Peer reviewed, 2016)
For the space of $C^3$ quintics on the Powell–Sabin 12-split of a triangle, we determine explicitly the six symmetric simplex spline bases that reduce to a B-spline basis on each edge and have a positive partition of ...
• #### Symbols and exact regularity of symmetric pseudo-splines of any arity ﻿

(Journal article; Peer reviewed, 2017)
Pseudo-splines form a family of subdivision schemes that provide a natural blend between interpolating schemes and approximating schemes, including the Dubuc–Deslauriers schemes and B-spline schemes. Using a generating ...
• #### Symmetries of canal surfaces and Dupin cyclides ﻿

(Journal article; Peer reviewed, 2017)
We develop a characterization for the existence of symmetries of canal surfaces defined by a rational spine curve and rational radius function. In turn, this characterization inspires an algorithm for computing the symmetries ...
• #### Symmetry Detection of Rational Space Curves from their Curvature and Torsion ﻿

(Journal article; Peer reviewed, 2015)
We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method ...