statistical methods in analyzing the shape of maxillary dental arches for dental applications norli

239 Pages·2016·9.36 MB·English

STATISTICAL METHODS IN ANALYZING THE SHAPE OF
MAXILLARY DENTAL ARCHES FOR DENTAL
APPLICATIONS

NORLI ANIDA BINTI ABDULLAH

FACULTY OF SCIENCE
UNIVERSITY OF MALAYA
KUALA LUMPUR

2016
STATISTICAL METHODS IN ANALYZING THE SHAPE OF
MAXILLARY DENTAL ARCHES FOR DENTAL APPLICATIONS

NORLI ANIDA BINTI ABDULLAH

THESIS SUBMITTED IN FULFILLMENT
OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

FACULTY OF SCIENCE
UNIVERSITY OF MALAYA
KUALA LUMPUR

2016
UNIVERSITY OF MALAYA
ORIGINAL LITERARY WORK DECLARATION

Name of Candidate: Norli Anida Binti Abdullah (I.C No: 851121-14-6336)
Registration/Matric No: SHB090010
Name of Degree: Doctor of Philosophy
Title of Project Paper/Research Report/Dissertation/Thesis (“this Work”):
STATISTICAL METHODS IN ANALYZING THE SHAPE OF MAXILLARY
DENTAL ARCHES FOR DENTAL APPLICATIONS

Field of Study:
Applied Statistics
I do solemnly and sincerely declare that:
(1) I am the sole author/writer of this Work;
(2) This Work is original;
(3) Any use of any work in which copyright exists was done by way of fair
dealing and for permitted purposes and any excerpt or extract from, or
reference to or reproduction of any copyright work has been disclosed
expressly and sufficiently and the title of the Work and its authorship have
been acknowledged in this Work;
(4) I do not have any actual knowledge nor do I ought reasonably to know that
the making of this work constitutes an infringement of any copyright work;
(5) I hereby assign all and every rights in the copyright to this Work to the
University of Malaya (“UM”), who henceforth shall be owner of the
copyright in this Work and that any reproduction or use in any form or by any
means whatsoever is prohibited without the written consent of UM having
been first had and obtained;
(6) I am fully aware that if in the course of making this Work I have infringed
any copyright whether intentionally or otherwise, I may be subject to legal
action or any other action as may be determined by UM.

Candidate’s Signature Date:

Subscribed and solemnly declared before,

Witness’s Signature Date:

Name:
Designation:

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ABSTRACT
This study aimed to propose shape features and statistical shape models to
develop a novel shape discrimination procedure for the maxillary dental arch with
important applications in dentistry. Standardized digital images of randomly selected
dental casts were obtained and the image calibration and registration were attended to
enable comparison of shape of the dental arches. A collective teeth positions from the
digital images were proposed as a novel shape feature of the dental arch. Each tooth
position is established from origin defined from stable anatomical landmarks. The mean
shape category obtained from clustering method and the probability distribution of each
shape category was further investigated to provide better statistical inference for the
shape models of the dental arch. A modified COVRATIO statistics which incorporates
the problem of small sample size and minimal model assumptions was then proposed as
a discrimination method of shape and compared to the linear discrimination method.
The proposed shape discrimination method was then used to determine suitable arch
shape and indicate natural teeth positions. The results from this study show that
multivariate normal and multivariate complex normal shape models together with the
use of the proposed discrimination method can be used to discriminate shape of the
dental arch. Consequently guides to determining suitable impression trays and
predicting teeth positions for the edentulous patients (patients with all teeth missing) are
provided. Verification of the proposed guides show that 91.42% of the sample studied
indicates appropriate fitting to the resultant impression trays, and the original teeth
positions (with an average error of 0.95 mm for each tooth position) were adequately
estimated by 80% of the arches studied. The presented statistical methods may be
beneficial in assisting inexperienced dentists and dental laboratory technicians to choose
the most appropriate impression tray and to determine natural teeth positions for the
Malaysian population.
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ABSTRAK

Kajian ini mencadangkan ciri-ciri serta model bentuk statistik untuk
menghasilkan prosedur diskriminasi yang baru bagi bentuk arkus pergigian pada rahang
atas dengan aplikasi penting dalam bidang pergigian. Imej digital yang seragam dari
acuan pergigian dipilih secara rawak dan penentukuran serta padanan imej dilakukan
untuk membolehkan perbandingan bentuk arkus pergigian. Kedudukan gigi secara
kolektif dari imej-imej digital dicadangkan sebagai ciri-ciri bentuk arkus pergigian yang
baru. Setiap kedudukan gigi ditentukan daripada penanda anatomi yang stabil. Nilai
purata setiap kategori bentuk dianggarkan daripada kaedah kelompok dan taburan
kebarangkalian setiap kategori bentuk seterusnya disiasat untuk memberikan inferens
statistik yang lebih baik untuk model bentuk arkus pergigian. Statistik COVRATIO
yang diubahsuai untuk disesuaikan dengan masalah saiz sampel yang kecil dan andaian
model yang minimum kemudiannya dicadangkan sebagai kaedah diskriminasi bentuk
serta dibandingkan dengan fungsi diskriminasi linear. Kaedah diskriminasi yang
dicadangkan ini kemudiannya digunakan untuk menentukan bentuk arkus dan
kedudukan gigi asal. Hasil daripada kajian ini menunjukkan bahawa model bentuk
multivariat normal dan multivariat kompleks normal dengan kombinasi kaedah
diskriminasi yang dicadangkan boleh digunakan untuk membezakan bentuk arkus
pergigian. Ini seterusnya membolehkan dua panduan dicadangkan dalam pemilihan
ceper impresi yang sesuai dan meramalkan kedudukan gigi untuk pesakit edentulus
(pesakit dengan ketiadaan gigi). Kajian pengesahan untuk panduan-panduan yang
dicadangkan menunjukkan bahawa 91.42% daripada sampel yang dikaji menunjukkan
pemilihan ceper impresi yang sesuai, dan 80% daripada arkus pergigian yang dikaji
boleh menganggarkan kedudukan gigi asal (dengan ralat purata 0.95 mm untuk setiap
posisi gigi). Kaedah statistik yang dicadangkan boleh dimanfaatkan dalam membantu
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doktor gigi dan juruteknik makmal pergigian yang tidak berpengalaman untuk memilih
ceper impresi yang sesuai dan memudahkan anggaran kedudukan gigi asal untuk
penduduk Malaysia.

