Ray-Based Camera Parametrization

• Ray-based camera parametrization is a method that models imaging systems through bundles of rays, capturing both spatial and angular characteristics.
• It extends traditional pinhole models to include multi-view geometry, robust calibration, and simulation techniques using representations like TPP and rational camera models.
• This approach enhances camera design and optimization for applications in light field imaging, virtual reality, and sensor fusion.

Ray-based camera parametrization refers to the modeling and representation of cameras and optical systems by explicitly considering the paths, bundles, or distributions of rays that describe the mapping between scene points and image points. This approach generalizes the traditional pinhole or thin-lens models by treating the physical and computational imaging pipeline in terms of how rays propagate, interact with optical elements, and encode spatial or angular information. Ray-based parametrization provides foundational tools for the analysis and design of conventional, plenoptic, light field, and non-centric cameras, supports advanced calibration and simulation methods, and enables both robust multi-view geometry and physically accurate rendering.

1. Foundations of Ray-Based Parametrization

At its core, ray-based parametrization breaks the convention of mapping single points in the scene to single points in the image (as with the pinhole model) and instead analyzes how a camera represents each scene point by bundles of rays, often linked to each location or region on the camera's aperture or lens element. Notable formalizations include:

• Superposition of Views: Lens imaging can be reconsidered as the superposition of complete, sharp elemental images produced by each point (or pinhole) on the lens. Each lens subregion acts as an independent camera obscura, with all elemental images partially overlapping and yielding a sharp image only where they coincide (Grusche, 2015).
• Rational Camera Models: Scene points $x \in \mathbb{P}^3$ are mapped to rays via the “essential map,” and these rays are intersected with the image plane. Concrete analytical expressions map rays to image points and vice versa, allowing more general, nonlinear, or multi-slit camera geometries, with intrinsic parameters uniquely tied to ray geometry (Trager et al., 2016).
• Two-Parallel-Plane (TPP) Representation: Rays are parameterized by their intersections with two parallel planes (often applied in light field and plenoptic cameras), capturing both spatial and angular characteristics, and enable models with multiple projection centers (Zhang et al., 2018).

These concepts extend naturally to multi-view, light field, event-based, and non-traditional imaging systems, facilitating comprehensive modeling strategies for real and synthetic cameras.

2. Analytical and Calibration Frameworks

Ray-based parametrization is instrumental in developing robust analytical frameworks and calibration algorithms for a variety of camera types:

• Intrinsic and Extrinsic Parameters: In rational camera formalism, intrinsic calibration matrices may include unique 3D parameters (slit spacing, magnifications) not present in pinhole cameras, and extrinsics are tied to orbits under projective transformations (Trager et al., 2016).
• Light Field Camera Calibration: Calibration algorithms for multi-center systems employ linear homography extraction and Cholesky factorization to estimate parameters mapping pixel coordinates to ray coordinates. Nonlinear optimization (minimizing reprojection error) subsequently refines these estimates and corrects for radial distortions (Zhang et al., 2018, Jin et al., 2020).
• Refraction-Aware Calibration: The analytical refractive imaging (ARI) equation parameterizes the effects of refraction at interfaces between the lens/camera and different media, enabling joint optimization of camera and interface parameters using physically meaningful matrix representations. This yields significantly increased accuracy compared to ray-tracing or polynomial fitting approaches (Wang et al., 15 Aug 2025).
• Omnidirectional Camera Triangulation: Ray-based optimization on the projective sphere enables direct, closed-form triangulation via quadratic minimization, dramatically reducing computation time compared to iterative methods while unifying treatment for omnidirectional and narrow field-of-view cameras (Eising, 2022).

These calibration approaches benefit from the explicit coupling between ray geometry and camera parameters, facilitating robust estimation of pose and scene structure even across complex optical configurations.

3. Simulation and Rendering via Ray-Transfer and Ray-Tracing Methods

Simulating physical cameras and evaluating novel designs is greatly enabled by ray-based parametrizations:

• Ray-Transfer Functions: Multivariate polynomial models are fitted to input-output data from lens design tools (e.g., Zemax), replacing traditional ABCD matrices for general lens systems. These polynomial transfer functions are integrated into physically-based rendering engines (such as PBRT), yielding both computational efficiency and agreement with actual lens performance (Goossens et al., 2022).
• Ray Tracing-Guided Camera Design: Full lens geometry and aberrations (beyond paraxial approximations) are modeled by tracing bundles of rays, allowing precise focus and disparity constraint satisfaction in the design of plenoptic cameras. Optimization procedures align sensor and lens parameters for prescribed depth of field, disparity, and image quality (Michels et al., 2022).
• 4D Gaussian Ray Tracing: Integration of 4D Gaussian Splatting methods with hardware-accelerated ray tracing supports simulation of multiple camera effects—such as fisheye distortion, depth of field, and rolling shutter—leading to controllable, physically accurate data generation for benchmarking and robust vision model training. Performance metrics such as PSNR, SSIM, LPIPS, and rendering speed are rigorously evaluated on synthetic dynamic scene benchmarks (Liu et al., 13 Sep 2025).

