Post on 03-Feb-2023
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Using The Right Tool For The Right Job:
An Introduction To LATEX
Gabriel Obed Fosugabrielobedpeters@gmail.comDepartment of Mathematics
March 2014
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What is LATEX
TeX pronounced “Tech“, is a markup language created byDonald Knuth to typeset documents attractively andconsistently.
LaTeX also pronounced either “Lah-tech“ or, less often,“Lay-tech” is a macro package based on TeX created by LeslieLamport. Its purpose is to simplify TeX typesetting, especiallyfor documents containing mathematical formulae.
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What is Needed
LATEX works on all operating systems.
( MikTeX for windows
( TexLive for Linux
( MacTeX for Mac Ox
LATEX editors
TeXstudio, TeXniccenter, kile, winedit, winshell, TeXshop
Referencing
Jabref and Java
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Why Should I Use LATEX
( Very powerful control of document generation,particularly large technical documents
( Very easy for formatting, numbering, andreferencing
( You can learn all about it in a couple of hours.
( It is the standard for scientific documents
( Easy processing mathematical symbols andformulas
( The ability to comment and suppress
( Its FREE
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Why Should I Use LATEX
( Very powerful control of document generation,particularly large technical documents
( Very easy for formatting, numbering, andreferencing
( You can learn all about it in a couple of hours.
( It is the standard for scientific documents
( Easy processing mathematical symbols andformulas
( The ability to comment and suppress
( Its FREE
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Why Should I Use LATEX
( Very powerful control of document generation,particularly large technical documents
( Very easy for formatting, numbering, andreferencing
( You can learn all about it in a couple of hours.
( It is the standard for scientific documents
( Easy processing mathematical symbols andformulas
( The ability to comment and suppress
( Its FREE
Beamer Poster
Why Should I Use LATEX
( Very powerful control of document generation,particularly large technical documents
( Very easy for formatting, numbering, andreferencing
( You can learn all about it in a couple of hours.
( It is the standard for scientific documents
( Easy processing mathematical symbols andformulas
( The ability to comment and suppress
( Its FREE
Beamer Poster
Why Should I Use LATEX
( Very powerful control of document generation,particularly large technical documents
( Very easy for formatting, numbering, andreferencing
( You can learn all about it in a couple of hours.
( It is the standard for scientific documents
( Easy processing mathematical symbols andformulas
( The ability to comment and suppress
( Its FREE
Beamer Poster
Why Should I Use LATEX
( Very powerful control of document generation,particularly large technical documents
( Very easy for formatting, numbering, andreferencing
( You can learn all about it in a couple of hours.
( It is the standard for scientific documents
( Easy processing mathematical symbols andformulas
( The ability to comment and suppress
( Its FREE
Beamer Poster
Why Should I Use LATEX
( Very powerful control of document generation,particularly large technical documents
( Very easy for formatting, numbering, andreferencing
( You can learn all about it in a couple of hours.
( It is the standard for scientific documents
( Easy processing mathematical symbols andformulas
( The ability to comment and suppress
( Its FREE
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Numbering In LaTeX
Figures
Tables
Equations
Table of Contents
List of Figures
List of Tables
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Referencing In LaTeX
JabRef is an open source bibliography reference manager.
Article
Conference
Incollection
Thesis
Patent
Proceedings
Unpublished
Standard
Inbook
Book
Electronic
Inproceedings
Periodical
Booklets
Techreport
Manual
Misc
Other
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Referencing In LaTeX
JabRef is an open source bibliography reference manager.
Article
Conference
Incollection
Thesis
Patent
Proceedings
Unpublished
Standard
Inbook
Book
Electronic
Inproceedings
Periodical
Booklets
Techreport
Manual
Misc
Other
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Beamer
This is LATEX class for creating presentations.
A Beamer presentation is like any other LaTeX document:
The body contains sections and subsections.The different slides are put in environments.Slides are structured using itemize and enumerateenvironments, or plain text.
ExampleBEAMER
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Poster
What is a Poster?
Describe a work in progress
The job of a poster is to get people talking to you aboutyour research.
A simple result that you are proud of
How you applied an existing technique to a new problem
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Poster
What is a Poster?
Describe a work in progress
The job of a poster is to get people talking to you aboutyour research.
A simple result that you are proud of
How you applied an existing technique to a new problem
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Digital Image Processing Via Singular Value Decomposition
G. K. Gogovigideonobama@hotmail.com
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi.
abstractIn this paper, well studied linear algebra theory “singular value decomposition" andits applications is presented. Singular Value Decomposition is extraordinarily usefuland has many applications such as signal processing, pattern recognition, objectsdetection and weather prediction. Some of these application areas discussed includethe Moore-Penrose psuedoinverse, the the low rank approximation of matrices andimage face recognition. To perform face recognition with SVD, we treated the set ofknown faces as vectors in a subspace, called “face space", spanned by a small groupof “basefaces". The projection of a new image onto the baseface is then compared tothe set of known faces to identify the face. We also investigated the characteristicsof singular values and singular vectors in image processing. MATLAB R2012a isused as the development tool for implementing the algorithm.
IntroductionSingular value decomposition (SVD) was developed in the mid 19th century but mostof its applications are emerged in the 21st century (Soumya, & Soman, 2009). SVD forsquare matrices was developed by E. Beltrami (1873), C. Jordan (1874), J. J. Sylvester(1889) and Autonne (1915). Eckart and Young developed SVD in the 1930s for rectangularmatrices. Many modern computational algorithms are based on SVD because the problemof computing the eigenvalues of a general matrix is well-conditioned. In numerical analysis,the SVD provides a measure of the effective rank of a given matrix. In statistics and timeseries analysis, the SVD is a particularly useful tool for finding least-squares solutions andapproximations.
