scholarly journals ADVANCES IN MULTIDIMENSIONAL SIZE THEORY

2011 ◽  
Vol 29 (1) ◽  
pp. 19 ◽  
Author(s):  
Andrea Cerri ◽  
Patrizio Frosini
Keyword(s):  
Computer Vision ◽  
Pattern Recognition ◽  
Continuous Functions ◽  
Research Topic ◽  
Topological Spaces ◽  
Topological Approach ◽  
Shape Comparison ◽  
Size Function ◽  
Multidimensional Information ◽  
Vector Valued

Size Theory was proposed in the early 90's as a geometrical/topological approach to the problem of Shape Comparison, a very lively research topic in the fields of Computer Vision and Pattern Recognition. The basic idea is to discriminate shapes by comparing shape properties that are provided by continuous functions valued in R, called measuring functions and defined on topological spaces associated to the objects to be studied. In this way, shapes can be compared by using a descriptor named size function, whose role is to capture the features described by measuring functions and represent them in a quantitative way. However, a common scenario in applications is to deal with multidimensional information. This observation has led to considering vector-valued measuring functions, and consequently the multidimensional extension of size functions, namely the k-dimensional size functions. In this work we survey some recent results about size functions in this multidimensional setting, with particular reference to the localization of their discontinuities.

scholarly journals Vector Measures on Topological Spaces

2007 ◽  
Vol 14 (4) ◽  
pp. 687-698
Author(s):  
Surjit Singh Khurana
Keyword(s):  
Continuous Functions ◽  
Linear Operators ◽  
Topological Spaces ◽  
Vector Measures ◽  
Completely Regular ◽  
Measure Representation ◽  
Integrable Functions ◽  
Linear Maps ◽  
Vector Case ◽  
Vector Valued

Abstract Let 𝑋 be a completely regular Hausdorff space, 𝐸 a quasi-complete locally convex space, 𝐶(𝑋) (resp. 𝐶𝑏(𝑋)) the space of all (resp. all, bounded), scalar-valued continuous functions on 𝑋, and 𝐵(𝑋) and 𝐵0(𝑋) be the classes of Borel and Baire subsets of 𝑋. We study the spaces 𝑀𝑡(𝑋,𝐸), 𝑀 τ (𝑋,𝐸), 𝑀 σ (𝑋,𝐸) of tight, τ-smooth, σ-smooth, 𝐸-valued Borel and Baire measures on 𝑋. Using strict topologies, we prove some measure representation theorems of linear operators between 𝐶𝑏(𝑋) and 𝐸 and then prove some convergence theorems about integrable functions. Also, the Alexandrov's theorem is extended to the vector case and a representation theorem about the order-bounded, scalar-valued, linear maps from 𝐶(𝑋) is generalized to the vector-valued linear maps.

scholarly journals R-continuous functions

1992 ◽  
Vol 15 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Ch. Konstadilaki-Savvapoulou ◽  
D. Janković
Keyword(s):  
Continuous Functions ◽  
Strong Form ◽  
Topological Spaces ◽  
Strong Continuity ◽  
Closed Graph ◽  
Continuity Properties

A strong form of continuity of functions between topological spaces is introduced and studied. It is shown that in many known results, especially closed graph theorems, functions under consideration areR-continuous. Several results in the literature concerning strong continuity properties are generalized and/or improved.

Computer Vision and robotics in postal automation

1999 ◽  
Vol 18 (3-4) ◽  
pp. 265-273
Author(s):  
Giovanni B. Garibotto
Keyword(s):  
Image Processing ◽  
Computer Vision ◽  
Pattern Recognition ◽  
Material Handling ◽  
State Of The Art ◽  
Short Description ◽  
The Other ◽  
Functional Requirements ◽  
Postal Automation ◽  
And Robotics

The paper is intended to provide an overview of advanced robotic technologies within the context of Postal Automation services. The main functional requirements of the application are briefly referred, as well as the state of the art and new emerging solutions. Image Processing and Pattern Recognition have always played a fundamental role in Address Interpretation and Mail sorting and the new challenging objective is now off-line handwritten cursive recognition, in order to be able to handle all kind of addresses in a uniform way. On the other hand, advanced electromechanical and robotic solutions are extremely important to solve the problems of mail storage, transportation and distribution, as well as for material handling and logistics. Finally a short description of new services of Postal Automation is referred, by considering new emerging services of hybrid mail and paper to electronic conversion.

scholarly journals Binary Image Classification: A Genetic Programming Approach to the Problem of Limited Training Instances

2016 ◽  
Vol 24 (1) ◽  
pp. 143-182 ◽  
Author(s):  
Harith Al-Sahaf ◽  
Mengjie Zhang ◽  
Mark Johnston
Keyword(s):  
Computer Vision ◽  
Pattern Recognition ◽  
Genetic Programming ◽  
Visual System ◽  
Image Classification ◽  
Human Visual System ◽  
Binary Classification ◽  
Programming Approach ◽  
Data Sets ◽  
New Class

In the computer vision and pattern recognition fields, image classification represents an important yet difficult task. It is a challenge to build effective computer models to replicate the remarkable ability of the human visual system, which relies on only one or a few instances to learn a completely new class or an object of a class. Recently we proposed two genetic programming (GP) methods, one-shot GP and compound-GP, that aim to evolve a program for the task of binary classification in images. The two methods are designed to use only one or a few instances per class to evolve the model. In this study, we investigate these two methods in terms of performance, robustness, and complexity of the evolved programs. We use ten data sets that vary in difficulty to evaluate these two methods. We also compare them with two other GP and six non-GP methods. The results show that one-shot GP and compound-GP outperform or achieve results comparable to competitor methods. Moreover, the features extracted by these two methods improve the performance of other classifiers with handcrafted features and those extracted by a recently developed GP-based method in most cases.

scholarly journals Diameter-preserving linear bijections of function spaces

2001 ◽  
Vol 70 (3) ◽  
pp. 323-336 ◽  
Author(s):  
T. S. S. R. K. Rao ◽  
A. K. Roy
Keyword(s):  
Maximal Ideal ◽  
Convex Set ◽  
Compact Convex ◽  
Extreme Points ◽  
Continuous Functions ◽  
Ideal Space ◽  
Function Algebras ◽  
Compact Convex Set ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractIn this paper we give a complete description of diameter-preserving linear bijections on the space of affine continuous functions on a compact convex set whose extreme points are split faces. We also give a description of such maps on function algebras considered on their maximal ideal space. We formulate and prove similar results for spaces of vector-valued functions.

scholarly journals On Softβ-Open Sets and Softβ-Continuous Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Metin Akdag ◽  
Alkan Ozkan
Keyword(s):  
Continuous Functions ◽  
Soft Set ◽  
Topological Spaces

We introduce the concepts softβ-interior and softβ-closure of a soft set in soft topological spaces. We also study softβ-continuous functions and discuss their relations with soft continuous and other weaker forms of soft continuous functions.

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