Shape visualization and processing are fundamental tasks in many fields from mechanical engineering to physics, biology, chemical engineering, medicine, astronomy, etc., and are the subject of very active research in image processing and computer graphics. For there is a huge variety of applications and a large variety of capture systems, there are many discrete models for representing a shape:...

We present first insights into the relation between two popular yet apparently dissimilar approaches to denoising of one dimensional signals, based on (i) total variation (TV) minimization and (ii) ideas from topological persistence. While a close relation between (i) and (ii) might phenomenologically not be unexpected, our work appears to be the first to make this connection precise for one di...

We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the total curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails ...

We propose a new algorithm for the computation of Willmore flow. This is the L2-gradient flow for the Willmore functional, which is the classical bending energy of a surface. Willmore flow is described by a highly nonlinear system of PDEs of fourth order for the parametrization of the surface. The spatially discrete numerical scheme is stable and consistent. The discretization relies on an adeq...

A new type of range searching problem, called the partial enclosure range searching problem, is introduced in this paper. Given a set of geometric objects S and a query region Q, our goal is to identify those objects in S which intersect the query region Q by at least a fixed proportion of their original size. Two variations of this problem are studied. In the first variation the objects in S a...

We prove that harmonic morphisms preserve the Jacobi operator along harmonic maps. We apply this result to prove infinitesimal and local rigidity (in the sense of Toth) of harmonic morphisms to a sphere. 1. Harmonic morphisms Harmonic maps φ : (M, g) → (N, h) between two smooth Riemannian manifolds are critical points of the energy functional E(φ,Ω) = 1 2 ∫ Ω |dφ| dvg for any compact domain Ω ⊆...

in the present study, for the first time, we document discovery of the predatory mite n. californicus in some rose greenhouses in yasouj, iran. furthermore, variation in spermathecal calyx shape is also discussed.