Lecture 01.2 – Introduction to Human Models

Lecture Slides: Introduction to Human Models

This lecture explores the evolution, mathematical foundations, and applications of human body modeling for virtual humans. We discuss how human body models have developed from early anatomical studies to modern computational representations like the Skinned Multi-Person Linear (SMPL) model, which can generate realistic virtual humans while remaining mathematically elegant and computationally efficient.

1. Historical Context of Human Body Modeling

Human body modeling has evolved considerably through history, with each stage building upon previous advances:

Early Developments

  • Renaissance Anatomical Studies: Leonardo da Vinci and Andreas Vesalius established detailed qualitative understanding of human form through careful observation and documentation.

  • Anthropometry: The measurement of human bodies using lengths, proportions, and circumferences emerged as a field to characterize body shape quantitatively, though these sparse measurements couldn’t capture detailed 3D variations.

Mid-20th Century Approaches

  • Geometric Approximations: Ernest Hanavan’s 1964 model represented the body as 15 interconnected geometric solids (cylinders, ellipsoids), parameterized by anatomical measurements.

  • Early Computer Graphics Models: Kinematic stick figures and rigid link models defined by artists or engineers, with manual tuning of segment lengths and shapes.

Data-Driven Revolution (1990s-2000s)

  • 3D Scanning Datasets: Large-scale scanning projects like CAESAR (Civilian American and European Surface Anthropometry Resource) captured thousands of 3D body scans.

  • Registration Methods: Techniques were developed to establish point-to-point correspondence across different body scans by fitting a common template mesh to all scans.

  • Statistical Shape Modeling: Allen et al. (2003) pioneered the application of principal component analysis (PCA) to registered body scans, creating a low-dimensional “shape space” that captured human shape variation efficiently.

  • SCAPE Model: Anguelov et al. (2005) introduced the Shape Completion and Animation of People (SCAPE) model, combining articulated skeleton rotation with learned non-rigid deformations to handle both shape and pose variations.

  • SMPL Model: Loper et al. (2015) developed the Skinned Multi-Person Linear (SMPL) model, which improved upon SCAPE with greater simplicity and compatibility with standard animation pipelines.

2. Mathematical Foundations of Human Body Models

The SMPL Model

SMPL represents a state-of-the-art parametric human body model that encodes body shape and pose in a low-dimensional vector of parameters. Mathematically, SMPL can be represented as a function:

\[M(\boldsymbol{\theta}, \boldsymbol{\beta}) \rightarrow Mesh(V, F)\]

where: - \(\boldsymbol{\theta}\) represents the pose parameters (joint angles) - \(\boldsymbol{\beta}\) represents the shape parameters - \(V\) is the set of mesh vertices (typically ~6890 vertices) - \(F\) defines the fixed mesh faces (connectivity)

The model consists of several key components:

  1. Template Mesh \(\bar{T}\): A triangulated surface representing a canonical human in a neutral pose and shape.

  2. Shape Blend Shapes \(B_S\): A set of basis vectors defining how the mesh deviates from the template for different body shapes:

    \[V_{shape}(\boldsymbol{\beta}) = \bar{T} + B_S \cdot \boldsymbol{\beta}\]

    where \(\boldsymbol{\beta}\) contains the PCA shape coefficients (typically 10 components).

  3. Pose Blend Shapes \(B_P\): Corrective shape deformations that account for non-rigid effects of pose:

    \[\Delta V_{pose}(\boldsymbol{\theta}) = B_P \cdot posemap(\boldsymbol{\theta})\]

    where \(posemap(\boldsymbol{\theta})\) converts joint rotations to an intermediate representation.

  4. Kinematic Skeleton: A set of joints \(J(\boldsymbol{\beta})\) with blend weights \(\mathcal{W}\) that attach vertices to the skeleton.

The final posed mesh is created through linear blend skinning:

\[v_i' = \sum_{j=1}^{K} W_{i,j} \cdot G_j(\boldsymbol{\theta}, J(\boldsymbol{\beta})) \cdot \tilde{v}_i\]

where: - \(\tilde{v}_i\) is the vertex after applying shape and pose blend shapes - \(G_j\) is the global transformation for joint \(j\) - \(W_{i,j}\) is the skinning weight for vertex \(i\) and joint \(j\)

PCA-Based Statistical Shape Modeling

Principal Component Analysis (PCA) enables the creation of a low-dimensional shape space:

  1. After registering scans to a common template, each individual’s shape is represented as a vector \(\mathbf{s}_m\) of length \(3N\) (the concatenated coordinates of all vertices).

