An investigation on 3D shape similarity assessment
for design re-usage
by
Quan lulin
全璐琳
Master of Science in Electromechanical Engineering
2009
Faculty of Science and Technology
University of Macau
An investigation on 3D shape similarity assessment
for design re-usage
by
Quan lulin
A thesis submitted in partial fulfillment of the
requirements for the degree of
Master of Science (M. Sc.)
In
Electromechanical Engineering
Faculty of Science and Technology
University of Macau
2009
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Supervisor
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__________________________________________________
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Date __________________________________________________________
In presenting this thesis in partial fulfillment of the requirements for a Master's
degree at the University of Macau, I agree that the Library and the Faculty of
Science and Technology shall make its copies freely available for inspection.
However, reproduction of this thesis for any purposes or by any means shall
not be allowed without my written permission. Authorization is sought by
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T
ABSTRACT
his thesis proposed a novel integrated Similarity Assessment Method (SAM)
particularly suitable for the 3D shape design re-usage domain, and focused on the
shape descriptor representation, algorithm development, similarity computation,
and shape query interface.
The popularity of CAD/CAM technique in product design and manufacturing industry
has resulted in a large number of 3D shapes being generated. This provides the
possibility to use customized design by applying shape re-usage technology, where
existing shapes are retrieved and redesigned to obtain a new product. Shape re-usage
could result in a marked increase in product variability to fulfill various customer
demands, while not causes a significant increase in design and manufacturing cost. One
of the key points of implementing shape re-usage technology is how to efficiently assess
the similarity levels between the newly designed model and customer’s intention. SAMs
for 3D shapes have been studied for decades, and well documented in literatures.
However, the SAMs designed particularly for the 3D shape re-usage domain are rare.
To explore a suitable SAM on the 3D shape re-usage domain, firstly, a survey on the
current content based SAMs for 3D models was carried out. Secondly, University of
Macau Database of Shoes shapes (UMDS) was also built and organized into different
categories of re-used features, in addition to the Princeton shape benchmarking (PSB),
for the purpose of providing basic platform for further experiments. It follows a problem
analysis, where the functional requirements and specific characteristics of 3D shape
re-usage were investigated and matched to prevailing similarity measures. The matched
SAMs were implemented, and their algorithm performances were verified via a
preliminary experiment. The experiment methods, including the common indicators
“precision-recall diagram (P-R)”, “Express classification case study”, and a new indicator
“Average errors in top 9 results (E9)”, were adopted. The result of preliminary
experiment identified three appropriate SAMs. Distance Shape Histogram (DSH)
method shows an optimal performance on discriminating shape categorization, however
is insensitive on detail comparison for shapes in the same category. On the contrary,
Solid Angle (SA) method displays a higher accuracy on identifying shapes within single
category than shapes across multiply categorizes. When Isotropic factor is applied to
DSH (IsoDSH), it achieves an excellent capability of discriminating shape series in
different sizes.
Inspired by the histogram distribution of DSH algorithm, a novel SAH algorithm was
defined based on SA algorithm. Its accuracy is greatly enhanced when compared to the
SA algorithm. A quick anisotropic rescaled algorithm was proposed for the pre-process
procedure of ISODSH method to improve the efficiency. This avoids the expensive
computational consumption on the initial iterative method. Furthermore, The DSISAH
algorithm was projected to intelligently integrate DSH, SAH and ISODSH methods,
which broadens the describing perspectives of a model by embodying multiple feature
descriptors. These three sub-algorithms complement each other in term of advantages
and weakness, which results in a more balance method.
From experiments, four key parameters of DSISAH algorithm were defined and verified.
