Purpose: This study was to investigate the effect of irregularity in shape of field size of electron beam on the percentage depth dose and the output factor. Study the variety of the Percentage Depth Dose (PDD) and the output factors for rectangular and small field sizes when one of field dimensions less than the Practical Range (Rp) of the electron energy used. Compare the measured output fact...

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...

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...