Research
My research interests lie at the intersection of computer graphics, computer vision, and simulations. Here are some of the research topics I have explored in depth.
Neural Networks
Deep learning fundamentals, forward/backward propagation, and optimization.
- Mathematical foundations of neural networks including forward propagation, backpropagation, and gradient descent.
- Comprehensive study of activation functions, loss functions, and optimization algorithms.
- Analysis of regularization techniques including L1/L2 regularization and dropout for preventing overfitting.
- Theoretical understanding of training dynamics, convergence, and generalization in deep learning systems.
Neural Networks Deep Learning ML CNN
Mesh Representations
A review of commonly used mesh representations and their trade-offs.
- Comprehensive analysis of mesh data structures including face-based, edge-based, and vertex-based representations.
- Memory consumption and performance trade-offs between adjacency lists, indexed face sets, and connectivity structures.
- Edge-based representations: winged-edge, half-edge, and directed-edge data structures for efficient mesh traversal.
- Render-optimized approaches including corner tables and hybrid geometric-topological representations.
Computational Geometry Data Structures Topology
Monte Carlo Light Transport
Light transport, Monte Carlo methods, and MCML.
- Deep dive into radiometry, light transport theory, reflectance distribution functions, and Monte Carlo methods.
- Comprehensive study of the Monte Carlo Multi-Layered (MCML) algorithm for accurate simulation of photon propagation.
- Theoretical foundations of subsurface scattering and the radiative transfer equation.
- Analysis of material properties and their effects on light transport in complex mediums.
Light Transport Monte Carlo Methods MCML BRDF Subsurface Scattering
Skin Rendering
Real-time physically-based skin rendering with subsurface scattering.
- Advanced shading techniques for real-time rendering of human skin combining surface reflection and subsurface scattering.
- Implementation of physically-based reflectance models including Kelemen/Szirmay-Kalos specular BRDF and Cook-Torrance approximations.
- Screen-space and texture-space diffusion approaches for real-time subsurface scattering using Gaussian approximations.
- Translucency effects and transmittance modeling using translucent shadow maps and attenuation functions.
BRDF BSSRDF Subsurface Scattering Real-Time Rendering Physically-Based Rendering