Virtual Humans Tutorial

Welcome to these expanaded course notes for the Virtual Humans lecture series.

This material is based on—but not officially affiliated with—the original Virtual Humans lecture series from the Max Planck Insitute for Informatics MPI-INF. The original course material was developed by:

• Prof. Dr. Gerard Pons-Moll (MPI-INF, University of Tübingen)

• Xianghui Xie

• Yuxuan Xue

• Berna Kabadayi

For the original lecture slides, videos, and official resources, please visit: Virtual Humans MPI-INF

This document was created with assistance of AI to expand upon the original course material.

Attribution

This document was created with AI assistance to expand upon concepts, provide alternative explanations, and include additional details and derivations from the original lectures. All foundational content and credit belong entirely to the original authors listed above.

This supplementary material does not replace the original lecture content. It is intended solely to aid in the understanding and further exploration of topics covered in the original course.

Below you will find an overview of the core lectures on image formation, rotations & kinematics, surface representations, and Procrustes alignment.

Contents:

• Lecture 01.1 – Historical Body Models
  • Introduction
  • Early Origins: Simplified Primitives and Kinematic Skeletons (1970s–1980s)
  • Advances in the 1990s: Superquadrics, Differentiable Fitting, and Physical Models
  • The Impact of 3D Scanning and Data: From Anthropometry to Statistical Models (1990s–2000s)
  • SCAPE and the Emergence of Pose-Aware Models (Mid-2000s)
  • Consolidation in the 2010s: SMPL and Integration with Learning-Based Methods
  • Deep Learning and Neural Implicit Models (Late 2010s–Present)
  • Timeline Summary of Milestones
  • Conclusion
• Lecture 01.2 – Introduction to Human Models
  • 1. Historical Context of Human Body Modeling
  • 2. Mathematical Foundations of Human Body Models
  • 3. Applications of Human Body Models
  • 4. Challenges and Future Directions
  • 5. Conclusion
• Lecture 01.3 – Introduction to Human Models (Overview)
  • 1. Historical Context
  • 2. Mathematical Foundations
  • 3. Image Formation and Rendering
  • 4. Surface Representation Methods
  • 5. Motion Capture and Behavior Synthesis
  • 6. Clothing Modeling
  • 7. Human-Object Interaction
  • 8. Applications
  • 9. Challenges and Future Directions
• Lecture 02.1 – Image Formation
  • 1. Historical Developments in Image Formation
  • 2. The Pinhole Camera Model
  • 3. Camera Intrinsics and the Projection Matrix
  • 4. Image Distortions & Correction
  • 5. Properties of Perspective Projection
  • 6. Advanced Theoretical Extensions
  • 7. Applications in Modern Vision and Graphics
  • 8. Python Example: Simulating Image Formation
• Lecture 02.2 – Rotations and Kinematic Chains
  • 1. Representations of 3D Rotations
  • 2. Lie Algebra \(so(3)\) and Exponential Map
  • 3. Rodrigues’ Rotation Formula
  • 4. Kinematic Chains: Forward & Inverse Kinematics
  • Comparison of Rotation Representations
• Lecture 03.1 – Surface Representations
  • 1. Mathematical Foundations of Surface Representations
  • 2. Surface Differential Properties
  • 3. Discrete Surface Representations
  • 4. Advanced Surface Representations
  • 5. Comparative Analysis and Applications
  • 6. Implementation Examples
  • 7. Advanced Topics and Future Directions
• Lecture 03.2 – Procrustes Alignment
  • Introduction
  • Goal: Learning a Model of Pose and Shape
  • The Challenge of Registration
  • Surface Representation: Mesh
  • The Procrustes Alignment Problem: Mathematical Formulation
  • Rigid Transformations
  • Procrustes Alignment Solution
  • Complete Mathematical Derivation
  • Summary of Procrustes Alignment Algorithm
  • Python Implementation Example
  • Practical Applications
  • Interactive Visualization Ideas
• Lecture 4.1: Iterative Closest Point
  • Introduction to Shape Alignment and Registration
  • Review: Procrustes Analysis
  • Problem: Unknown Correspondences
  • The Iterative Closest Point (ICP) Algorithm
  • Point-to-Point vs. Point-to-Plane ICP
  • Gradient-based ICP for Non-Rigid Registration
  • Improving ICP’s Robustness
  • Point-to-Surface Distance
  • ICP Variants and Extensions
  • Applications of ICP
  • Implementing ICP
  • Conclusion
• Lecture 04.2 - Body Models: Vertex-Based Models and SMPL
  • 1. Body Models as Parameterized Functions
  • 2. Rotations, Articulation, and Pose Representation
  • 3. Linear Blend Skinning and its Limitations
  • 4. The SMPL Body Model
  • 5. Comparison with SCAPE
  • 6. Alignment Techniques: Procrustes Analysis and ICP
  • 7. Image Formation and the Pinhole Camera Model
  • 8. Extensions and Advanced Applications
  • Conclusion
• Lecture 5.1 - Training a Body Model and Fitting SMPL to Scans
  • Introduction
  • Body Models Based on Triangle Deformations
  • Training a Body Model from Registrations
  • Obtaining Registrations: Fitting SMPL to Scans
  • Joint Registration and Model Training
  • Summary
• Lecture 05.2 - 3D Registration: From Classical ICP to Modern Methods
  • Introduction
  • 1. Rigid Registration and the ICP Algorithm
  • 2. Classical Non-Rigid Registration
  • 3. Parametric Models and the SMPL Body Model
