Shape Analysis and 3D Deep Learning

Contents

Knowledge: After successful completion of the module, students know

• different representations for 3D shapes (e.g. meshes, voxel grids, point clouds, implicit functions)
• how to analyse single shapes (e.g. feature descriptors, global/partial symmetries, segmentations, decompositions)
• 3D deep learning (e.g. suitable representations, shape encoding, decoding and generation, learning high-level structures)

Skills: After successful completion of the module, students will be able to

• explain algorithms and methods for analyzing and generating 3D geometry
• understand geometry related aspects and challenges in the domain of deep learning
• implement neural networks for basic geometry related tasks

Competencies: Based on the knowledge and skills acquired in the module, students will be able to

• discuss how shape analysis can be used for high- and low-level geometry processing tasks
• make an informed choice in how to represent 3D shapes for different tasks
• make an informed choice in opting for a model-driven, a data-driven, or a hybrid approach, depending on the data availability

The lecture covers the following topics:

• Data Analysis Fundamentals

  • Dimensionality Reduction
  • Clustering

• Classical Shape Analysis

  • Shape Representations
  • Global and Local Shape Descriptors
  • Shape Distance Measures and Structures

• 3D Deep Learning

  • Shape Encoding and Decoding

    • Images
    • Neural Radiance Fields
    • Point Clouds
    • Voxels
    • Implicit Functions
    • Graphs and Manifolds

  • Methods for 3D Shape Generation

    • Vector Quantized Variational Autoencoders
    • Autoregressive Transformers
    • Generative Adversarial Networks
    • Diffusion Models

Organizational

• Weekly exercises (mandatory practical, optional theoretical)
• Practical part in Python
• 120 minutes exam
• Exam admittance requires 50% of practical exercise points
• Small exam bonus for 75% of practical exercise points

Prerequisites

• Basic understanding of Neural Networks is recommended, but we will provide an "Introduction to Deep Learning"
• The lecture "Basic Techniques in Computer Graphics" and "Geometry Processing" is considered helpful, but not a hard requirement