Computer Science

We propose a novel framework for computing descriptors for characterizing points on three-dimensional surfaces. First, we present a new non-learned feature that uses graph wavelets to decompose the Dirichlet energy on a surface. We call this new feature wavelet energy decomposition signature (WEDS). Second, we propose a new multiscale graph convolutional network (MGCN) to transform a non-learned feature to a more discriminative descriptor. Our results show that the new descriptor WEDS is more discriminative than the current state-of-the-art non-learned descriptors and that the combination of WEDS and MGCN is better than the state-of-the-art learned descriptors. An important design criterion for our descriptor is the robustness to different surface discretizations including triangulations with varying numbers of vertices. Our results demonstrate that previous graph convolutional networks significantly overfit to a particular resolution or even a particular triangulation, but MGCN generalizes well to different surface discretizations. In addition, MGCN is compatible with previous descriptors and it can also be used to improve the performance of other descriptors, such as the heat kernel signature, the wave kernel signature, or the local point signature.

Vector field design on surfaces was originally motivated by applications in graphics such as texture synthesis and rendering. In this paper, we consider the idea of vector field design with a new motivation from computational topology. We are interested in designing and visualizing vector fields to aid the study of Morse functions, Morse vector fields, and Morse-Smale complexes. To achieve such a goal, we present MVF Designer, a new interactive design system that provides fine-grained control over vector field geometry, enables the editing of vector field topology, and supports a design process in a simple and efficient way using elementary moves, which are actions that initiate or advance our design process. Our system allows mathematicians to explore the complex configuration spaces of Morse functions, their gradients, and their associated Morse-Smale complexes. Understanding these spaces will help us expand further their applicability in topological data analysis and visualization.

We introduce a method to analyze and modify a shape to make it manufacturable for a given additive manufacturing (AM) process. Different AM technologies, process parameters or materials introduce geometric constraints on what is manufacturable or not. Given an input 3D model and minimum printable feature size dictated by the manufacturing process characteristics and parameters, our algorithm generates a corrected geometry that is printable with the intended AM process. A key issue in model correction for manufacturability is the identification of critical features that are affected by the printing process. To address this challenge, we propose a topology aware approach to construct the allowable space for a print head to traverse during the 3D printing process. Combined with our build orientation optimization algorithm, the amount of modifications performed on the shape is kept at minimum while providing an accurate approximation of the as-manufactured part. We demonstrate our method on a variety of 3D models and validate it by 3D printing the results.

In this paper we propose an approach for computing multiple high-quality near-isometric dense correspondences between a pair of 3D shapes. Our method is fully automatic and does not rely on user-provided landmarks or descriptors. This allows us to analyze the full space of maps and extract multiple diverse and accurate solutions, rather than optimizing for a single optimal correspondence as done in most previous approaches. To achieve this, we propose a compact tree structure based on the spectral map representation for encoding and enumerating possible rough initializations, and a novel efficient approach for refining them to dense pointwise maps. This leads to a new method capable of both producing multiple high-quality correspondences across shapes and revealing the symmetry structure of a shape without a priori information. In addition, we demonstrate through extensive experiments that our method is robust and results in more accurate correspondences than state-of-the-art for shape matching and symmetry detection.

Restricting path tracing to a small number of paths per pixel for performance reasons rarely achieves a satisfactory image quality for scenes of interest. However, path space filtering may dramatically improve the visual quality by sharing information across vertices of paths classified as proximate. Unlike screen space-based approaches, these paths neither need to be present on the screen, nor is filtering restricted to the first intersection with the scene. While searching proximate vertices had been more expensive than filtering in screen space, we greatly improve over this performance penalty by storing, updating, and looking up the required information in a hash table. The keys are constructed from jittered and quantized information, such that only a single query very likely replaces costly neighborhood searches. A massively parallel implementation of the algorithm is demonstrated on a graphics processing unit (GPU).

