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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

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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

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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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Outputs

PS or DVI ?

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Outputs

.dvi file

.pdf file

.ps file

.html file

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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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Writing and Publishing of Book

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Integrating Stastical Software with LATEX

Sweave

knitr

MATweave

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Use the right tool for the right job

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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

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THANK YOU