SVD and Image ProcessingIn SVD transformation, an m×n matrix A can be decomposed into three matrices thatare of the same size as the original matrix. The SVD of A is defined as
A = USV T (1)where U and V are orthogonal matrices and S is a diagonal matrix whose diagonalentries are the singular values.According to Robert M. Gray and David L. Neuhoff, a digital image is a discrete two-dimensional function, f (x, y) which has been quantized over its domain and range. Thedistinct coordinates in this image is the pixel. This is summarized in the figure below.
f (x, y) =
f (0, 0) f (0, 1) · · · f (0, Y − 1)f (1, 0) f (1, 1) · · · f (1, Y − 1)
... ... ... ...f (X − 1, 0) f (X − 1, 1) · · · f (X − 1, Y − 1)
Formulae for FR with SVDWe redefined the matrix A as set of the training face. Assume each face image hasm × n = M pixels, and represented as an M × 1 column vector fi , a ‘training set’ Swith N number of face images of known individuals forms an M ×N matrix:S = [f1, f2, f3, ..., fN ]The mean image f of set S, is given by
f = 1N
N∑
i=1fi (2)
A = [a1, a2, ..., aN ]M×N , where ai = fi − f, i = 1, 2, 3, ..., N.Since {u1, u2, ..., ur} form an orthonormal basis for R(A). Then the scalar projection off − f onto the basefaces is
X = [u1, u2, ..., ur]T (f − f )This coordinate vector X is used to find which of the training faces best describes theface f . That is to find some training face fi, i = 1, 2, ..., N , that minimizes the distance:
εi =‖ X −Xi ‖2= [(X −Xi)T (X −Xi)]12 (3)
Number of face images used, N = 40 and ε0 = threshold (Jain & Gautam, 2012).
Flowchart of FR with SVD
Image Data
From training set?
Compute themean face f
ai = fi − f , create A
Calculate theSVD of A
Compute the vectorXi in the basespace
Computethe vector
X inbasespace
εi =‖ X − Xi ‖2
εi ≤ ε0?
Face is in thetraining set
Face not in thetraining set
Yes
No
YesNo
Figure 1: Flow chart of Face Recognition with SVD
RGB Images of the Training Set
Figure 2: Grayscale Images of the Training Set
Figure 3: Meanface of the 10Training Set Im-ages
Figure 4: Meanface of all the 40Training Set Im-ages
Result of Exchanged SVs with Singular Vectors for three faceimages
1U1S1V T1
2U1S1V T2
3U1S1V T3
10U1S2V T1
11U1S2V T2
12U1S2V T3
4U2S1V T1
5U2S1V T2
6U2S1V T3
13U2S2V T1
14U2S2V T2
15U2S2V T3
7U3S1V T1
8U3S1V T2
9U3S1V T3
16U3S2V T1
17U3S2V T2
18U3S2V T3
19U1S3V T1
20U1S3V T2
21U1S3V T3
1U1S1V T1
10U1S2V T1
19U1S3V T1
22U2S3V T1
23U2S3V T2
24U2S3V T3
5U2S1V T2
14U2S2V T2
23U2S3V T2
25U3S3V T1
26U3S3V T2
27U3S3V T3
9U3S1V T3
18U3S2V T3
27U3S3V T3
Exchanged SVs with Singular Vectors for a face image and aflower
(a)U1S1V T1
(b)U2S1V T1
(c)U1S2V T1
(d)U2S2V T1
(a)U1S1V T1
(c)U1S2V T1
(e)U1S1V T2
(f )U2S1V T2
(g)U1S2V T2
(h)U2S2V T2
(h)U2S2V T2
(f )U2S1V T2
ConclusionBased on the theory and result of experiments, it was found that singular value decom-position is a stable and effective method to decompose a system into a set of linearlyindependent components.The SVD approach is robust, simple, easy and fast to implement. It provides a practicalsolution to image recognition problem. Finally, from the result we see that, though thesingular values are unique, the singular vectors are more important for image processing.
References1. Jain, P., & Gautam, B. (2012). Performance estimation for face recognition using SVD.International Journal of Engineering and Innovative Technology (IJEIT), 2 , 361-364.2. Soumya, T., Soumya, V., & Soman, K. (2009). Singular value decomposition a classroomapproach. International Journal of Recent Trends in Engineering, 1.
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Paper Publication
Most journal have the template in LaTeX.
About 95% of the journals in the Thomson Reutersmaster list accept manuscript in LATEXformat.
How do you get your paper published if do not know howto use LaTeX
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Accounting, Organizations and Society
Advanced Engineering Informatics
Advances in Applied Mathematics
Agriculture, Ecosystems & Environment
Biochemical Engineering Journal
British Journal of Medical and Surgical Urology
Computer Communications
Economic Modelling
Food Chemistry
Human Pathology
Journal of English for Academic Purposes
Management Accounting Research
Physics Letters
Technological Forecasting and Social Change
Zoology
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How to get LaTeX on Your Machine
MiKTeX
MiKTeX is a typesetting system for Microsoft Windows.Go the the website http://www.miktex.org/
TeXstudio
TeXstudio is a cross-platform open source LaTeX editor.Go the the website http://texstudio.sourceforge.net/
Jabref
JabRef is a reference management software that uses BibTeXas its native format.Go the the websitehttp://jabref.sourceforge.net/download.php