Welcome to a Mini-Conference on Digital Geometry to be organized by Uppsala University on September 24, 2009!
Venue: The Ångström Laboratory, Uppsala, Sweden.
In the morning we will be in Room 80121 (Level 0, House 8, Room 80121).
In the afternoon, in the Siegbahn Hall (Level 0, House 1)
Abstract: I present in this talk the use of arithmetic discrete straight lines, defined by Jean-Pierre Reveillès in 1989, to analyse discrete curves. Properties of arithmetic discrete straight lines are presented and a linear and incremental algorithm of recognition is deduced. Then algorithms for the segmentation, the polygonalization and the analysis (length, curvature) of discrete curves are proposed. Extensions of these results to 3D discrete lines are also presented. In the last part of my talk, I will show how to analyse noisy discrete curves by using an adapted recognition algorithm. Examples of applications are also given.
Abstract: We will discuss strong discrete concavity properties of Taylor coefficients of multivariate polynomials with prescribed non-vanishing properties. We provide examples and applications such as the tropical Grassmannian in tropical geometry, the minimum matching problem in combinatorics, and Horn's problem in matrix theory.
Abstract: While arithmetical discrete lines and rational arithmetical planes have been deeply studied since their introduction by Jean-Pierre Reveillès in 1991, only partial results on their topology have been exhibited. In the present lecture, after having introduced the basic notions concerning arithmetical discrete planes, I will focus on how to compute the minimal thickness connecting an arithmetical discrete plane with a given normal vector.
Abstract: I will describe how a characterization of subharmonic functions that are piecewise harmonic—such as the maximum of a finite number of harmonic functions—can help in understanding the asymptotic properties of zeroes of families of polynomials in one variable, arising as eigenvalues to ordinary differential equations. This is built on ideas of Hans Rullgård, and joint work with Borcea, Björk and Shapiro.
Abstract: In this talk I will propose a novel formulation of the Chan—Vese model for pose invariant shape prior segmentation as a continuous graph cut problem. The model is based on the classic L2 shape dissimilarity measure and with pose invariance under the full (Lie) group of similarity transforms in the plane. To overcome the common numerical problems associated with step size control for translation, rotation and scaling in the discretization of the pose model, a new gradient descent procedure for the pose estimation is introduced. This procedure is based on the construction of a Riemannian structure on the group of transformations and a derivation of the corresponding pose energy gradient. Numerically this amounts to an adaptive step size selection in the discretization of the gradient descent equations. Together with efficient numerics for TV-minimization we get a fast and reliable implementation of the model. Moreover, the theory introduced is generic and reliable enough for ap- plication to more general segmentation- and shape models.