Basic Notation

1981 ◽  
pp. 1-2
Author(s):  
I. A. Ibragimov ◽  
R. Z. Has’minskii
Keyword(s):  
Basic Notation

Basic Notation and Definitions

1994 ◽  
pp. 21-30
Author(s):  
James S. Royer ◽  
John Case
Keyword(s):  
Basic Notation

Explaining feature detection Mechanisms: A Survey

2021 ◽  
pp. 51-64
Author(s):  
Ahmed A. Elngar ◽  
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◽  
◽  
◽  
...  
Keyword(s):  
Feature Detection ◽  
Feature Matching ◽  
Image Features ◽  
Mathematical Concepts ◽  
Detection Algorithms ◽  
Feature Detectors ◽  
Essential Components ◽  
Basic Notation ◽  
Computer Vision Applications ◽  
Detection Mechanisms

Feature detection, description and matching are essential components of various computer vision applications; thus, they have received a considerable attention in the last decades. Several feature detectors and descriptors have been proposed in the literature with a variety of definitions for what kind of points in an image is potentially interesting (i.e., a distinctive attribute). This chapter introduces basic notation and mathematical concepts for detecting and describing image features. Then, it discusses properties of perfect features and gives an overview of various existing detection and description methods. Furthermore, it explains some approaches to feature matching. Finally, the chapter discusses the most used techniques for performance evaluation of detection algorithms.

Spaces of Maps into Eilenberg-Maclane Spaces

1981 ◽  
Vol 33 (4) ◽  
pp. 782-785 ◽  
Author(s):  
Vagn Lundsgaard Hansen
Keyword(s):  
Main Tool ◽  
Homotopy Groups ◽  
Base Points ◽  
Continuous Maps ◽  
Basic Notation

In this note we provide alternative and unified proofs for two theorems on the homotopy groups of spaces of (continuous) maps into Eilenberg-MacLane spaces. The first theorem is due to Thorn, and independently Federer, and deals with spaces of maps into Eilenberg- MacLane spaces of type (π, n) for n ≧ 1 with π abelian. The second theorem is due to Gottlieb and deals with spaces of maps into Eilenberg- MacLane spaces of type (π, 1) with π nonabelian. As a main tool we shall use the homotopy sequences for certain fibrations of spaces of maps.2. Basic notation and some preliminary remarks. For any pair of connected CW-complexes X and Y with base points, we denote by M(X, Y), respectively F(X, Y), the space of free maps, respectively based maps, of X into Y.

Boolean extensions which efface the Mahlo property

1974 ◽  
Vol 39 (2) ◽  
pp. 254-268 ◽  
Author(s):  
William Boos
Keyword(s):  
Set Theory ◽  
Large Cardinals ◽  
Large Cardinal ◽  
Boolean Algebras ◽  
Partial Coverage ◽  
Transitive Model ◽  
Consistency Results ◽  
Lower Case ◽  
Basic Notation ◽  
Generic Extensions

The results that follow are intended to be understood as informal counterparts to formal theorems of Zermelo-Fraenkel set theory with choice. Basic notation not explained here can usually be found in [5]. It will also be necessary to assume a knowledge of the fundamentals of boolean and generic extensions, in the style of Jech's monograph [3]. Consistency results will be stated as assertions about the existence of certain complete boolean algebras, B, C, etc., either outright or in the sense of a countable standard transitive model M of ZFC augmented by hypotheses about the existence of various large cardinals. Proofs will usually be phrased in terms of the forcing relation ⊩ over such an M, especially when they make heavy use of genericity. They are then assertions about Shoenfield-style P-generic extensions M(G), in which the ‘names’ are required without loss of generality to be elements of MB = (VB)M, B is the boolean completion of P in M (cf. [3, p. 50]: the notation there is RO(P)), the generic G is named by Ĝ ∈ MB such that (⟦p ∈ Ĝ⟧B = p and (cf. [11, p. 361] and [3, pp. 58–59]), and for p ∈ P and c1, …, cn ∈ MB, p ⊩ φ(c1, …, cn) iff ⟦φ(c1, …, cn)⟧B ≥ p (cf. [3, pp. 61–62]).Some prior acquaintance with large cardinal theory is also needed. At this writing no comprehensive introductory survey is yet in print, though [1], [10], [12]and [13] provide partial coverage. The scheme of definitions which follows is intended to fix notation and serve as a glossary for reference, and it is followed in turn by a description of the results of the paper. We adopt the convention that κ, λ, μ, ν, ρ and σ vary over infinite cardinals, and all other lower case Greek letters (except χ, φ, ψ, ϵ) over arbitrary ordinals.

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