  2. PCA computes the covariance matrix \(C = \frac{1}{M}\sum_m (\mathbf{s}_m - \bar{\mathbf{s}})(\mathbf{s}_m - \bar{\mathbf{s}})^T\) and its eigenvectors.

  3. The top \(n_\beta\) eigenvectors form a basis \(\Phi = [\mathbf{e}_1, \mathbf{e}_2, ..., \mathbf{e}_{n_\beta}]\) (the shape blend shapes matrix \(B_S\)).

  4. Any individual’s shape can be approximated as:

    \[\mathbf{s} \approx \bar{\mathbf{s}} + \sum_{i=1}^{n_\beta} \beta_i \mathbf{e}_i\]

This provides an extremely efficient representation, with just 10 parameters explaining ~90% of human shape variation across a population.

Kinematic Modeling

The articulated human skeleton is modeled as a kinematic tree:

  1. Forward Kinematics (FK): Computes the position and orientation of each body part based on joint angles \(\boldsymbol{\theta}\). The global transform of each joint is:

    \[G_j = G_{parent(j)} \cdot \text{Trans}(L_{parent(j)}) \cdot R_j(\theta_j)\]

  2. Inverse Kinematics (IK): Solves for joint angles that position an end-effector (e.g., hand, foot) at a desired location. This typically uses iterative numerical methods with the Jacobian:

    \[J(\boldsymbol{\theta}) = \frac{\partial \mathbf{p}}{\partial \boldsymbol{\theta}}\]

    which relates changes in joint angles to changes in end-effector position.

3. Applications of Human Body Models

Human body models find applications across numerous fields:

Computer Animation and Visual Effects

  • Digital humans for film, gaming, and VR

  • Motion capture retargeting to create digital doubles

  • Character animation in standard graphics pipelines

Virtual Humans and Avatars

  • Personalized avatars for AR/VR experiences

  • Real-time tracking and animation of user movement

  • Telepresence and social VR applications

Biomechanics and Ergonomics

  • Analysis of human movement and forces in sports science and medicine

  • Ergonomic assessment for workspace design

  • Testing designs across different body types using statistical models

Human-Computer Interaction (HCI)

  • Virtual try-on systems for online retail

  • Gesture recognition interfaces

  • Fitness applications with posture feedback

Computer Vision and AI

  • Pose and shape estimation from images or video

  • Action recognition using pose information

  • Person tracking and understanding in scenes

Education and Training

  • Medical training simulations

  • Virtual reality training for various professions

  • Customizable avatars for diverse training scenarios

4. Challenges and Future Directions

Despite significant progress, several challenges remain in human body modeling:

Computational Efficiency

  • Optimizing for real-time performance in interactive applications

  • Efficient evaluation of complex models with high vertex counts

  • Real-time fitting of models to sensor data

Accuracy and Detail

  • Capturing fine details like facial expressions, hands, and feet

  • Modeling realistic soft-tissue deformation

  • Representing wrinkles, muscle definition, and skin dynamics

Generalization

  • Handling extreme body types and poses outside the training distribution

  • Ensuring biomechanical plausibility for all generated shapes

  • Robust modeling across diverse populations

Clothing and Accessories

  • Integrating clothing into body models

  • Simulating realistic garment-body interactions

  • Disentangling body shape from clothing in scans

Emerging Approaches

  1. Neural Implicit Models: Representing humans with neural implicit functions instead of explicit meshes: - Networks like NASA (Neural Articulated Shape Approximation) learn pose-conditioned occupancy - Can capture arbitrary topology and fine detail without fixed mesh resolution

  2. Deep Learning-Based Modeling: - Nonlinear shape spaces using variational autoencoders or generative models - Neural networks that predict body parameters from data - Deep generative models for motion synthesis

  3. Biomechanical Integration: - Models with physical awareness and joint constraints - Internal skeletal structure and muscle simulation - Physically plausible animation

  4. Personalization: - Creating accurate models from minimal input (few photos) - Capturing individual-specific details efficiently - Hybrid parametric-implicit approaches for personalization

5. Conclusion

Human body modeling has evolved from simple geometric approximations to sophisticated data-driven models that can represent diverse human shapes and realistic motion. The SMPL model exemplifies the current state-of-the-art approach with its balance of expressiveness, simplicity, and computational efficiency.

As we look to the future, neural networks and implicit representations promise even greater realism and flexibility, while the integration of biomechanical principles will ensure physical plausibility. These developments will enable increasingly realistic virtual humans for applications spanning entertainment, medicine, training, and human-computer interaction.