The optimal sample size, in terms of the number of description sample points for
presenting a 3D shape under study, was achieved into a balance between the stability of
the shape descriptors and the algorithm efficiency. The meaningful solid angle value
range for the SAH shape descriptor was also identified, using the method of analyzing
the effective range of the original histogram distribution. The maximal difference
between two similar shapes was demarcated, according to the statistic of human
awareness criterion for similarity evaluation. The optimized weighting solution that
combines sub-algorithms together was also derived, via the method of approximation, to
maximize its accuracy in similarity assessment.
The feasibility of DSISAH algorithm is verified, by comparing its similarity evaluation
and similar retrieval performance with DSH, SAH and IsoDSH methods. DSISAH
algorithm shows a promising performance not only in shape categorization
discrimination, but also in detail surface deformation and series identification.
DSISAH algorithm was also implemented into a retrieval engine. A friendly user
interface was developed for database management and shape query. With this search
engine, users can conveniently retrieve the most similar shapes from the database or
directly assess the similarity between the specified shapes using their favorite method
among DSH, SAH, IsoDSH and DSISAH methods.
This thesis solved a fundamental problem in design re-usage. The performance of the
proposed new method is promising in a large range of products. The proposed DSISAH
method could play a key role in model retrieval and act as an evaluation tool in
customized design in virtually any product domains. It has the potential to leverage
current prevailing search engine from currently text-based abstracted query to directly 3D
shape-based search.
KEY WORDS
3D similarity assessment
3D shape re-usage
Shape histogram
Weighting factor
Shape Retrieval platform
TABLE OF CONTENTS
List of figures………………………………………………………………………. v List of tables………………………………………………………………………... ix Glossary……………………………………………………………………………. xi LIST of Abbreviations…………………………………………………………….. xv PREFACE………………………………………………………………………… xvii Acknowledgments………………………………………………………………… xix Chapter 1: Introduction……………………………………………………………… 1 1.1 Background………………………………………………………………….. 1 1.2 3D shape re-usage…………………………………………………………… 4 1.3 Similarity assessment technology…………………………………………… 5 1.4 Research objective, challenges and significance……………………………. 8 1.5 Thesis organization………………………………………………………….. 9 Chapter 2: Related work in Similarity assessments for 3D models………………… 11 2.1 Overview…………………………………………………………………… 11 2.2 Feature based measures……………………………………………………. 13 2.2.1 Description based on global feature…………………………… 13 2.2.2 Description based on surface feature………………………….. 14 2.2.3 Description based on 2D contour……………………………… 17 2.3 Graph based measures……………………………………………………... 20 2.3.1 Model graph based…………………………………………….. 20 2.3.2 Manufacturing feature based…………………………………... 21 2.3.3 Skeleton based…………………………………………………. 22 2.4 Multi approach……………………………………………………………... 25 2.4.1 Direct integration………………………………………………. 26 2.4.2 Relevance feedback integration (RFI)…………………………. 29 2.4.3 Other combination approach…………………………………… 32 2.5 Neurual network based measures………………………………………….. 