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

An RBF-based reparameterization method for constrained texture mapping

Texture mapping has long been used in computer graphics to enhance the realism of virtual scenes. However, to match the 3D model feature points with the corresponding pixels in a texture image, surface parameterization must satisfy specific positional constraints. However, despite numerous research efforts, the construction of a mathematically robust, foldover‐free parameterization that is subject to positional constraints continues to be a challenge. In the present paper, this foldover problem is addressed by developing radial basis function (RBF) based reparameterization. Given initial 2D embedding of a 3D surface, the proposed method can reparameterize 2D embedding into a foldover ‐free 2D mesh, satisfying a set of user‐specified constraint points. In addition, this approach is mesh‐free. Therefore, generating smooth texture mapping results is possible without extra smoothing optimization

3D mesh metamorphosis from spherical parameterization for conceptual design

Engineering product design is an information intensive decision-making process that consists of several phases including design specification definition, design concepts generation, detailed design and analysis, and manufacturing. Usually, generating geometry models for visualization is a big challenge for early stage conceptual design. Complexity of existing computer aided design packages constrains participation of people with various backgrounds in the design process. In addition, many design processes do not take advantage of the rich amount of legacy information available for new concepts creation. The research presented here explores the use of advanced graphical techniques to quickly and efficiently merge legacy information with new design concepts to rapidly create new conceptual product designs. 3D mesh metamorphosis framework 3DMeshMorpher was created to construct new models by navigating in a shape-space of registered design models. The framework is composed of: i) a fast spherical parameterization method to map a geometric model (genus-0) onto a unit sphere; ii) a geometric feature identification and picking technique based on 3D skeleton extraction; and iii) a LOD controllable 3D remeshing scheme with spherical mesh subdivision based on the developedspherical parameterization. This efficient software framework enables designers to create numerous geometric concepts in real time with a simple graphical user interface. The spherical parameterization method is focused on closed genus-zero meshes. It is based upon barycentric coordinates with convex boundary. Unlike most existing similar approaches which deal with each vertex in the mesh equally, the method developed in this research focuses primarily on resolving overlapping areas, which helps speed the parameterization process. The algorithm starts by normalizing the source mesh onto a unit sphere and followed by some initial relaxation via Gauss-Seidel iterations. Due to its emphasis on solving only challenging overlapping regions, this parameterization process is much faster than existing spherical mapping methods. To ensure the correspondence of features from different models, we introduce a skeleton based feature identification and picking method for features alignment. Unlike traditional methods that align single point for each feature, this method can provide alignments for complete feature areas. This could help users to create more reasonable intermediate morphing results with preserved topological features. This skeleton featuring framework could potentially be extended to automatic features alignment for geometries with similar topologies. The skeleton extracted could also be applied for other applications such as skeleton-based animations. The 3D remeshing algorithm with spherical mesh subdivision is developed to generate a common connectivity for different mesh models. This method is derived from the concept of spherical mesh subdivision. The local recursive subdivision can be set to match the desired LOD (level of details) for source spherical mesh. Such LOD is controllable and this allows various outputs with different resolutions. Such recursive subdivision then follows by a triangular correction process which ensures valid triangulations for the remeshing. And the final mesh merging and reconstruction process produces the remeshing model with desired LOD specified from user. Usually the final merged model contains all the geometric details from each model with reasonable amount of vertices, unlike other existing methods that result in big amount of vertices in the merged model. Such multi-resolution outputs with controllable LOD could also be applied in various other computer graphics applications such as computer games

Arbitrary topology meshes in geometric design and vector graphics

Meshes are a powerful means to represent objects and shapes both in 2D and 3D, but the techniques based on meshes can only be used in certain regular settings and restrict their usage. Meshes with an arbitrary topology have many interesting applications in geometric design and (vector) graphics, and can give designers more freedom in designing complex objects. In the first part of the thesis we look at how these meshes can be used in computer aided design to represent objects that consist of multiple regular meshes that are constructed together. Then we extend the B-spline surface technique from the regular setting to work on extraordinary regions in meshes so that multisided B-spline patches are created. In addition, we show how to render multisided objects efficiently, through using the GPU and tessellation. In the second part of the thesis we look at how the gradient mesh vector graphics primitives can be combined with procedural noise functions to create expressive but sparsely defined vector graphic images. We also look at how the gradient mesh can be extended to arbitrary topology variants. Here, we compare existing work with two new formulations of a polygonal gradient mesh. Finally we show how we can turn any image into a vector graphics image in an efficient manner. This vectorisation process automatically extracts important image features and constructs a mesh around it. This automatic pipeline is very efficient and even facilitates interactive image vectorisation

