Noise-resistant fitting for spherical harmonics

Zernike like functions on spherical cap: principle and applications in optical surface fitting and graphics rendering

Zernike circular polynomials (ZCP) are widely used in optical testing, fabrication and adaptive optics. However, their ability to characterize information on spherical cap is often limited by aperture angle, with highly curved surface being particularly challenging. In this study, we propose a simple and systematic process to derive Zernike like functions that are applicable to all types of spherical cap. The analytical expressions of three function sets are calculated using Gram-Schmidt algorithm. They are hemispherical harmonics (HSH), Zernike spherical function (ZSF) and longitudinal spherical function (LSF). HSH satisfies Laplacian equation and composes a subset of spherical harmonics (SH). ZSF and LSF can be applied to arbitrary spherical cap and their orthogonality is invariant to aperture. The achieved functions, with their complete and orthogonal performance, can serve as essential tools for surface characterization required for a wide range of applications like large-angle lenses description in illumination design, aberration analysis in high aperture systems, human cornea measurement fitting, geomagnetic field modelling, etc. Moreover, they are important for graphics rendering in virtual reality and games by solving the reflectance equation efficiently.

All-frequency lighting with multiscale spherical radial basis functions

This paper proposes a novel multiscale spherical radial basis function (MSRBF) representation for all-frequency lighting. It supports the illumination of distant environment as well as the local illumination commonly used in practical applications, such as games. The key is to define a multiscale and hierarchical structure of spherical radial basis functions (SRBFs) with basis functions uniformly distributed over the sphere. The basis functions are divided into multiple levels according to their coverage (widths). Within the same level, SRBFs have the same width. Larger width SRBFs are responsible for lower frequency lighting while the smaller width ones are responsible for the higher frequency lighting. Hence, our approach can achieve the true all-frequency lighting that is not achievable by the single-scale SRBF approach. Besides, the MSRBF approach is scalable as coarser rendering quality can be achieved without reestimating the coefficients from the raw data. With the homogeneous form of basis functions, the rendering is highly efficient. The practicability of the proposed method is demonstrated with real-time rendering and effective compression for tractable storage.

Efficient relighting of RBF-based illumination adjustable images

An illumination adjustable image (IAI) contains a large number of prerecorded images under various light directions. Relighting a scene under complicated lighting conditions can be achieved from the IAI. Using the radial basis function (RBF) approach to represent an IAI is proven to be more efficient than using the spherical harmonic approach. However, to represent high-frequency lighting effects, we need to use many RBFs. Hence, the relighting speed could be very slow. This brief investigates a partial reconstruction scheme for relighting an IAI based on the locality of RBFs. Compared with the conventional RBF and spherical harmonics (SH) approaches, the proposed scheme has a much faster relighting speed under the similar distortion performance.

Tileable BTF

This paper presents a modular framework to efficiently apply the bidirectional texture functions (BTF) onto object surfaces. The basic building blocks are the BTF tiles. By constructing one set of BTF tiles, a wide variety of objects can be textured seamlessly without re-synthesizing the BTF. The proposed framework nicely decouples the surface appearance from the geometry. With this appearance-geometry decoupling, one can build a library of BTF tile sets to instantaneously dress and render various objects under variable lighting and viewing conditions. The core of our framework is a novel method for synthesizing seamless high-dimensional BTF tiles, that are difficult for existing synthesis techniques. Its key is to shorten the cutting paths and broaden the choices of samples so as to increase the chance of synthesizing seamless BTF tiles. To tackle the enormous data, the tile synthesis process is performed in compressed domain. This not just allows the handling of large BTF data during the synthesis, but also facilitates compact storage of the BTF in GPU memory during the rendering.