34 2.6 Summary…………………………………………………………………… 35 Chapter 3: Construction of benchmarking 3D shapes for design re-usage………… 38 3.1 Overview…………………………………………………………………… 38 3.2 3D shape re-usage………………………………………………………….. 39 3.3 model Format………………………………………………………………. 41 3.4 Dataset architecture………………………………………………………… 42 3.5 Database design…………………………………………………………….. 46 3.6 Similar prediction set definition……………………………………………. 48 3.7 Summary…………………………………………………………………… 49 Chapter 4: DSISAH algorithm -- A function with integrated elements…………… 50 4.1 Overview…………………………………………………………………... 50 4.2 Problem analysis and hypothesis of DSISAH algorithm………………….. 51 4.3 Sub algorithm I-- Distance Shape Histogram based algorithm (DSH)……. 52 4.3.1 Shape descriptor……………………………………………….. 52 4.3.2 Distance and similarity calculation……………………………. 56 4.3.3 Computational complexity…………………………………….. 57 4.3.4 Advantage……………………………………………………… 58 4.3.5 Weakness……………………………………………………… 59 4.4 Sub algorithm II: Solid Aangle Histogram based algorithm (SAH)………. 60 4.4.1 Definition of solid angle………………………………………. 60 4.4.2 Connolly’s Solid-Angle (SA) shape descriptor……………….. 61 4.4.3 An novel SAH based algorithm……………………………….. 63 4.4.4 Distance and similarity calculation……………………………. 68 4.4.5 Computational complexity…………………………………….. 68 4.4.6 Advantage……………………………………………………… 68 4.4.7 Weakness………………………………………………………. 69 4.5 Sub algorithm III: Isotropic scaled DSH based algorithm (IsoDSH)……… 70 4.5.1 Definition of Isotropic…………………………………………. 70 4.5.2 Calculation of anisotropic factor………………………………. 71 4.5.3 Isotropic distance shape distribution………………………...… 75 4.5.4 Computational complexity…………………………………….. 76 4.5.5 Advantage……………………………………………………… 76 4.5.6 Weakness………………………………………………………. 77 ii
4.6 Combination into DSISAH………………………………………………… 77 4.6.1 Basic logic……………………………………………………… 77 4.6.2 Distance boundary……………………………………………… 79 4.6.3 Weighting factors………………………………………………. 80 4.6.4 Advantage…………………………………………………….... 82 4.7 Summary…………………………………………………………………… 84 Chapter 5: Experiments and Analysis……………………………………………… 86 5.1 Overview…………………………………………………………………… 86 5.2 Experimental platform……………………………………………………... 86 5.2.1 Hardware platform……………………………………………... 86 5.2.2 Software platform……………………………………………… 86 5.3 3D Shape retrieval interface for design re-usage…………………………... 87 5.4 Performance evaluation of similarity measures……………………………. 96 5.4.1 Average errors in top 9 results…………………………………. 96 5.4.2 Express classification………………………………………….. 98 5.4.3 Precision and recall diagram…………………………………… 98 5.5 Experimental plan………………………………………………………… 100 5.5.1 Demarcate parameter…………………………………………. 100 5.5.2 Performance test……………………………………………… 101 5.6 Result analysis……………………………………………………………. 101 5.6.1 Demarcate parameter…………………………………………. 101 5.6.2 Performance test……………………………………………… 111 5.7 Application on design re-usage…………………………………………… 113 5.7.1 Case study in similar search…………………………………... 114 5.7.2 Case study in new product inspection………………………… 115 5.8 Summary………………………………………………………………….. 117 Chapter 6: Conclusion and future work…………………………………………... 119 6.1 Conclusion………………………………………………………………… 119 6.2 Prospective of Future work……………………………………………….. 120 Bibliography………………………………………………………………………. 121 APPENDIX A: Model Format……………………………………………………. 128 I. OFF file……………………………………………………………….. 128 iii
II.
STL file…………………………………………………………….. 129 III.
