printer friendly pageCME 251: Geometric and Topological Data Analysis (CS 233)
Mathematical and computational tools for the analysis of data with geometric content, such images, videos, 3D scans, GPS traces -- as well as for other data embedded into geometric spaces. Linear and non-linear dimensionality reduction techniques. Graph representations of data and spectral methods. The rudiments of computational topology and persistent homology on sampled spaces, with applications. Global and local geometry descriptors allowing for various kinds of invariances. Alignment, matching, and map/correspondence computation between geometric data sets. Annotation tools for geometric data. Geometric deep learning on graphs and sets. Function spaces and functional maps. Networks of data sets and joint learning for segmentation and labeling. Prerequisites: discrete algorithms at the level of
CS161; linear algebra at the level of Math51 or
CME103.
Terms: Win, Spr
| Units: 3
Instructors:
Guibas, L. (PI)
;
Weng, Y. (TA)
CS 233: Geometric and Topological Data Analysis (CME 251)
Mathematical and computational tools for the analysis of data with geometric content, such images, videos, 3D scans, GPS traces -- as well as for other data embedded into geometric spaces. Linear and non-linear dimensionality reduction techniques. Graph representations of data and spectral methods. The rudiments of computational topology and persistent homology on sampled spaces, with applications. Global and local geometry descriptors allowing for various kinds of invariances. Alignment, matching, and map/correspondence computation between geometric data sets. Annotation tools for geometric data. Geometric deep learning on graphs and sets. Function spaces and functional maps. Networks of data sets and joint learning for segmentation and labeling. Prerequisites: discrete algorithms at the level of
CS161; linear algebra at the level of Math51 or
CME103.
Terms: Win
| Units: 3
Instructors:
Guibas, L. (PI)
;
Weng, Y. (TA)
CS 348A: Computer Graphics: Geometric Modeling & Processing
The mathematical tools needed for the geometrical aspects of computer graphics and especially for modeling smooth shapes. The course covers classical computer-aided design, geometry processing, and data-driven approaches for shape generation. Fundamentals: homogeneous coordinates and transformation. Theory of parametric and implicit curve and surface models: polar forms, Bézier arcs and de Casteljau subdivision, continuity constraints, B-splines, tensor product, and triangular patch surfaces. Subdivision surfaces and multi-resolution representations of geometry. Surface reconstruction from scattered data points. Geometry processing on meshes, including simplification and parametrization. Deep neural generative models for 3D geometry: parametric and implicit approaches, VAEs and GANs. Prerequisite: linear algebra at the level of
CME103. Recommended:
CS248.
Last offered: Winter 2021
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