Li-Yi Wei

Bilateral blue noise sampling

Blue noise sampling is an important component in many graphics applications, but existing techniques consider mainly the spatial positions of samples, making them less effective when handling problems with non-spatial features. Examples include biological distribution in which plant spacing is influenced by non-positional factors such as tree type and size, photon mapping in which photon flux and direction are not a direct function of the attached surface, and point cloud sampling in which the underlying surface is unknown a priori. These scenarios can benefit from blue noise sample distributions, but cannot be adequately handled by prior art. Inspired by bilateral filtering, we propose a bilateral blue noise sampling strategy. Our key idea is a general formulation to modulate the traditional sample distance measures, which are determined by sample position in spatial domain, with a similarity measure that considers arbitrary per sample attributes. This modulation leads to the notion of bilateral blue noise whose properties are influenced by not only the uniformity of the sample positions but also the similarity of the sample attributes. We describe how to incorporate our modulation into various sample analysis and synthesis methods, and demonstrate applications in object distribution, photon density estimation, and point cloud sub-sampling.

Mapping virtual and physical reality

Real walking offers higher immersive presence for virtual reality (VR) applications than alternative locomotive means such as walking-in-place and external control gadgets, but needs to take into consideration different room sizes, wall shapes, and surrounding objects in the virtual and real worlds. Despite perceptual study of impossible spaces and redirected walking, there are no general methods to match a given pair of virtual and real scenes. We propose a system to match a given pair of virtual and physical worlds for immersive VR navigation. We first compute a planar map between the virtual and physical floor plans that minimizes angular and distal distortions while conforming to the virtual environment goals and physical environment constraints. Our key idea is to design maps that are globally surjective to allow proper folding of large virtual scenes into smaller real scenes but locally injective to avoid locomotion ambiguity and intersecting virtual objects. From these maps we derive altered rendering to guide user navigation within the physical environment while retaining visual fidelity to the virtual environment. Our key idea is to properly warp the virtual world appearance into real world geometry with sufficient quality and performance. We evaluate our method through a formative user study, and demonstrate applications in gaming, architecture walkthrough, and medical imaging.

Structure and appearance optimization for controllable shape design

The field of topology optimization seeks to optimize shapes under structural objectives, such as achieving the most rigid shape using a given quantity of material. Besides optimal shape design, these methods are increasingly popular as design tools, since they automatically produce structures having desirable physical properties, a task hard to perform by hand even for skilled designers. However, there is no simple way to control the appearance of the generated objects. In this paper, we propose to optimize shapes for both their structural properties and their appearance, the latter being controlled by a user-provided pattern example. These two objectives are challenging to combine, as optimal structural properties fully define the shape, leaving no degrees of freedom for appearance. We propose a new formulation where appearance is optimized as an objective while structural properties serve as constraints. This produces shapes with sufficient rigidity while allowing enough freedom for the appearance of the final structure to resemble the input exemplar. Our approach generates rigid shapes using a specified quantity of material while observing optional constraints such as voids, fills, attachment points, and external forces. The appearance is defined by examples, making our technique accessible to casual users. We demonstrate its use in the context of fabrication using a laser cutter to manufacture real objects from optimized shapes.

Capturing braided hairstyles

From fishtail to princess braids, these intricately woven structures define an important and popular class of hairstyle, frequently used for digital characters in computer graphics. In addition to the challenges created by the infinite range of styles, existing modeling and capture techniques are particularly constrained by the geometric and topological complexities. We propose a data-driven method to automatically reconstruct braided hairstyles from input data obtained from a single consumer RGB-D camera. Our approach covers the large variation of repetitive braid structures using a family of compact procedural braid models. From these models, we produce a database of braid patches and use a robust random sampling approach for data fitting. We then recover the input braid structures using a multi-label optimization algorithm and synthesize the intertwining hair strands of the braids. We demonstrate that a minimal capture equipment is sufficient to effectively capture a wide range of complex braids with distinct shapes and structures.

Perceptually-guided foveation for light field displays

A variety of applications such as virtual reality and immersive cinema require high image quality, low rendering latency, and consistent depth cues. 4D light field displays support focus accommodation, but are more costly to render than 2D images, resulting in higher latency. The human visual system can resolve higher spatial frequencies in the fovea than in the periphery. This property has been harnessed by recent 2D foveated rendering methods to reduce computation cost while maintaining perceptual quality. Inspired by this, we present foveated 4D light fields by investigating their effects on 3D depth perception. Based on our psychophysical experiments and theoretical analysis on visual and display bandwidths, we formulate a content-adaptive importance model in the 4D ray space. We verify our method by building a prototype light field display that can render only 16% -- 30% rays without compromising perceptual quality.

Spoke-Darts for High-Dimensional Blue Noise Sampling

Blue noise sampling has proved useful for many graphics applications, but remains underexplored in high-dimensional spaces due to the difficulty of generating distributions and proving properties about them. We present a blue noise sampling method with good quality and performance across different dimensions. The method, spoke-dart sampling, shoots rays from prior samples and selects samples from these rays. It combines the advantages of two major high-dimensional sampling methods: the locality of advancing front with the dimensionality-reduction of hyperplanes, specifically line sampling. We prove that the output sampling is saturated with high probability, with bounds on distances between pairs of samples and between any domain point and its nearest sample. We demonstrate spoke-dart applications for approximate Delaunay graph construction, global optimization, and robotic motion planning. Both the blue-noise quality of the output distribution and the adaptability of the intermediate processes of our method are useful in these applications.

Tensor field design in volumes

The design of 3D tensor fields is important in several graphics applications such as procedural noise, solid texturing, and geometry synthesis. Different fields can lead to different visual effects. The topology of a tensor field, such as degenerate tensors, can cause artifacts in these applications. Existing 2D tensor field design systems cannot handle the topology of 3D tensor fields. We present, to our best knowledge, the first 3D tensor field design system. At the core of our system is the ability to specify and control the type, number, location, shape, and connectivity of degenerate tensors. To enable such capability, we have made a number of observations of tensor field topology that were previously unreported. We demonstrate applications of our method in volumetric synthesis of solid and geometry texture as well as anisotropic Gabor noise.

Tile-based Pattern Design with Topology Control

Patterns with desired aesthetic appearances and physical structures are ubiquitous. However, such patterns are challenging to produce -- manual authoring requires significant expertise and efforts while automatic computation lacks sufficient flexibility and user control. We propose a method that automatically synthesizes vector patterns with visual appearance and topological structures designated by users via input exemplars and output conditions. The input can be an existing vector graphics design or a new one manually drawn by the user through our interactive interface. Our system decomposes the input pattern into constituent components (tiles) and overall arrangement (tiling). The tile sets are general and flexible enough to represent a variety of patterns, and can produce different outputs with user specified conditions such as size, shape, and topological properties for physical manufacturing.