“Eigenanalysis in Computer Graphics” by Bargteil and Olano
Conference:
Type(s):
Title:
- Eigenanalysis in Computer Graphics
Organizer(s):
Presenter(s)/Author(s):
Abstract:
Like a semester long graduate seminar on Eigenanalysis, Singular Value Decompositions, and Principal Component Analysis in Computer Graphics and Interactive Techniques, this course looks at matrix diagonalization and analysis through the lens of 13 technical papers selected by the lecturers. The lecturers will highlight trends, similarities, differences, and historical threads through the papers. The papers will cover a range of topics including numerical solutions, objective functions, discrete and continuous optimization, dimensionality reduction, and frictional contact. Applications will range from image stitching to truss structures to real-time rendering. Note that we slightly abuse the term Eigenanalysis to include the Singular Value Decomposition and Principal Component Analysis as all three techniques rely on matrix diagonalization. The course will also serve as a retrospective on the selected papers, placing them in historical perspective and highlighting significant contributions as well as forgotten gems.
Additional Information:
- Linear Color Representations for Full Spectral Rendering.
- Peercy, SIGGRAPH 1993. Creating an orthogonal set of spectral bases for full-spectral rendering.
- Solving polynomial systems for curve, surface and solid modeling.
- Manocha, SMA 1993. Curve/surface intersections by solving the resultant using SVD.
- OBBTree: a hierarchical structure for rapid interference detection.
- Gottschalk, Lin, Manocha, SIGGRAPH 1996. Eigen- vectors of the covariance matrix form a reasonable set of axes for an oriented bounding box.
- Feline: fast elliptical lines for anisotropic texture mapping.
- McCormack, Perry, Farkas, Jouppi, SIGGRAPH 1999. For anisotropic texture filtering.
- Normalized Cuts and Image Segmentation.
- Shi and Malik, PAMI 2000. Image segmentation through solving a generalized Eigenproblem.
- Style Machines.
- Brand and Hertzmann, SIGGRAPH 2000.
- Using Principal Component Analysis to identify a style subspace of human motion.
- Line direction matters: an argument for the use of principal directions in 3D line drawings.
- Girschick, Interrante, Haker, Lemoine, NPAR 2000.
- Eigenvectors of 2nd fundamental form are the principal directions of greatest and least curvature. Applications to NPR stroke guiding among others.
- Invertible finite elements For Robust Simulation of Large Deformation.
- Irving, Teran, and Fedkiw, SCA 2004.
- The SVD of the deformation gradient can be used to handle degenerate and inverted finite elements, leading to highly robust simulation of a wide range of material models.
- Real-Time Subspace Integration for St.Venant-Kirchhoff De- formable Models.
- Barbic and James, SIGGRAPH 2005.
- A generalized Eigenproblem constructed from finite element system matrices, known as Modal Analysis, leads to very efficient simulation.
- Model Reduction for Real-time Fluids.
- Treuille, Lewis, and Popovic, SIGGRAPH 2006.
- Principal Component Analysis of fluids simulations leads to a low-dimensional basis for fast simulation.
- Spectral Surface Quadrangulation.
- Dong, Bremer, Garland, Pascucci, and Hart, SIGGRAPH 2006.
- Eigenanalysis of geometry to resample surface meshes with quadrilaterals.
- Reconstructing surfaces of particle-based fluids using anisotropic kernels.
- Yu and Turk, ACM TOG 2013.
- Principal Component Analysis to define a better surface for particle-based fludis.
- Extracting Microfacet-based BRDF Parameters from Arbitrary Materials with Power Iterations.
- Dupuy, Heita, Iehl, Poulin, Ostromoukhov, EGSR 2015.
- BRDF fitting.
- Image Denoising Based on Nonlocal Bayesian Singular Value Thresholding and Stein’s Unbiased Risk Estimator.
- Li, Xie, Fan, Xu, Huffel, Sisson, IEEE TIP 2019.
- Applications to Monte- Carlo denoising.
Beginner
Prerequisite: Calculus and Linear Algebra
Topics: Math
List of topics and approximate times:
Additional Info: Like a semester long graduate seminar on Eigenanalysis, Singular Value Decompositions, and Principal Component Analysis in Computer Graphics and Interactive Techniques, this course looks at matrix diagonalization and analysis through the lens of 13 technical papers selected by the lecturers.
