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Description
Quad-dominant (QD) meshes, i.e., three-dimensional, 2-manifold polygonal meshes comprising mostly four-sided faces (i.e., quads), are a popular choice for many applications such as polygonal shape modeling, computer animation, base meshes for spline and subdivision surface, simulation, and architectural design. This thesis investigates the topic of connectivity control, i.e., exploring different choices of mesh connectivity to represent the same 3D shape or surface. One key concept of QD mesh connectivity is the distinction between regular and irregular elements: a vertex with valence 4 is regular; otherwise, it is irregular. In a similar sense, a face with four sides is regular; otherwise, it is irregular. For QD meshes, the placement of irregular elements is especially important since it largely determines the achievable geometric quality of the final mesh.
Traditionally, the research on QD meshes focuses on the automatic generation of pure quadrilateral or QD meshes from a given surface. Explicit control of the placement of irregular elements can only be achieved indirectly. To fill this gap, in this thesis, we make the following contributions. First, we formulate the theoretical background about the fundamental combinatorial properties of irregular elements in QD meshes. Second, we develop algorithms for the explicit control of irregular elements and the exhaustive enumeration of QD mesh connectivities. Finally, we demonstrate the importance of connectivity control for QD meshes in a wide range of applications.
Traditionally, the research on QD meshes focuses on the automatic generation of pure quadrilateral or QD meshes from a given surface. Explicit control of the placement of irregular elements can only be achieved indirectly. To fill this gap, in this thesis, we make the following contributions. First, we formulate the theoretical background about the fundamental combinatorial properties of irregular elements in QD meshes. Second, we develop algorithms for the explicit control of irregular elements and the exhaustive enumeration of QD mesh connectivities. Finally, we demonstrate the importance of connectivity control for QD meshes in a wide range of applications.
ContributorsPeng, Chi-Han (Author) / Wonka, Peter (Thesis advisor) / Maciejewski, Ross (Committee member) / Farin, Gerald (Committee member) / Razdan, Anshuman (Committee member) / Arizona State University (Publisher)
Created2014
Description
Sparse learning is a powerful tool to generate models of high-dimensional data with high interpretability, and it has many important applications in areas such as bioinformatics, medical image processing, and computer vision. Recently, the a priori structural information has been shown to be powerful for improving the performance of sparse learning models. A graph is a fundamental way to represent structural information of features. This dissertation focuses on graph-based sparse learning. The first part of this dissertation aims to integrate a graph into sparse learning to improve the performance. Specifically, the problem of feature grouping and selection over a given undirected graph is considered. Three models are proposed along with efficient solvers to achieve simultaneous feature grouping and selection, enhancing estimation accuracy. One major challenge is that it is still computationally challenging to solve large scale graph-based sparse learning problems. An efficient, scalable, and parallel algorithm for one widely used graph-based sparse learning approach, called anisotropic total variation regularization is therefore proposed, by explicitly exploring the structure of a graph. The second part of this dissertation focuses on uncovering the graph structure from the data. Two issues in graphical modeling are considered. One is the joint estimation of multiple graphical models using a fused lasso penalty and the other is the estimation of hierarchical graphical models. The key technical contribution is to establish the necessary and sufficient condition for the graphs to be decomposable. Based on this key property, a simple screening rule is presented, which reduces the size of the optimization problem, dramatically reducing the computational cost.
ContributorsYang, Sen (Author) / Ye, Jieping (Thesis advisor) / Wonka, Peter (Thesis advisor) / Wang, Yalin (Committee member) / Li, Jing (Committee member) / Arizona State University (Publisher)
Created2014
Description
Vectorization is an important process in the fields of graphics and image processing. In computer-aided design (CAD), drawings are scanned, vectorized and written as CAD files in a process called paper-to-CAD conversion or drawing conversion. In geographic information systems (GIS), satellite or aerial images are vectorized to create maps. In graphic design and photography, raster graphics can be vectorized for easier usage and resizing. Vector arts are popular as online contents. Vectorization takes raster images, point clouds, or a series of scattered data samples in space, outputs graphic elements of various types including points, lines, curves, polygons, parametric curves and surface patches. The vectorized representations consist of a different set of components and elements from that of the inputs. The change of representation is the key difference between vectorization and practices such as smoothing and filtering. Compared to the inputs, the vector outputs provide higher order of control and attributes such as smoothness. Their curvatures or gradients at the points are scale invariant and they are more robust data sources for downstream applications and analysis. This dissertation explores and broadens the scope of vectorization in various contexts. I propose a novel vectorization algorithm on raster images along with several new applications for vectorization mechanism in processing and analysing both 2D and 3D data sets. The main components of the research are: using vectorization in generating 3D models from 2D floor plans; a novel raster image vectorization methods and its applications in computer vision, image processing, and animation; and vectorization in visualizing and information extraction in 3D laser scan data. I also apply vectorization analysis towards human body scans and rock surface scans to show insights otherwise difficult to obtain.
ContributorsYin, Xuetao (Author) / Razdan, Anshuman (Thesis advisor) / Wonka, Peter (Committee member) / Femiani, John (Committee member) / Maciejewski, Ross (Committee member) / Arizona State University (Publisher)
Created2016