Measurement is an integral part of modern science, providing the fundamental means for evaluation, comparison, and prediction. In the context of visualization, several different types of measures have been proposed, ranging from approaches that evaluate particular aspects of individual visualization techniques, their perceptual characteristics, and even economic factors. Furthermore, there are approaches that attempt to provide means for measuring general properties of the visualization process as a whole. Measures can be quantitative or qualitative, and one of the primary goals is to provide objective means for reasoning about visualizations and their effectiveness. As such, they play a central role in the development of scientific theories for visualization. In this chapter, we provide an overview of the current state of the art, survey and classify different types of visualization measures, characterize their strengths and drawbacks, and provide an outline of open challenges for future research.

Micro-appearance models have brought unprecedented fidelity and details to cloth rendering. Yet, these models neglect fabric mechanics: when a piece of cloth interacts with the environment, its yarn and fiber arrangement usually changes in response to external contact and tension forces. Since subtle changes of a fabric's microstructures can greatly affect its macroscopic appearance, mechanics-driven appearance variation of fabrics has been a phenomenon that remains to be captured. We introduce a mechanics-aware model that adapts the microstructures of cloth yarns in a physics-based manner. Our technique works on two distinct physical scales: using physics-based simulations of individual yarns, we capture the rearrangement of yarn-level structures in response to external forces. These yarn structures are further enriched to obtain appearance-driving fiber-level details. The cross-scale enrichment is made practical through a new parameter fitting algorithm for simulation, an augmented procedural yarn model coupled with a custom-design regression neural network. We train the network using a dataset generated by joint simulations at both the yarn and the fiber levels. Through several examples, we demonstrate that our model is capable of synthesizing photorealistic cloth appearance in a %dynamic and mechanically plausible way.

Virtual Reality (VR) enabled applications are becoming very important to visualize the terrain features in 3D. In general 3D datasets generated from high-resolution satellites and DEM occupy large volumes of data. However, lightweight datasets are required to create better user experiences on VR platforms. So, the present study develops a methodology to generate datasets compatible with VR using Indian Remote Sensing satellite (IRS) sensors. A Linear Imaging Self-Scanning System - IV (LISS IV) with 5.8 m spatial resolution and Carto DEM are used for generating the 3D view using the Arc environment and then converted into virtual reality modeling language (VRML) format. In order to reduce the volume of the VRML dataset a quadratic edge collapse decimation method is applied which reduces the number of faces in the mesh while preserving the boundary and/or normal. A granitic terrain in the south-west part of Hyderabad comprising of dyke intrusion is considered for the generation of 3D VR dataset, as it has high elevation differences thus rendering it most suitable for the present study. Further, the enhanced geomorphological features such as hills and valleys, geological structures such as fractures, intrusive (dykes) are studied and found suitable for better interpretation.

3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation restricts the learning capability of their networks. In this paper, we propose a novel pooling operation for mesh datasets with the same connectivity but different geometry, by building a mesh hierarchy using mesh simplification. For this purpose, we develop a modified mesh simplification method to avoid generating highly irregularly sized triangles. Our pooling operation effectively encodes the correspondence between coarser and finer meshes in the hierarchy. We then present a variational auto-encoder structure with the edge contraction pooling and graph-based convolutions, to explore probability latent spaces of 3D surfaces. Our network requires far fewer parameters than the original mesh VAE and thus can handle denser models thanks to our new pooling operation and convolutional kernels. Our evaluation also shows that our method has better generalization ability and is more reliable in various applications, including shape generation, shape interpolation and shape embedding.

The analysis of vector fields is crucial for the understanding of several physical phenomena, such as natural events (e.g., analysis of waves), diffusive processes, electric and electromagnetic fields. While previous work has been focused mainly on the analysis of 2D or 3D vector fields on volumes or surfaces, we address the meshless analysis of a vector field defined on an arbitrary domain, without assumptions on its dimension and discretisation. The meshless approximation of the Helmholtz-Hodge decomposition of a vector field is achieved by expressing the potential of its components as a linear combination of radial basis functions and by computing the corresponding conservative, irrotational, and harmonic components as solution to a least-squares or to a differential problem. To this end, we identify the conditions on the kernel of the radial basis functions that guarantee the existence of their derivatives. Finally, we demonstrate our approach on 2D and 3D vector fields measured by sensors or generated through simulation.