• Conformal Surface Parameterization for Texture Mapping 

      Haker, Steven; Angenent, Sigurd; Tannenbaum, Allen R.; Kikinis, Ron; Sapiro, Guillermo; Halle, Michael (Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 2000-04)
      We give an explicit method for mapping any simply connected surface onto the sphere in a manner which preserves angles. This technique relies on certain conformal mappings from differential geometry. Our method provides a ...
    • Finsler Active Contours 

      Melonakos, John; Pichon, Eric; Angenent, Sigurd; Tannenbaum, Allen R. (Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 2008-03)
      In this paper, we propose an image segmentation technique based on augmenting the conformal (or geodesic) active contour framework with directional information. In the isotropic case, the euclidean metric is locally ...
    • Mathematical Methods in Medical Image Processing 

      Angenent, Sigurd; Pichon, Eric; Tannenbaum, Allen R. (Georgia Institute of TechnologyAmerican Mathematical Society, 2006-07)
      In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing ...
    • Minimizing Flows for the Monge–Kantorovich Problem 

      Angenent, Sigurd; Haker, Steven; Tannenbaum, Allen R. (Georgia Institute of TechnologySociety for Industrial and Applied Mathematics, 2003)
      In this work, we formulate a new minimizing flow for the optimal mass transport (Monge–Kantorovich) problem. We study certain properties of the flow, including weak solutions as well as short- and long-term existence. ...
    • Nondistorting Flattening Maps and the 3-D Visualization of Colon CT Images 

      Haker, Steven; Angenent, Sigurd; Tannenbaum, Allen R.; Kikinis, Ron (Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 2000-07)
      Considers a novel three-dimensional (3-D) visualization technique based on surface flattening for virtual colonoscopy. Such visualization methods could be important in virtual colonoscopy because they have the potential ...
    • On the Affine Heat Equation for Non-Convex Curves 

      Angenent, Sigurd; Sapiro, Guillermo; Tannenbaum, Allen R. (Georgia Institute of TechnologyAmerican Mathematical Society, 1998-07)
      In this paper, we extend to the non-convex case the affine invariant geometric heat equation studied by Sapiro and Tannenbaum for convex plane curves. We prove that a smooth embedded plane curve will converge to a point ...
    • On the Laplace–Beltrami Operator and Brain Surface Flattening 

      Angenent, Sigurd; Haker, Steven; Tannenbaum, Allen R.; Kikinis, Ron (Georgia Institute of TechnologyInstitute of Electrical and Electronics Engineers, 1999-08)
      In this paper, using certain conformal mappings from uniformization theory, the authors give an explicit method for flattening the brain surface in a way which preserves angles. From a triangulated surface representation ...