Modelling of imaged ellipse intensity profiles using Euclidean geometry

Euclidean Geometry before non-Euclidean Geometry

In [3], in my argument for the primacy of Euclidean geometry on the basis of rigid motions and the existence of similar but non-congruent triangles, I wrote the following: A: “The mobility of rigid objects is now recognized as one of the things every normal human child learns in infancy, and this learning appears to be part of our biological progaramming.” B. “. . . we are all used to thinking ...

A Review of Geometry Based Symmetric Key Encryption Using Ellipse

Cryptography is the way to secure the data to achieve higher reliability during the communication process. There exist a number of cryptographic approaches. This paper defines a geometry based Symmetric cryptography algorithm that is used to encrypt the input data. As the name suggests the approach is based on the geometric figure to perform the cryptography. In this work, we will define an ell...

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

Basic Notions of Geometry and Euclidean Geometry

Non-Euclidean classification of medically imaged objects via s-reps

Classifying medically imaged objects, e.g., into diseased and normal classes, has been one of the important goals in medical imaging. We propose a novel classification scheme that uses a skeletal representation to provide rich non-Euclidean geometric object properties. Our statistical method combines distance weighted discrimination (DWD) with a carefully chosen Euclideanization which takes ful...