The aim of our robust technique using watermarking is to reconstruct watermark from geometric attacks. Various geometric transformations, such as rotation, scaling, cropping, shear, translation, resize, scattering, bending, and so on, provides the displacement of some of its picture elements. The existing watermarking algorithms countermeasures the attacks related to pixel positions. In our pap...

We formulate an approach to the geometry of Riemann–Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart–Moffat and Finsler–Lag...

We formulate an approach to the geometry of Riemann–Cartan spaces provided with nonholonomic distributions defined by generic off–diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart–Moffat and Finsler–Lag...

Here (the last paper in a series of eight) we end our presentation of the basics of a systematical approach to the differential geometry of smooth manifolds which uses the geometric algebras of multivector and extensors (fields) developed in previous papers. The theory of the Riemann and Ricci fields associated to a given geometric structure, i.e., a triple (M,γ, g) where M is a smooth manifold...

Bradley C. Davis: Medical Image Analysis via Fréchet Means of Diffeomorphisms. (Under the direction of Sarang C. Joshi.) The construction of average models of anatomy, as well as regression analysis of anatomical structures, are key issues in medical research, e.g., in the study of brain development and disease progression. When the underlying anatomical process can be modeled by parameters in ...

We exhibit a model structure on 2-Cat, obtained by transfer from sSet across the adjunction C2 ◦ Sd a Ex ◦ N2. A certain class of homotopies in this model structure turns out to be in 1-to-1 correspondence with strong simulations among labeled transitions systems, formalising the geometric intuition of simulations as deformations. The correspondence still holds in the cubical setting, character...

We consider geometric biomembranes governed by an L-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of t...

In this article, we give a perspective on several results, old and new, concerning geometric structures of moduli spaces of Riemann surfaces with respect to the L2 metric (Weil-Petersson metric) on deformations of hyperbolic metrics. In doing so, we aim to demonstrate that the Weil-Petersson metric is suited to account for the geometry of moduli spaces while the topological type, genus in parti...

The paper introduces a new alternative towards fabrication of auxetic metamaterials (materials with negative Poisson’s ratio) controlled by geometric transformations. These transformations are derived from the theory of small (infinitesimal) elastic deformation superimposed on finite elastic deformations. By using this theory, a cylindrical region filled with initial deformed foam is transforme...

In computer aided design (CAD), the availability of many types of surface editing which ease creating the geometric models is important. This paper describes a wavelets-based mulresolution representation for endpoint-interpolating cubic B-spline surface and algorithms to support the surface editing at different scales, allowing structural features (global shape) deformations as well as detail f...