Constrained Texture Mapping And Foldover-free Condition

Texture mapping has been widely used in image processing and graphics to enhance the realism of CG scenes. However to perfectly match the feature points of a 3D model with the corresponding pixels in texture images, the parameterisation which maps a 3D mesh to the texture space must satisfy the positional constraints. Despite numerous research efforts, the construction of a mathematically robust foldover-free parameterisation subject to internal constraints is still a remaining issue. In this paper, we address this challenge by developing a two-step parameterisation method. First, we produce an initial parameterisation with a method traditionally used to solve structural engineering problems, called the bar-network. We then derive a mathematical foldover-free condition, which is incorporated into a Radial Basis Function based scheme. This method is therefore able to guarantee that the resulting parameterization meets the hard constraints without foldovers

Constrained parameterization with applications to graphics and image processing.

Surface parameterization is to establish a transformation that maps the points on a surface to a specified parametric domain. It has been widely applied to computer graphics and image processing fields. The challenging issue is that the usual positional constraints always result in triangle flipping in parameterizations (also called foldovers). Additionally, distortion is inevitable in parameterizations. Thus the rigid constraint is always taken into account. In general, the constraints are application-dependent. This thesis thus focuses on the various constraints depended on applications and investigates the foldover-free constrained parameterization approaches individually. Such constraints usually include, simple positional constraints, tradeoff of positional constraints and rigid constraint, and rigid constraint. From the perspective of applications, we aim at the foldover-free parameterization methods with positional constraints, the as-rigid-as-possible parameterization with positional constraints, and the well-shaped well-spaced pre-processing procedure for low-distortion parameterizations in this thesis. The first contribution of this thesis is the development of a RBF-based re-parameterization algorithm for the application of the foldover-free constrained texture mapping. The basic idea is to split the usual parameterization procedure into two steps, 2D parameterization with the constraints of convex boundaries and 2D re-parameterization with the interior positional constraints. Moreover, we further extend the 2D re-parameterization approach with the interior positional constraints to high dimensional datasets, such as, volume data and polyhedrons. The second contribution is the development of a vector field based deformation algorithm for 2D mesh deformation and image warping. Many presented deformation approaches are used to employ the basis functions (including our proposed RBF-based re-parameterization algorithm here). The main problem is that such algorithms have infinite support, that is, any local deformation always leads to small changes over the whole domain. Our presented vector field based algorithm can effectively carry on the local deformation while reducing distortion as much as possible. The third contribution is the development of a pre-processing for surface parameterization. Except the developable surfaces, the current parameterization approaches inevitably incur large distortion. To reduce distortion, we proposed a pre-processing procedure in this thesis, including mesh partition and mesh smoothing. As a result, the resulting meshes are partitioned into a set of small patches with rectangle-like boundaries. Moreover, they are well-shaped and well-spaced. This pre-processing procedure can evidently improve the quality of meshes for low-distortion parameterizations

User-appropriate viewer for high resolution interactive engagement with 3D digital cultural artefacts.

The core mission of museums and cultural institutions is the preservation, study and presentation of cultural heritage content. In this technological age, the creation of digital datasets and archives has been widely adopted as one way of seeking to achieve some or all of these goals. However, there are many challenges with the use of these data, and in particular the large numbers of 3D digital artefacts that have been produced using methods such as non- contact laser scanning. As public expectation for more open access to information and innovative digital media increases, there are many issues that need to be rapidly addressed. The novel nature of 3D datasets and their visualisation presenting unique issues that impede use and dissemination. Key questions include the legal issues associated with 3D datasets created from cultural artefacts; the complex needs of users who are interacting with them; a lack of knowledge to texture and assess the visual quality of the datasets; and how the visual quality of the presented dataset relates to the perceptual experience of the user. This engineering doctorate, based on an industrial partnership with the National Museums of Liverpool and Conservation Technologies, investigates these questions and offers new ways of working with 3D cultural heritage datasets. The research outcomes in the thesis provide an improved understanding of the complexity of intellectual property law in relation to 3D cultural heritage datasets and how this impacts dissemination of these types of data. It also provides tools and techniques that can be used to understand the needs of a user when interacting with 3D cultural content. Additionally, the results demonstrate the importance of the relationship between texture and polygonal resolution and how this can affect the perceived visual experience of a visitor. It finds that there is an acceptable cost to texture and polygonal resolution to offer the best perceptual experience with 3D digital cultural heritage. The results also demonstrate that a non-textured mesh may be as highly received as a high resolution textured mesh. The research presented provides methodologies and guidelines to improve upon the dissemination and visualisation of 3D cultural content; enhancing and communicating the significance of their 3D collections to their physical and virtual visitors. Future opportunities and challenges for disseminating and visualising 3D cultural content are also discussed