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

3D photogrammetric data modeling and optimization for multipurpose analysis and representation of Cultural Heritage assets

This research deals with the issues concerning the processing, managing, representation for further dissemination of the big amount of 3D data today achievable and storable with the modern geomatic techniques of 3D metric survey. In particular, this thesis is focused on the optimization process applied to 3D photogrammetric data of Cultural Heritage assets. Modern Geomatic techniques enable the acquisition and storage of a big amount of data, with high metric and radiometric accuracy and precision, also in the very close range field, and to process very detailed 3D textured models. Nowadays, the photogrammetric pipeline has well-established potentialities and it is considered one of the principal technique to produce, at low cost, detailed 3D textured models. The potentialities offered by high resolution and textured 3D models is today well-known and such representations are a powerful tool for many multidisciplinary purposes, at different scales and resolutions, from documentation, conservation and restoration to visualization and education. For example, their sub-millimetric precision makes them suitable for scientific studies applied to the geometry and materials (i.e. for structural and static tests, for planning restoration activities or for historical sources); their high fidelity to the real object and their navigability makes them optimal for web-based visualization and dissemination applications. Thanks to the improvement made in new visualization standard, they can be easily used as visualization interface linking different kinds of information in a highly intuitive way. Furthermore, many museums look today for more interactive exhibitions that may increase the visitors’ emotions and many recent applications make use of 3D contents (i.e. in virtual or augmented reality applications and through virtual museums). What all of these applications have to deal with concerns the issue deriving from the difficult of managing the big amount of data that have to be represented and navigated. Indeed, reality based models have very heavy file sizes (also tens of GB) that makes them difficult to be handled by common and portable devices, published on the internet or managed in real time applications. Even though recent advances produce more and more sophisticated and capable hardware and internet standards, empowering the ability to easily handle, visualize and share such contents, other researches aim at define a common pipeline for the generation and optimization of 3D models with a reduced number of polygons, however able to satisfy detailed radiometric and geometric requests. iii This thesis is inserted in this scenario and focuses on the 3D modeling process of photogrammetric data aimed at their easy sharing and visualization. In particular, this research tested a 3D models optimization, a process which aims at the generation of Low Polygons models, with very low byte file size, processed starting from the data of High Poly ones, that nevertheless offer a level of detail comparable to the original models. To do this, several tools borrowed from the game industry and game engine have been used. For this test, three case studies have been chosen, a modern sculpture of a contemporary Italian artist, a roman marble statue, preserved in the Civic Archaeological Museum of Torino, and the frieze of the Augustus arch preserved in the city of Susa (Piedmont- Italy). All the test cases have been surveyed by means of a close range photogrammetric acquisition and three high detailed 3D models have been generated by means of a Structure from Motion and image matching pipeline. On the final High Poly models generated, different optimization and decimation tools have been tested with the final aim to evaluate the quality of the information that can be extracted by the final optimized models, in comparison to those of the original High Polygon one. This study showed how tools borrowed from the Computer Graphic offer great potentialities also in the Cultural Heritage field. This application, in fact, may meet the needs of multipurpose and multiscale studies, using different levels of optimization, and this procedure could be applied to different kind of objects, with a variety of different sizes and shapes, also on multiscale and multisensor data, such as buildings, architectural complexes, data from UAV surveys and so on

Structural Surface Mapping for Shape Analysis

Natural surfaces are usually associated with feature graphs, such as the cortical surface with anatomical atlas structure. Such a feature graph subdivides the whole surface into meaningful sub-regions. Existing brain mapping and registration methods did not integrate anatomical atlas structures. As a result, with existing brain mappings, it is difficult to visualize and compare the atlas structures. And also existing brain registration methods can not guarantee the best possible alignment of the cortical regions which can help computing more accurate shape similarity metrics for neurodegenerative disease analysis, e.g., Alzheimer’s disease (AD) classification. Also, not much attention has been paid to tackle surface parameterization and registration with graph constraints in a rigorous way which have many applications in graphics, e.g., surface and image morphing. This dissertation explores structural mappings for shape analysis of surfaces using the feature graphs as constraints. (1) First, we propose structural brain mapping which maps the brain cortical surface onto a planar convex domain using Tutte embedding of a novel atlas graph and harmonic map with atlas graph constraints to facilitate visualization and comparison between the atlas structures. (2) Next, we propose a novel brain registration technique based on an intrinsic atlas-constrained harmonic map which provides the best possible alignment of the cortical regions. (3) After that, the proposed brain registration technique has been applied to compute shape similarity metrics for AD classification. (4) Finally, we propose techniques to compute intrinsic graph-constrained parameterization and registration for general genus-0 surfaces which have been used in surface and image morphing applications