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

      Lyche, Tom; Muntingh, Agnar Georg Peder (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 

      Barrowclough, Oliver Joseph David; Muntingh, Agnar Georg Peder; Nainamalai, Varatharajan; Stangeby, Ivar Haugaløkken (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 

      Alcazar, Juan Gerardo; Hermoso, Carlos; Muntingh, Agnar Georg Peder (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 

      Alcazar, Juan Gerardo; Hermoso, Carlos; Muntingh, Agnar Georg Peder (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 

      Alcazar, Juan Gerardo; Hermoso, Carlos; Muntingh, Agnar Georg Peder (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 

      Lyche, Tom Johan; Muntingh, Agnar Georg Peder (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 

      Muntingh, Agnar Georg Peder (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 

      Alcazar, Juan Gerardo; Dahl, Heidi Elisabeth Iuell; Muntingh, Agnar Georg Peder (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 

      Alcazar, Juan Gerardo; Hermoso, Carlos; Muntingh, Agnar Georg Peder (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 ...