v
To my honey, Hafiz

To my awesome buddies, Iqbal & Yati
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ACKNOWLEDGEMENTS

Praise to the Almighty, for giving me the strength to complete this work and
blessed me with loving people around me.
My greatest gratitude goes to my respected supervisors Assoc. Prof. Dr. Omar
Mohd Rijal and Assoc. Prof. Dr. Zakiah Mohd Isa for their guidance throughout my
study. Their supervision has taught me to appreciate knowledge by heart and never
giveup on your dreams.
Special thanks to Assoc. Prof. Dr. Yong Zulina, Dr. Ali Zaid, Dr. Mamun,
Professor Dr. Hanif, Professor Dr. Imon, Professor Dr. Rao and Professor Dr. Sahar for
their willingness to read through my thesis and suggest necessary improvements. To my
friends Iqbal, Yati, Omar, Adia, Adzhar, Rany, Dela, Siti, Zanariah, Faizol, and
Hafrizal, Kuna, Katz, Laili, Maz and Meksu, thank you for always being there, listening
and motivating me throughout these years – you guys are the best. Not forgetting the
staff at the Center of Foundation Study in Science, Institute of Mathematical Science
and Dean Office of Faculty of Science for their assistance right up to the completion of
this thesis.
My heartfelt appreciation goes to my beloved husband, for his continuous love
and the shoulder that I always look for to cry on. To mak, abah, mama, papa, my
siblings, and my favourite uncle Pak itam, thank you for your continuous prayers which
have driven me to complete this thesis. Not forgetting my two boys, Hamza and Aqeel,
that would never fail to make me smile everyday.
To my late sister, Maria, I miss you so much and may Allah place you in a
garden of paradise with the righteous ones.

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TABLE OF CONTENTS

ABSTRACT iii
ABSTRAK iv
ACKNOWLEDGEMENT vii
TABLE OF CONTENTS viii
LIST OF FIGURES xv
LIST OF TABLES xx
LIST OF SYMBOLS AND ABBREVIATIONS xxv
LIST OF APPENDICES xxvii

CHAPTER 1: INTRODUCTION 1
1.1 General Introduction: Shape Analysis 1
1.2 Relevance of Shape in Dentistry 2
1.3 Issues Related to Shape Analysis of the Dental Arch in Dentistry 3
1.3.1 Discriminating Shape of the Dental Arch 3
1.3.2 Shape Feature of the Dental Arch 3
1.3.3 Statistical Shape Model of the Dental Arch 4
1.3.4 Issues with Stock Impression Trays 5
1.3.5 Issues with Rehabilitating the Edentulous Patients 5
1.4 Objectives of the Study 6
1.5 Thesis Outline 6

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CHAPTER 2: LITERATURE REVIEW 9
2.1 Shape Analysis from Digital Images: Image Acquisition and Storing 9
2.2 Quantitative Description of the Dental Shape from 2D Images 12
2.2.1 Multivariate Morphometrics 12
2.2.2 Boundary Morphometrics 13
2.3 Discrete Fourier Transform (DFT) 18
2.3.1 Derivation of DFT 19
2.3.2 Application of DFT in 2D Shape Analysis 20
2.4 Shape Classification from Digital Images 22
2.4.1 Shape Alignment: Comparing two or more Arch Shapes 22
2.4.2 Arch Shape Classification 24
2.5 Statistical Shape Model of the Dental Arches 26
2.6 Discrimination of Shape 33
2.7 Multivariate Normal Distribution and its Tests 34
2.7.1 Mardia’s Multivariate Skewness and Kurtosis Tests 35
2.7.2 Doornik and Hansen Omnibus Test 36
2.7.3 Royston Test 38
2.7.4 Henze-Zirkler Test 40
2.8 Multivariate Complex Normal Distribution (MVCN) 41
2.8.1 The Univariate and Multivariate Complex Random Variables and
Distributions 42
2.8.2 Properties of the MVCN Distribution 43
2.8.3 Parameter Estimation and Hypothesis testing of the MVCN
Distribution 44
2.9 Missing Values Analysis 47
2.9.1 Data Augmentation (DA) Algorithm 47
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