STEP file………………………………………………………….. 130 APPENDIX B: PBM Dataset categories hierarchy………………………………. 132 APPENDIX C: Comparison examples…………………………………………… 133 APPENDIX D: Retrieval examples………………………………………………. 135 iv
LIST OF FIGURES
Number
Page
Figure 1-1 popular used 3D models ..............................................................................1 Figure 1-2 Model reuse example ..................................................................................2 Figure 1-3 A typical 3D model database system ..........................................................5 Figure 2-1 Classifications of similarity assessment algorithms for 3D models..........12 Figure 2-2 Histogram distribution examples ..............................................................15 Figure 2-3 Distance of random points in different classifications ..............................16 Figure 2-4 Rays are generated by ray-based method for car model ...........................18 Figure 2-5 Extracting Silhouette FV example of chair model ....................................19 Figure 2-6 An example model and its basic voxels for CSG tree ...............................20 Figure 2-7 Sample skeletal graphs ..............................................................................23 Figure 2-8 A Reeb graph example of a 3D model ......................................................24 Figure 2-9 2D model example of building MRG........................................................24 Figure 2-10 AMR-x multiresolution shape feature calculation. .................................32 Figure 2-11 Schematic diagram of a traditional NN system.......................................34 Figure 3-1 Shape re-usage example in shoes design ..................................................40 Figure 3-2 Constrained surface deformation example in shoes design ......................40 Figure 3-3 A sphere in STL file ..................................................................................41 Figure 3-4 A segment of the database categories .......................................................43 Figure 3-5 Shoes templates .........................................................................................43 Figure 3-6 One example shoes from Class C..............................................................43 Figure 3-7 Examples of independent assortments of partition patterns ......................45 Figure 3-8 Design view of shoes model dataset .........................................................45 Figure 3-9 Feature extraction process model ..............................................................46 Figure 3-10 Database design view ..............................................................................47 Figure 3-11 Similar prediction definition example .....................................................48 Figure 4-1 Developing process of DSISAH algorithm ...............................................50 Figure 4-2 Sampling example of a horse model .........................................................53 v
Figure 4-3 Sample a random point on a shoes model .................................................53 Figure 4-4 Reverse calculation from even samples example of a block model..........53 Figure 4-5 A shoes model and its distance shape histogram (DSH) diagram ............55 Figure 4-6 Example DSH diagrams of four typical models .......................................55 Figure 4-7 Similarity assessment for Multi categorizes shapes with DSH method ...57 Figure 4-8 DSH test in few shape categorizes from database ....................................58 Figure 4-9 Similarity assessment for unique categorize shapes with DSH method ...60 Figure 4-10 Steradian (Wikipedia) .............................................................................61 Figure 4-11 Object with different shapes at surface points p1 and p2. ........................62 Figure 4-12 A Classification result from sold angle method ......................................63 Figure 4-13 Solid angle (SA) calculation process for point O ....................................65 Figure 4-14 Example SAH diagrams of an insect model ...........................................67 Figure 4-15 Example SAH diagrams of four typical models .....................................67 Figure 4-16 Similarity assessment for unique categorize shapes with SAH method .69 Figure 4-17 Similarity assessment for multi categorizes shapes with SAH method ..70 Figure 4-18 Isotropic match example (Kazhdan, M., 2004 ) ......................................71 Figure 4-19 A iterative anisotropic rescaling example ...............................................72 Figure 4-20 A anisotropic rescaled model example ...................................................74 Figure 4-21 An instance of combing anisotropic factor with DSH distribution ........75 Figure 4-22 Similarity assessment in the same design series with IsoDSH method ..76 Figure 4-23 Boundary distance and similarity value ..................................................79 Figure 4-24 Three descriptors HD, HI, and HA for sphere model and plane model ...80 Figure 4-25 Similarity assessment example I with DSISAH method ........................83 Figure 4-26 Similarity assessment example II with DSISAH method .......................84 Figure 5-1 Browse dialog of shape retrieval interface for design re-usage ................88 Figure 5-2 Visual manipulation module .....................................................................88 Figure 5-3 A shoes model displayed in sample points mode......................................89 Figure 5-4 File input/output module ...........................................................................89 Figure 5-5 Database management module ..................................................................90 Figure 5-6 Insert a new model ....................................................................................91 Figure 5-7 Update model information ........................................................................91 Figure 5-8 Delete existing model or models from database .......................................91 vi
