Chapter 28: Multi-View Geometry and Differentiable Rendering

Learning Objectives

• Derive the epipolar constraint and the fundamental matrix from projective geometry, and explain their role in multi-view 3D reconstruction
• Formulate bundle adjustment as a nonlinear least-squares problem and connect it to RF array calibration
• State the rendering equation and explain how differentiable renderers enable gradient-based inverse rendering
• Contrast optical and RF rendering in terms of wavelength scale, coherence, and forward model structure
• Describe early, mid-level, and late fusion architectures for multi-modal perception and their tradeoffs
• Formulate PINNs for the Helmholtz equation and explain spectral bias limitations
• Apply Fourier Neural Operators to learn resolution-independent mappings for wave propagation