Understanding the Structure of 3D Shapes

Compact representations of three dimensional objects are very often used in computer graphics to create effective ways to analyse, manipulate and transmit 3D models. Their ability to abstract from the concrete shapes and expose their structure is important in a number of applications, spanning from computer animation, to medicine, to physical simulations. This thesis will investigate new methods for the generation of compact shape representations. In the first part, the problem of computing optimal PolyCube base complexes will be considered. PolyCubes are orthogonal polyhedra used in computer graphics to map both surfaces and volumes. Their ability to resemble the original models and at the same time expose a very simple and regular structure is important in a number of applications, such as texture mapping, spline fitting and hex-meshing. The second part will focus on medial descriptors. In particular, two new algorithms for the generation of curve-skeletons will be presented. These methods are completely based on the visual appearance of the input, therefore they are independent from the type, number and quality of the primitives used to describe a shape, determining, thus, an advancement to the state of the art in the field

Understanding the Structure of 3D Shapes

Compact representations of three dimensional objects are very often used in computer graphics to create effective ways to analyse, manipulate and transmit 3D models. Their ability to abstract from the concrete shapes and expose their structure is important in a number of applications, spanning from computer animation, to medicine, to physical simulations. This thesis will investigate new methods for the generation of compact shape representations. In the first part, the problem of computing optimal PolyCube base complexes will be considered. PolyCubes are orthogonal polyhedra used in computer graphics to map both surfaces and volumes. Their ability to resemble the original models and at the same time expose a very simple and regular structure is important in a number of applications, such as texture mapping, spline fitting and hex-meshing. The second part will focus on medial descriptors. In particular, two new algorithms for the generation of curve-skeletons will be presented. These methods are completely based on the visual appearance of the input, therefore they are independent from the type, number and quality of the primitives used to describe a shape, determining, thus, an advancement to the state of the art in the field

Learning Material-Aware Local Descriptors for 3D Shapes

Material understanding is critical for design, geometric modeling, and analysis of functional objects. We enable material-aware 3D shape analysis by employing a projective convolutional neural network architecture to learn material- aware descriptors from view-based representations of 3D points for point-wise material classification or material- aware retrieval. Unfortunately, only a small fraction of shapes in 3D repositories are labeled with physical mate- rials, posing a challenge for learning methods. To address this challenge, we crowdsource a dataset of 3080 3D shapes with part-wise material labels. We focus on furniture models which exhibit interesting structure and material variabil- ity. In addition, we also contribute a high-quality expert- labeled benchmark of 115 shapes from Herman-Miller and IKEA for evaluation. We further apply a mesh-aware con- ditional random field, which incorporates rotational and reflective symmetries, to smooth our local material predic- tions across neighboring surface patches. We demonstrate the effectiveness of our learned descriptors for automatic texturing, material-aware retrieval, and physical simulation. The dataset and code will be publicly available.Comment: 3DV 201

Physics based supervised and unsupervised learning of graph structure

Graphs are central tools to aid our understanding of biological, physical, and social systems. Graphs also play a key role in representing and understanding the visual world around us, 3D-shapes and 2D-images alike. In this dissertation, I propose the use of physical or natural phenomenon to understand graph structure. I investigate four phenomenon or laws in nature: (1) Brownian motion, (2) Gauss\u27s law, (3) feedback loops, and (3) neural synapses, to discover patterns in graphs

Size effect on strength and fracture energy for numerical concrete with realistic aggregate shapes

Fracture of concrete at the scale of the aggregate structure (or smaller) is a complicated process. Simple simulation models may be of help in understanding fracture in more detail, provided that the material structure is incorporated in as much detail as possible. A combined approach using computed tomography and image processing allows us to model concrete close to reality. The shape of the aggregates is included in a 3D beam lattice model for fracture. Fracture of concrete beams is simulated under 3-point bending with different sizes, aggregate densities and aggregates shapes, focusing on the size effect on structural strength and fracture energ