Figure 5-9 Over view the database .............................................................................92 Figure 5-10 Query results dialog for querying model ................................................93 Figure 5-11 Query dialog ............................................................................................94 Figure 5-12 Direct similarity assessment module .......................................................94 Figure 5-13 Direct similarity assessing using DSH based approach ..........................95 Figure 5-14 A instance of error result in top 9 retrieved shapes .................................97 Figure 5-15 Precision and Recall definition illustration .............................................99 Figure 5-16 Shape descriptor diagrams based on different number of samples .......103 Figure 5-17 Solid value range test on direct similarity assessment ..........................105 Figure 5-18 Precision comparison for solid angle value range.................................106 Figure 5-19 Statistic of errors in top 9 for initial set weighting factors ....................106 Figure 5-20 Relation between weighting factor WS and E9 ......................................108 Figure 5-21 P-R diagrams for example weighting methods in contrast ...................110 Figure 5-22 Dendogram similarity classification for given models .........................112 Figure 5-23 P-R diagram comparison with DSH, SAH and IsoDSH based method112 Figure 5-24 Average computational time consuming comparison of four methods 113 Figure 5-25 Flow chart of designing a new product .................................................114 Figure 5-26 Instance of similar search ......................................................................115 Figure 5-27 A1, B1 and C1 shapes in a re-usage case study ....................................116 Figure 5-28 Case study of similarity evaluation in new product inspection.............117 Figure A-1 A face model in OFF file........................................................................129 Figure A-2 A high level structure of STEP file (Loffredo, D.) ................................131 Figure A-3 A NURBS curve example with curvature information ..........................131 Figure C-1 Direct similarity assessment example I based on DSISAH algorithm ...133 Figure C-2 Direct similarity assessment example II based on DSISAH algorithm ..134 Figure D-1 A instance of retrieval result using DSH based method.........................135 Figure D-2 A instance of retrieval result using SAH based method.........................136 Figure D-3 A instance of retrieval result using IsoDSH based method ....................137 Figure D-4 A instance of retrieval result using DSISAH based method ..................138 Figure D-5 Another instance of retrieval result using DSH based method ..............139 Figure D-6 Another instance of retrieval result using SAH based method ..............140 Figure D-7 Another instance of retrieval result using IsoDSH based method .........141 vii
Figure D-8 Another instance of retrieval result using DSISAH based method ........142 viii
LIST OF TABLES
Number
Page
Table 1-1 Model re-usage examples of shoes ...............................................................4 Table 2-1 Summarized comparison of representative similarity measures (1)...........36 Table 2-2 Summarized comparison of representative similarity measures (2)...........37 Table 3-1 Shoes patterns for Class D, E, F and G ......................................................44 Table 4-1 Algorithm to generate random samples for distance shape histogram .......52 Table 4-2 Pseudo code for calculating DSH shape descriptor ...................................54 Table 4-3 Algorithm to generate SAH distribution of a specific model A .................64 Table 4-4 Algorithm to calculate SA value for a specific vertical O ..........................65 Table 4-5 Quick isotropic scaling algorithm ..............................................................74 Table 4-6 Comparison on Quick isotropic scaling and iterative scaling ....................75 Table 4-7 DSISAH algorithm procedure for model A and B .....................................78 Table 4-8 Rough optimization of Weighting factors for DSISAH algorithm ............81 Table 4-9 Detail optimization of Weighting factors for DSISAH algorithm .............82 Table 5-1 Brief procedure to adjust the weighting factors for DSH and SAH .........107 Table 5-2 E9 contrast of weighting factor test for WS and WD..................................107 Table 5-3 Brief procedure to adjust the weighting factors for DSH, SAH and
IsoDSH .....................................................................................................................108 Table 5-4 E9 contrast of weighting factor test for WS, WD and WI ...........................109 Table 5-5 Classification discrimination experimental result ....................................111 Table A-1 ASCII OFF file syntax .............................................................................128 Table A-2 An Example of OFF file ..........................................................................128 Table A-3 ASCII STL file syntax .............................................................................130 ix
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GLOSSARY
Anisotropic filtering
When a surface has a property of characteristic that is not
the same in all directions, anisotropic filtering can be used
to blend those features in one direction only so as not to
diminish the separation detail.
Attribute
A property of a 3D object that can be adjusted. Attributes
are sometimes called parameters, and they are usually
animatable. Attributes are found within nodes.
