Differentiable Volume Renderer Using Gaussian Ellipsoids
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Solution Overview
Problem
Conventional rendering techniques face challenges in interpretability and modifiability, particularly with hard boundaries blocking gradients and the absence of gradients toward invisible components, limiting their ability to simulate real-world optical properties effectively.
Innovation Solution
A differentiable volume renderer using neural Gaussian Ellipsoids (VoGE) combines explicit object geometries with ray tracing volume density aggregation, providing excellent interpretability and modifiability while resolving mutual occlusion with full differentiability, and offering an approximate closed-form solution for efficient volume density aggregation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Shape
If conventional rendering techniques use hard boundaries for object components, then object geometry is well-defined, but gradients are blocked and differentiability is lost
Solution Approach 1:
The patent transforms discrete object components into continuous Gaussian ellipsoid representations with soft boundaries. By parameterizing objects as sums of Gaussian functions with continuous parameters (mean, covariance, amplitude), the rendering becomes differentiable while maintaining geometric definition. This resolves the contradiction by changing from hard geometric boundaries to soft probabilistic boundaries.
Solution Approach 2:
The patent replaces traditional geometric rendering mechanics with probabilistic field-based rendering. Instead of using explicit geometric primitives with hard boundaries, it substitutes a continuous density field represented by Gaussian ellipsoids, enabling gradient flow through the rendering process while preserving shape information.
2Reliability
If volume rendering traces rays through volume density aggregation, then realistic optical properties are achieved, but computational complexity increases
Solution Approach 1:
The patent changes the computational approach by parameterizing volume density as a sum of Gaussian functions. This allows analytical integration along rays using the closed-form solution for Gaussian integrals, reducing computational complexity from numerical integration to simple parameter evaluation while maintaining realistic optical rendering.
Solution Approach 2:
The patent uses Gaussian ellipsoid representations that can be analytically integrated, effectively copying the beneficial properties of Gaussian functions (analytical tractability) into the volume rendering framework. This allows the rendering to maintain optical realism while achieving computational efficiency through closed-form solutions.
3Adaptability or versatility
If explicit object geometries are used, then interpretability and modifiability improve, but gradient flow is blocked by hard boundaries
Solution Approach 1:
The patent maintains explicit object representations but changes their mathematical form from hard geometric primitives to soft Gaussian field representations. This allows the objects to remain interpretable and modifiable through their Gaussian parameters while enabling gradient flow through the soft boundaries, resolving the contradiction between interpretability and differentiability.
Data Source
AI summary
The present disclosure describes techniques of rendering images using explicit object representation via rays tracing volume density aggregation. The techniques comprise reconstructing an object into a plurality of Gaussian ellipsoids; determining a volume density of each of the plurality of Gaussian ellipsoids along each of a plurality of viewing rays; determining a weight of each of the plurality of Gaussian ellipsoids based on the volume density; and synthesizing an image of the object using the determined weight on each pixel of the image to interpolate attributes of each of the plurality of Gaussian ellipsoids.