In previous documents we have outlined an approach for the analysis of 2 and 3D shape vectors using measurement covariances for the situation where the measurements are known to be independent. The purpose of this document is to explain the mathematics required to extend this approach to “pseudolandmarks”, where information is provided at a given 2 or 3D location only in 1D. We show that the us...

The purpose of this paper is the assessment of a family of shape factors for oo-line signature veriication. The initial method, suggested in 1], which extracts geometric features, is modiied to assess the performance of veriication in the general case of forgery. W e c o n-tribute to the information coded by adapting the coding method to the image and by i n tegrating a spatial distance into th...

Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tens...

We propose two differential geometric representations of planar shapes using: (i) direction functions and (ii) curvature functions, of their boundaries. Under either representation, planar shapes are treated as elements of infinite-dimensional shape spaces. Pairwise differences between the shapes are quantified using the lengths of geodesics connecting them on the shape spaces. We specify the g...

A generator of Lie point symmetries admitted by a Lane–Emden equation of the second-kind for arbitrary shape factor k is used to determine invariant boundary conditions admitted by the equation. The generator of Lie point symmetries is then used to reduce the order of the Lane–Emden equation. A phase plane analysis of the reduced equation indicates that the stability of the invariant boundary c...

A method of shape generation using shape grammars which take shape as primitive and have shape-specific rules is presented. A formalism for the complete, generative specification of a class of non-representational, geometric paintings or sculptures is defined which has shape grammars as its structural component. Paintings are material representations of two-dimensional shapes gen~rated by shape...

In deformable model segmentation, the geometric training process plays a crucial role in providing shape statistical priors and appearance statistics that are used as likelihoods. Also, the geometric training process plays a crucial role in providing shape probability distributions in methods finding significant differences between classes. The quality of the training seriously affects the fina...

In the present work, six-layered (Zirconia/Nickel) functionally graded materials were fabricated via powder metallurgy technique (PMT). The microstructure, fracture surface and the elemental analysis of the prepared components were studied, and their linear shrinkage, electrical conductivity, fracture toughness and Vickers hardness were evaluated. The results show that the linear shrinkage of t...