Omnidirectional 3D Gaussian Rendering With Polar Stretching
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional 3D Gaussian Splatting (3DGS) models are ill-suited for 3D reconstruction of omnidirectional cameras due to the distortion of light caused by the lens or mirror, violating the affine transformation assumption and leading to rendering quality and parallelization issues.
Innovation Solution
Adaptive methods and processors are developed to simulate the light distortion of omnidirectional cameras through affine transformations like translation, rotation, and stretching, applying weight masks to balance convergence rates, and using high-order approximations for polar stretching ratios to enhance rendering quality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional 3DGS models are used for omnidirectional cameras, then rendering speed is fast, but rendering quality deteriorates due to light distortion violating affine transformation assumption
Solution Approach 1:
The patent applies parameter changes by introducing polar stretching ratios and affine transformation parameters (translation, rotation, scaling) to adapt the 3DGS model to omnidirectional camera distortion. By modifying the projection parameters and introducing camera-specific transformation matrices, the system maintains the fast rendering speed of 3DGS while correcting the rendering quality degradation caused by light distortion.
Solution Approach 2:
The patent segments the rendering process into distinct transformation stages: first applying affine transformation to correct distortion, then performing the standard 3DGS projection. This segmentation allows each stage to be optimized independently, maintaining computational efficiency while improving rendering accuracy for omnidirectional cameras.
2Productivity
If conventional 3DGS models are used for omnidirectional cameras, then parallelization is efficient, but rendering quality deteriorates due to distortion violations
Solution Approach 1:
The patent applies preliminary action by pre-computing the affine transformation parameters and polar stretching ratios for each Gaussian blob before the main rendering loop. This preliminary computation separates the distortion correction from the parallelized projection step, allowing the computationally intensive parallelization to operate on already-corrected data, thus maintaining efficiency while improving quality.
3Manufacturing precision
If affine transformations are applied to simulate light distortion, then rendering quality improves, but computational complexity increases
Solution Approach 1:
The patent applies local quality by computing affine transformation parameters and polar stretching ratios specifically for each Gaussian blob based on its local position and orientation in the scene. Rather than applying a global transformation to all elements, each Gaussian receives localized transformation parameters tailored to its specific context, improving rendering quality while keeping computational overhead manageable through selective computation.
Data Source
AI summary
Methods and processors for rendering a 3D Gaussian are disclosed. The processor is configured to acquire the 3D Gaussian to be rendered, and a camera model representing an omnidirectional camera with an optical axis, updating a color of the 3D Gaussian using spherical harmonics, update a position of the 3D Gaussian by moving the 3D Gaussian towards the optical axis, update a scale of the 3D Gaussian by compressing the 3D Gaussian in at least one of a tangential direction and a polar direction relative to the optical axis, and render an updated 3D Gaussian onto a 2D plane using a 3DGS model.