We proceed with our recently-introduced geometric approach to sampling of manifolds and investigate the relationship that exists between the classical, i.e. Shannon type, and geometric sampling concepts and formalism. Some aspects of coding and the Gaussian channel problem are considered. A geometric version of Shannon’s Second Theorem is introduced. Applications to Pulse Code Modulation and Ve...

Suppose C is a [n, k, d] code over Fq, t < n is a positive integer. For any received vector y = (y1, · · · , yn) ∈ Fq , we refer to any code word c in C satisfying d(c,y) ≤ t as a tconsistent code word. A decoding problem is in fact the problem of finding an effective (or efficient) algorithm which can find t-consistent code words, and we call such an algorithm a decoding algorithm that can cor...

Relationships that exist between the classical, Shannontype, and geometric-based approaches to sampling are investigated. Some aspects of coding and communication through a Gaussian channel are considered. In particular, a constructive method to determine the quantizing dimension in Zador’s theorem is provided. A geometric version of Shannon’s Second Theorem is introduced. Applications to Pulse...

This paper addresses the subject which is too often overlooked in the analysis of a geometric model for wireless channel – the axioms corresponding to a priori properties of the channel that is modeled using geometric approach must represent realistic wave propagation. When constructing a model of propagation channel, people often create a substitute by giving an arbitrary shape or form to scat...

In geometric modeling of curves and surfaces, the overall shape of an individual patch is intuitively governed by the placement of control points, and a patch may be finely tuned by altering the weights of the basis functions—large weights pull the patch towards the corresponding control points. The control points also have a global meaning as the patch lies within the convex hull of the contro...

The geometric codes are the duals of the codes defined by the designs associated with finite geometries. The latter are generalized Reed-Muller codes, but the geometric codes are, in general, not. We obtain values for the minimum weight of these codes in the binary case, using geometric constructions in the associated geometries, and the BCH bound from coding theory. Using Hamada’s formula, we ...

The geometric codes are the orthogonals of the codes defined by the designs associated with finite geometries. The latter are generalized Reed-Muller codes, but the geometric codes are, in general, not. We obtain values for the minimum weight of these codes in the binary case, using geometric constructions in the associated geometries, and the BCH bound from coding theory. Using Hamada’s formul...

In this paper, a modified algorithm for object segmentation of binary images is presented, and denoted as 2D modified chain code algorithm. The 2D modified chain code algorithm can be applied to color images after being binarized. The segmented object is used to derive the chain code in the image. The definition of the 2Dmodified chain code algorithm is valid for shapes composed of triangular, ...

Existing 3-dimensional acoustic target tracking methods that use wired/wireless networked sensor nodes to track targets based on four sensing coverage do not always compute the feasible spatio-temporal information of target objects. To investigate this discrepancy in a formal setting, we propose a geometric model of the target tracking problem alongside its equivalent geometric dual model that ...

Real world computer vision applications pose many threats, not being able to capture a single large sized scene with the given imaging devices such as satellite sensor, camera or scanner in a single stretch because of their inherent limitations. This results in capturing large image in terms of split images. Later, these split images are to be mosaiced to create a single large image. This paper...