Bézier
A type of spline or patch that uses adjustable tangent
handles to control the curvature near each control vertex.
B-spline
Basis spline; a very smooth curve controlled by three or
more control vertices (CVs). The B-Spline always
intersects the first and last CV, but is usually only
influenced by the others.
Edge
The boundary between two faces of a mesh model. An
edge is a straight line connecting two vertices, and
bounded by a face on either side.
Extrude
A simple process of converting 2D shapes into 3D. A
copy of the 2D shape is moved perpendicular to the
original, then connected to the original to create a closed
surface.
Face Normal
A non-rendering line which points out perpendicular to the
surface of a face. Faces have only one normal, which
determines which side of the face is renderable. Special
two-sided faces will render regardless of the orientation of
the normal relative to the camera. Also called polygon
normals or surface normals.
Hierarchy
A structure of linkages among objects, necessary for
animation of systems with moving parts, such as
characters and vehicles. Also known as parenting, linking,
and forward kinematics. In a standard animation
hierarchy, child objects inherit transform information from
their parent. An object may have many children, but can
have only one parent.
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Level of Detail
A method for lowering the total number of polygons
describing a scene. Say there is an aircraft that is
described by 500 polygons. Up close you want to see
then all, but at a distance maybe 5 will suffice, because the
polygons are so much smaller. FS98 currently uses all
500 polygons to describe the airplane, even if it is so
distant that it appears only a few pixels big.
Mesh
A 3D object composed of triangular faces. A mesh object
has no true curvature. The appearance of curvature is
achieved by increasing the number of faces (level of
detail), and by edge smoothing during render time.
Modeling
Construction of geometric objects in 3D scenes. Models
describe the forms of objects, but not their material
properties or how they move.
Node
An abstract container of information. Nodes generally
have attributes which store data. In a 3D graphics
program, nodes are connected together to form a network
called a scene graph.
NURBS
Non-Uniform Rational Basis Spline. A special type of
B-spline, which has weighted control points. The more
weight a control vertex (CV) has, the more the curve is
attracted to it, and the sharper the curve bends.
Pivot Point
The center of an object’s transformation, and the center of
its local coordinate system. An object moves, rotates, and
scales relative to the location and orientation of its pivot
point. Also known as "anchor point".
Projection
The process of reducing three dimensions to two
dimensions for display is called Projection. It is the
mapping of the visible part of a three dimensional object
onto a two dimension screen.
Similarity
A measurement of how similar two samples are
Similarity
assessment
Tessellation
An evaluation of similarity
Decomposing a complex surface into a series of simple
ones that approximate the complex surface. When
drawing a surface, most API's have functions that allow
the programmer to define the surface and have the
program generate and place a number of triangles that
define that surface.
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Transformation
The mathematical reassignment of points to new locations.
The three transforms are translation, rotation, and scale.
These transforms control the location and orientation of
objects in 3D graphics applications.
Vertex
A vertex is a point in 3D space with a particular location,
usually given in terms of its x, y, and z coordinates.
Vertex Normal
Lines pointing out from each vertex of a 3D model. The
orientation of vertex normal determines how much light
the surrounding surface can receive. If a vertex normal is
pointing toward a light source, then the surface will be
illuminated. If a vertex normal is pointing away from a
light source, the surface will receive less illumination. A
vertex generally has several normal, one for each face
shared by the vertex. If four faces meet at a vertex, then
the vertex will have four normal.
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LIST OF ABBREVIATIONS
1R.
R‐precision 2R.
2R‐precision 2D.
Two dimensional
3D.
Three dimensional
11P.
11 point average precision AMR.
Alpha‐Multiresolution Representation DI.
Distance Integration DSH.
Distance shape histogram Fv.
Feature Vector GA.
Genetic algorithm IsoDSH
Isotropic introduced Distance shape histogram LFD.