  • 4. Modeling Clothing and Fine Details: SMPL+D
  • 5. Survey of 3D Registration Methods: From ICP to Deep Learning
  • Summary
• Lecture 06.1 - Fitting the SMPL Model to Images via Optimization
  • Introduction
  • Mathematical Background: Pinhole Camera and Projections
  • The SMPL Model as a Differentiable Function of Shape and Pose
  • Fitting SMPL to Images via Optimization (SMPLify)
  • Historical Progression and Method Comparisons
• Lecture 06.2 - Learning-Based Fitting of the SMPL Model to Images
  • Introduction
  • Foundations of Learning-Based SMPL Estimation
  • Early Regression Approaches: HMR and NBF
  • Evolving Architectures: Hybrid and Improved Regression Methods
  • Temporal Methods: From Single Images to Video Sequences
  • Comparison of Learning-Based Methods
  • Conclusion
• Lecture 07.1: Fitting SMPL to IMU Data Using Optimization-Based Methods
  • Introduction
  • Classical IMU-Based Pose Estimation: A Historical Perspective
  • Inertial Sensor Fundamentals and Orientation Representations
  • Optimization-Based SMPL Fitting with IMU Data
  • Pseudocode: SMPL Pose Estimation from IMU Sequence
  • IMU-Based Human Pose Datasets and Resources
• Lecture 07.2: Fitting SMPL to IMU Data Using Learning-Based Methods
  • Introduction
  • Optimization-Based vs. Learning-Based Approaches
  • Learning-Based IMU-to-Pose Estimation: Historical Overview of Key Models
  • Problem Formulation and Learning Task Definition
  • Model Architectures and Design Considerations
  • Training Pipeline and Pseudocode
  • Datasets, Benchmarks, and Resources
  • Challenges and Outlook
  • Conclusion
• Lecture 08.1: Vertex-Based Clothing Modeling for Virtual Humans
  • Introduction
  • Clothing Representation as Vertex Displacements
  • Registration of Clothed Human Scans
  • Estimating Body Shape Under Clothing: The BUFF Method
  • Multi-Layer Clothing Capture: The ClothCap Method
  • Applications of Multi-Layer Registration
  • Conclusion
• Lecture 09.1: Neural Implicit and Point-Based Representations for Clothed Human Modeling
  • Introduction
  • Background: Explicit vs. Implicit vs. Point-Based Representations
  • Expressiveness and Topology
  • Differentiability and Learning
  • Data Efficiency and Performance
  • Neural Implicit Function Foundations
  • Articulated Deformation Fields for Implicit Models
  • Generative Implicit Models for Clothed Bodies
  • Pose-Dependent Implicit Models and Animatable Avatars
  • Blueprint Algorithms for Key Methods
  • Historical Perspective and Future Outlook
  • Conclusion
• Neural Radiance Fields: A Historical and Theoretical Overview
  • Introduction
  • Foundations: 3D Scene Representation and Reconstruction Techniques
  • Emergence of Neural Radiance Fields (NeRF)
  • Theoretical and Mathematical Analysis of NeRF
  • Major Advancements and Extensions of NeRF
  • Comparison with Other 3D Representations
  • Datasets for NeRF Training and Evaluation
  • Conclusion
• 3D Gaussian Splatting: A Basic Introduction
  • Introduction
  • Foundations
  • The Evolution of Novel View Synthesis
  • 3D Gaussian Splatting: A Convergence of Approaches
  • Mathematical Formulation of 3D Gaussian Splatting
  • Training and Optimization
  • Optimization Process
  • Implementation and Real-Time Rendering
  • Comparison with Other Methods
  • NeRF vs. 3D Gaussian Splatting
  • Voxel-Based Representations vs. Gaussians
  • Traditional Point-Based Rendering vs. Gaussian Splatting
  • Applications and Extensions
  • Static Scene Reconstruction
  • Dynamic Scene Capture
  • Avatar Creation and Animation
  • Integration with Neural Rendering
  • Large-Scale Scene Rendering
  • Bézier Gaussian Triangles (BG-Triangle) for Sharper Rendering
  • Human Reconstruction with Gaussian Splatting and Priors
  • Dynamic Scene Reconstruction with 4D Gaussian Splatting
  • Implementation Details and Real-Time Performance
  • Benchmarks and Comparative Evaluation
  • Datasets and Resources
  • Future Directions
  • Conclusion
  • Glossary
• References
  • Lecture 01.1 (Historical Body Models)
  • Lecture 01.2 (Introduction to Human Models)
  • Lecture 01.3 (Introduction to Human Models Continued)
  • Lecture 02.1 (Image Formation)
  • Lecture 02.2 (Rotations & Kinematic Chains)
  • Lecture 03.1 (Surface Representations)
  • Lecture 03.2 (Procrustes Alignment)
  • Lecture 04.1 (Iterative Closest Points)
  • Lecture 04.2 (Body Models)
  • Lecture 05.1 (Body Model Training)
  • Lecture 05.2 (3D Registration)
  • Lecture 06.1 (Fitting SMPL to Images)
  • Lecture 06.1 (Optimization-Based Fitting of SMPL to Images)
  • Lecture 06.2 (Learning-Based Fitting of SMPL to Images)
  • Lecture 07.1 (Fitting SMPL to IMU Optimization)
  • Lecture 07.2 (Fitting SMPL to IMU Learning)
  • Datasets and Resources
  • Relevant Software and Libraries
  • Lecture 08.1: References for Vertex-Based Clothing Modeling for Virtual Humans
  • Body Models and Shape Estimation
  • Alternative Representations
  • Datasets
  • Software and Libraries
  • Lecture 09.1: References for Neural Implicit and Point-Based Representations for Clothed Human Modeling
  • Point-Based Models
  • Datasets and Resources
  • Related Software and Libraries
  • Review Papers and Tutorials
  • Neural Radiance Fields (NERF)
  • Gaussian Splatting