Thesis (M. Phil.)--University of Hong Kong, 1999. / Includes bibliographical references.

published_or_final_version / Computer Science and Information Systems / Master / Master of Philosophy

Thesis (MSc)--University of Stellenbosch, 2007. / Bibliography. Also available via the Internet.

Shape processing defines a set of theoretical and algorithmic tools for creating, measuring and modifying digital representations of shapes.  Such tools are of paramount importance to many disciplines of computer graphics, including modeling, animation, visualization, and image processing.  Many applications of shape processing can be found in the entertainment and medical industries. In an attempt to improve upon many previous shape processing techniques, the present thesis explores the theoretical and algorithmic aspects of a difference measure, which involves fitting a ball (disk in 2D and sphere in 3D) so that it has at least one tangential contact with each shape and the ball interior is disjoint from both shapes. We propose a set of ball-based operators and discuss their properties, implementations, and applications.  We divide the group of ball-based operations into unary and binary as follows: Unary operators include: * Identifying details (sharp, salient features, constrictions) * Smoothing shapes by removing such details, replacing them by fillets and roundings * Segmentation (recognition, abstract modelization via centerline and radius variation) of tubular structures Binary operators include: * Measuring the local discrepancy between two shapes * Computing the average of two shapes * Computing point-to-point correspondence between two shapes * Computing circular trajectories between corresponding points that meet both shapes at right angles * Using these trajectories to support smooth morphing (inbetweening) * Using a curve morph to construct surfaces that interpolate between contours on consecutive slices The technical contributions of this thesis focus on the implementation of these tangent-ball operators and their usefulness in applications of shape processing. We show specific applications in the areas of animation and computer-aided medical diagnosis.  These algorithms are simple to implement, mathematically elegant, and fast to execute.

by Leung Hoi-Chau. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 70-71). / Abstracts in English and Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Previous Works --- p.2 / Chapter 2.1. --- Facial animations and facial surgery simulations / Chapter 2.2. --- Facial Action Coding System (FACS) / Chapter 2.3. --- The Boundary Element Method (BEM) in Computer Graphics / Chapter Chapter 3. --- The Facial Expression System --- p.7 / Chapter 3.1. --- Input to the system / Chapter 3.1.1. --- Orientation requirements for the input mesh / Chapter 3.1.2. --- Topology requirements for the input mesh / Chapter 3.1.3. --- Type of the polygons of the facial mesh / Chapter 3.2. --- Facial Modeling and Feature Recognition / Chapter 3.3. --- User Control / Chapter 3.4. --- Output of the system / Chapter Chapter 4. --- Boundary Element Method (BEM) --- p.12 / Chapter 4.1. --- Numerical integration of the kernels / Chapter 4.1.1. --- P and Q are different / Chapter 4.1.2. --- P and Q are identical / Chapter 4.1.2.1. --- Evaluation of the Singular Traction Kernel / Chapter 4.1.2.2. --- Evaluation of the Singular Displacement Kernel / Chapter 4.2. --- Assemble the stiffness matrix / Chapter Chapter 5. --- Facial Modeling --- p.18 / Chapter 5.1. --- Offset of facial mesh / Chapter 5.2. --- Thickening of Face Contour / Chapter Chapter 6. --- Facial Feature Recognition --- p.22 / Chapter 6.1. --- Extract all contour edges from the facial mesh / Chapter 6.2. --- Separate different holes from the contour edges / Chapter 6.3. --- Locating the bounding boxes of different holes / Chapter 6.4. --- Determine the facial features / Chapter 6.4.1. --- Eye positions / Chapter 6.4.2. --- Mouth position and Face / Chapter 6.4.3. --- Nose position / Chapter 6.4.4. --- Skull position / Chapter Chapter 7. --- Boundary Conditions in the system --- p.28 / Chapter 7.1. --- Facial Muscles / Chapter 7.2. --- Skull Bone / Chapter 7.3. --- Facial Muscle recognition / Chapter 7.3.1. --- Locating muscle-definers / Chapter 7.3.2. --- Locating muscles / Chapter 7.4. --- Skull Bone Recognition / Chapter 7.5. --- Refine the bounding regions of the facial features / Chapter 7.6. --- Add/Remove facial muscles / Chapter Chapter 8. --- Muscles Movement --- p.40 / Chapter 8.1. --- Muscle contraction / Chapter 8.2. --- Muscle relaxation / Chapter 8.3. --- The Muscle sliders / Chapter Chapter 9. --- Pre-computation --- p.44 / Chapter 9.1. --- Changing the Boundary Values / Chapter Chapter 10 --- . Implementation --- p.46 / Chapter 10.1. --- Data Structure for the facial mesh / Chapter 10.2. --- Implementation of the BEM engine / Chapter 10.3. --- Facial modeling and the facial recognition / Chapter Chapter 11 --- . Results --- p.48 / Chapter 11.1. --- Example 1 (low polygon man face) / Chapter 11.2. --- Example 2 (girl face) / Chapter 11.3. --- Example 3 (man face) / Chapter 11.4. --- System evaluation / Chapter Chapter 12 --- . Conclusions --- p.67 / References --- p.70

[Truncated abstract] Image transition effects are commonly used on television and human computer interfaces. The transition between images creates a perception of continuity which has aesthetic value in special effects and practical value in visualisation. The work in this thesis demonstrates that better image transition effects are obtained by incorporating properties of projective geometry into image transition algorithms. Current state-of-the-art techniques can be classified into two main categories namely shape interpolation and warp generation. Many shape interpolation algorithms aim to preserve rigidity but none preserve it with perspective effects. Most warp generation techniques focus on smoothness and lack the rigidity of perspective mapping. The affine transformation, a commonly used mapping between triangular patches, is rigid but not able to model perspective effects. Image transition techniques from the view interpolation community are effective in creating transitions with the correct perspective effect, however, those techniques usually require more feature points and algorithms of higher complexity. The motivation of this thesis is to enable different views of a planar surface to be interpolated with an appropriate perspective effect. The projective geometric relationship which produces the perspective effect can be specified by two quadrilaterals. This problem is equivalent to finding a perspectively appropriate interpolation for projective transformation matrices. I present two algorithms that enable smooth perspective transition between planar surfaces. The algorithms only require four point correspondences on two input images. ...The second algorithm generates transitions between shapes that lie on the same plane which exhibits a strong perspective effect. It recovers the perspective transformation which produces the perspective effect and constrains the transition so that the in-between shapes also lie on the same plane. For general image pairs with multiple quadrilateral patches, I present a novel algorithm that is transitionally symmetrical and exhibits good rigidity. The use of quadrilaterals, rather than triangles, allows an image to be represented by a small number of primitives. This algorithm uses a closed form force equilibrium scheme to correct the misalignment of the multiple transitional quadrilaterals. I also present an application for my quadrilateral interpolation algorithm in Seitz and Dyer's view morphing technique. This application automates and improves the calculation of the reprojection homography in the postwarping stage of their technique. Finally I unify different image transition research areas into a common framework, this enables analysis and comparison of the techniques and the quality of their results. I highlight that quantitative measures can greatly facilitate the comparisons among different techniques and present a quantitative measure based on epipolar geometry. This novel quantitative measure enables the quality of transitions between images of a scene from different viewpoints to be quantified by its estimated camera path.

Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. / Image morphing is a popular technique used to create spectacular visual effects, by gradually transforming one image into another. This thesis explains what exactly is meant by the terms “image morphing” / “warping”, where it is used and how it is done. A few existing morphing techniques are described and finally an implementation using Delaunay triangulation and texture mapping is presented.