Light Field descriptor LOD.
Levels of Detail MEGA.
Maximizing Expected Generalization Algorithm NN.
Neural Network PC.
Precision‐ recall diagram PRF.
pseudo relevance feedback PSB.
Prinston shape benchmark QSI.
Qualitative similarity information RF.
Relevance Feedback RFI.
Reduced Feature Vector Integration RSI.
Relative similarity information xv
SD.
Shape descriptor SA
Solid Angle SAH
Solid Angle histogram SAM.
Similarity assessment measure SVM.
Support vector machines xvi
PREFACE
This thesis is the final work of my M.Sc. study at the Department of
Electromechanical Engineering, Faculty of Science and Technology, University of
Macau. It serves as documentation of my work during the study, which has been made
from autumn 2007 until October 2009. The study has been funded by the Research
Committee of University of Macau, and supervised by Prof. Yang Zhixin.
This study is about similarity assessment of 3D shapes, inspired by the requirement of
shoes companies, stimulated by the prosperity of retrieval system of 3D models. To
maintain the leadership of shoes companies from Pearl River delta region in shoes
industry, it is important to introduced customized design to cut their production period
and enhance their ability to responsible to user’s various requirements. Anticipating
most of their E-products are stored in the database as 3D constrained surface
deformation models, a friendly retrieval system which provides convenient
management for these models is one of the destinations of this thesis, of which
similarity assessment technology is the key problem.
The thesis consists of six chapters. Three chapters contain papers that are accepted by
or intended for an international journal or proceedings. These chapters cover various
aspects of stereology, such as integral geometry, geometric measure theory, sampling
theory, variance assessment, and implementation. In the first chapter, however, I have
given a general introduction to this thesis.
Writing this thesis has been hard, but in the process of writing I feel I have learned a
lot on our initial conceptions of digital processing of 3D shapes, I have dealt with a lot
of subjects, in an attempt to give this thesis a broad perspective on this topic.
The afterwards researchers who are interested in retrieval technology of 3D models
are welcome to read this thesis. And I am sure you won’t be disappointed.
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Acknowledgments
I
am grateful to many people who supported and encouraged me during the work
leading to this thesis: professors, colleagues, friends, and family. First and foremost,
my supervisor Prof. Yang Zhixin at University of Macau, and, led me to this magic
research topic and guided me throughout this research. His long term technical insights,
creativities and practical points of views have benefited not only this project but also my
personality immensely. I would like thank to him for his patient and encouraging attitude,
the helpful countless discussion and support he provided. I would like also to express my
thanks to the Research Committee of University of Macau of the financial support
throughout my program.
I will always remember the good experiences in working with my research colleagues in
the CAD/CAM Laboratory during my study. Among my research group, I would like to
express my special thanks to Shum Songon, the technician of our lab, who has been
always giving me powerful encouragement and technical assistance. I like the research
atmosphere he created. I enjoyed all the vivid discussions with my partner Xiao Difu and
Huang Jianming, bachelor students who is working on this project for final year project. I
got great amount of inspiration from their view and had lots of fun. Specially, I would
like to express my great appreciation to Lo Kim Man, another master student from Prof.
Yang, for he has done precious previous work for this program.
I would like to express my great appreciation to Patrick, who is the exchange student
from Swiss land, spending one month and a half in CAD/CAM lab of UMAC. He gave
me great help with a lot of petty and important detail work.
I would also thank my friends in the university, Abner, Nancy, Faye and Wang yi. They
always support me and influent me with their great passion for life.
Last, but of course not the least, I would like to express my sincere gratitude to my
family. For they have been delivering a wholesouled love to me for so many years; for
they formed me a positive attitude toward life by personal example; for they let me know
how to cherish the most valuable things. I feel so luck to be their daughter, my dear
father and mother.
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DEDICATION
The author wishes to dedicate this thesis
TO
My Parents
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