Ray-based simulation facilitates detailed exploration of system-level optical effects, teaching, and supports the generation of training data for downstream computer vision systems requiring accurate modeling of non-ideal camera properties.

4. Multi-View Geometry and Ray-Based Correspondences

Ray-based parametrization also underpins advances in multi-view geometry, structure-from-motion, and sensor fusion:

• Epipolar Constraints and Tensors: For non-pinhole cameras (e.g., two-slit cameras), two-view correspondences are characterized by higher-order (2×2×2×2) “epipolar tensors” encoding incidence relations between reprojected rays. These tensors generalize the fundamental matrix and permit structure-from-motion and self-calibration in unconventional imaging geometries (Trager et al., 2016).
• Camera-Radar Fusion and Cross-Attention: In robust 3D object detection, camera and radar feature fusion is achieved by sampling along camera rays and matching to radar range signals via ray-constrained cross-attention, resolving depth/elevation ambiguities and supporting robust, multi-modal fusion (Hwang et al., 2022).
• Ray-Based Query Strategies in 3D Detection: Ray-centric object query initialization (Radial segmentation and ray-adaptive sampling) aligns the distribution of queries with the optical properties of the camera, thus reducing feature ambiguity and improving 3D detection accuracy in multi-camera setups (Chu et al., 20 Jul 2024).
• Distributed Pose Estimation via Ray Bundles: Camera poses are represented not as global extrinsics, but as distributed bundles of rays (Plücker coordinates) regressed from image patches—facilitating bottom-up estimation and supporting uncertainty modeling via denoising diffusion (Zhang et al., 22 Feb 2024).

These approaches allow simultaneous optimization of geometric correspondences, camera pose, and scene structure with high flexibility across central and non-central, single- or multi-modal imaging systems.

5. Neural Fields, Ray Matching, and Joint Optimization

Recent directions leverage ray-based parametrizations for joint optimization of neural fields and camera parameters:

• Feature Volume Probing: Neural fields (e.g., multi-resolution hash-encoded volumes) are probed along camera rays, which accumulate geometric and photometric features used for rendering or correspondence. The process integrates multi-view consistencies such as epipolar and point-alignment losses, ensuring accurate and coherent geometry reconstruction and novel view synthesis (Lin et al., 2 Dec 2024).
• Matched Ray Coherence: Instead of pixel-based photometric consistency, coherence is enforced between accumulated features along matched key rays—weighted by similarity scores (e.g., cosine similarity)—discounted in the presence of mismatches, making optimization robust to pose noise and erroneous correspondences.

These innovations couple high-dimensional representation learning with physically meaningful constraints derived directly from ray geometry, offering improved efficiency and accuracy in both static and dynamic scene reconstruction.

6. Applications, Limitations, and Future Directions

Ray-based camera parametrization finds significant application in:

• Photogrammetry and Industrial Inspection: Accurate modeling through refractive and multi-element interfaces (Wang et al., 15 Aug 2025).
• Virtual Reality and Immersive Rendering: Efficient implementations for off-axis stereo projection in dynamic tracked environments, using host/shader code compatible with modern ray tracing libraries (Zellmann et al., 2023).
• Event-Based Vision and Visual Odometry: High-frequency motion estimation by continuous ray warping and volumetric contrast maximization, robust to challenging illumination (Wang et al., 2021).
• Camera Design Validation and Training Data Generation: Generation of synthetic, physically consistent video data for AI models, including a variety of camera effects (Liu et al., 13 Sep 2025).

Limitations include sensitivity to noise and calibration coverage, complexity in handling unknown refractive interfaces, and the nontrivial algebraic structure of generalized multi-view tensors. Further research is directed at generalizing ray-based approaches to non-rational optics (e.g., extreme lens distortions), integrating neural rendering with explicit ray matching, and expanding distributed representations for robust pose and geometry inference.

Ray-based camera parametrization constitutes a mathematically rigorous, physically motivated, and computationally practical foundation for modeling, calibration, simulation, and analysis in modern computational imaging and vision systems.