We provide a geometric interpretation of a new rational Landen transformation and establish the convergence of its iterates.

The aim of this paper is to investigate the geometrical behavior of the TVL1 model used in image processing, by making use of the notion of Cheeger sets. This mathematical concept was recently related to the celebrated Rudin-Osher-Fatemi image restoration model, yielding important advances in both fields. We provide the reader with a geometrical characterization of the TVL1 model. We show that,...

The problem of diagnostic filter design is studied. Algebraic and geometric approaches to solving this problem are investigated. Some relations between these approaches are established. New definitions of fault detectability and isolability are formulated. On the basis of these definitions, a procedure for diagnostic filter design is given in both algebraic and geometric terms.

It is well-known that fisheye cameras can be very useful in real applications due to their large field of view when compared to classic perspective cameras. This paper considers the fundamental problem of multiple-view triangulation for fisheye cameras. A geometric criterion is introduced in this paper for this problem, which consists of determining the scene point that minimizes the angles bet...

Human actions are the essence of a human life and a natural product of the human mind. Analysis of human activities by a machine has attracted the attention of many researchers. This analysis is very important in a variety of domains including surveillance, video retrieval, human-computer interaction, athlete performance investigation, etc. This dissertation makes three major contributions to a...

The geometry of “empty” scale space is investigated. By virtue of the proposed geometric axioms the generating PDE, the linear isotropic heat equation, can be presented in covariant, or geometrical form. The postulate of a metric for scale space cannot be upheld, as it is incompatible with the generating equation. Two familiar instances of scale spaces consistent with the geometric axioms are c...

This paper introduces a new and very effective method for high-precision geometric calibration of digital cameras. The internal and external geometry are estimated: (1) by extracting features with subpixel accuracy from various views of a planar calibration plate; and (2) by mapping these feature sets into the corresponding points of the undistorted and rectified image that would be generated b...

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to define Clifford algebras with scalars in arbitrary rings and provides new suggestions for an infinite-dimensional approach. Furthermore, I give a quick review...

Methods of window matching to estimate 3D points are the most serious factors affecting the accuracy, robustness, and computational cost of Multi-View Stereo (MVS) algorithms. Most existing MVS algorithms employ window matching based on Normalized CrossCorrelation (NCC) to estimate the depth of a 3D point. NCC-based window matching estimates the displacement between matching windows with sub-pi...

nature displays profound preference for certain specific ratios to design her life-forms. these are geometric relationships that are transcendent and originated from sacred geometry. the view that geometry had a ritual origin is a part of a wider view that civilization itself had a ritual origin, and therefore the history of utilization of sacred geometry by man goes back to many centuries ago....