Summer School on Shape Modelling Hosted by DA-IICT Gandhinagar (online)

Sponsored by Dassault Systèmes Foundation

Dates: 14 to 25 June 2021

Academic coordinator:

Aditya Tatu [email protected]

Organizing institution: DA-IICT Gandhinagar

Platform: Google Meet

Description of school:
Shape is a concept that all of us understand and use in our day-to-day life. Due to availability of 3D scanners and computational power, a lot of research as well as applications have come based on the shape of 3D objects. Some examples of the wide-ranging applications of 2D and 3D shape modeling are medical image diagnostics, Product design and 3D Animation. These applications are broadly based on concepts like automated classification of objects based on their Shapes, learning and parameterizing a plausible shape space, and computing a realistic shape deformation. The summer school aims to introduce students to the area of Shape modeling, analysis and processing. It will cover theory, algorithms and computational tools used in various applications.

List of topics and subtopics:

Linear Algebra and Optimization Refresher

Vector space, linear independence, span
Eigenvectors and eigenvalues
Gradient descent, Newton’s method

Statistical Shape Analysis

Landmarks pointset representation, shape correspondence
Shape optimization
Applications: hypothesis testing, shape priors

Curves and Surfaces

Parametric curves
First and second fundamental forms
Curvatures: principal, mean and Gaussian

Procedural Geometry

Procedural surfaces – blend surfaces, offset surfaces, sweep surfaces
Procedural curves - surface-surface intersection curves
Demonstrations

Discrete Surfaces

Level set curves and surfaces
Delaunay triangulation
Surface reconstruction

Laplace Beltrami on Manifolds and Meshes with Applications

Overview of Poisson, heat, wave, and Helmholtz equations
Discrete manifolds, discretization of the Laplacian and discrete solution
Applications: shape registration, distance field computation etc.

Shape Deformation/Animation

Skinning: linear and non-linear methods
Shape deformation
Interpolation

Non-Rigid Shape Matching

MDS
Spectral MDS

Geometric Deep Learning

Intro to graph neural networks/GDL
Types of layers: convolution, pooling/li>
Common applications

Proposed list of speakers:

Aditya Tatu (DAIICT Gandhinagar)
Ramanathan M (IIT Madras)
Suyash Awate (IIT Bombay)
Ojaswa Sharma (IIIT Delhi)
Kaushik Kalyanaraman (IIIT Delhi)
Sumukh Bansal (InterDigital Inc. France)
Satish Sonawane (Dassault Systèmes)
Aditya Intwala (Dassault Systèmes)
Vipul Lotke (Dassault Systèmes)

Background/prior courses recommended:

Linear algebra
Calculus
Skills in programming in MATLAB/Python3