Courses

Wednesday, 15 December | 9:00 AM - 12:45 PM | Room 314

Presented in English / 영어로 발표 됨

Scattered Data Interpolation for Computer Graphics

Tuesday, 14 December | 7:00 午後 - 10:45 午後 | Room 314

Interpolation is a fundamental topic in computer graphics. While textbooks have generally focused on "regular" interpolation schemes such as B-splines, scattered interpolation approaches also have been a wide variety of applications. These include topics in facial animation, skinning, morphing, rendering, and fluid simulation.

This best-practice guide to scattered data interpolation reviews the major algorithms for scattered interpolation, shows how and where they are applied in a variety of published graphics studies, and compares and contrasts them. The algorithms include Shepard interpolation, Wiener interpolation, Laplace and thin-plate interpolation, radial basis functions (RBFs), moving least squares, and kernel regression. The course summarizes stability and computational properties with a focus on real-time applications and provides some theoretical insights to broaden the course's engineering perspective.

Level

Intermediate

Intended Audience

Intermediate and advanced students, developers, and researchers working in many areas of graphics.

Presentation Language

Presented in English / 영어로 발표 됨

Prerequisites

Knowledge of linear algebra at the level required for intermediate or advanced graphics programming. The concluding section of the course requires basic calculus.

Syllabus

Introduction - Pighin
 Survey of Applications
   Morphing
   Skinning and facial animation
   Rendering: precomputed radiance transfer
   Fluid editing
   Others
Distinguishing Issues

Survey of Scattered Interpolation Algorithms - Pighin, Lewis
   Shepard's interpolation
   Wiener interpolation
   Natural neighbor interpolation
   Moving least-squares
   Kernel regression

Break

Radial Basis Function Variants - Pighin
   Kernels
   Normalized RBFs
   Adaptive RBFs 

Laplace and Thin-Plate Interpolation - Lewis
   Kernels
   Normalized RBFs
   Adaptive RBFs

Advanced Applications - Pighin
   Dynamics
   Interpolation on manifolds

Break

Where do RBFs Come From? - Lewis
   What kernels will interpolate?
   Kernels, differential operators, and roughness penalties
   Green's functions 

The Deeper Theory - Anjyo
   Functional analysis
   Reproducing kernel Hilbert spaces

J.P. Lewis
Weta Digital

Fred Pighin
Google, Inc.

Ken Anjyo
OLM Digital, Inc.

Instructor Bios

J.P. Lewis is a research lead at Weta Digital and a part-time senior lecturer at Victoria University in Wellington, New Zealand. He has worked in both academic research and in the film industry, and his algorithms have been adopted by Matlab and commercial graphics software packages. He has published research involving several approaches to scattered interpolation, and in particular his pose-space deformation skinning approach is the subject of several industry implementations.

Fred Pighin's research interests are in data-driven animation. Before joining the StreetView team at Google, he was a research assistant professor at the University of Southern California and a technical lead at Industrial Light & Magic. He has published research in areas including eye movement, automatic partitioning of blendshape models, emotional speech animation, and the use of scattered interpolation for directing fluid simulations, and his pioneering work on construction and animation of 3D facial models from images is widely recognized.

Ken Anjyo is the digital-effects and R&D supervisor at OLM Digital and an affiliate professor at Kyushu University. He has published research on topics including natural phenomena and non-photorealistic rendering, and his work on hair simulation, motion editing, and view morphing is widely cited. His current research interests include construction of mathematical and computationally tractable models for computer graphics.