Splat-Based Differentiable Rendering for Smooth Occlusion Gradients
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Solution Overview
Problem
Existing methods for computing derivatives of three-dimensional polygonal meshes are computationally expensive and difficult to implement, particularly at occlusion boundaries, due to discontinuities introduced by occlusion boundaries.
Innovation Solution
A method involving rasterization of a three-dimensional mesh into a two-dimensional raster, construction of splats at pixel coordinates, and determining updated color values based on splat weighting to generate a differentiable rendering, enabling smooth derivatives at occlusion boundaries.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If contemporary methods (mesh processing, custom derivative calculations) are used to compute derivatives at occlusion boundaries, then measurement precision can be improved, but device complexity and productivity deteriorate due to computational expense and implementation difficulty
Solution Approach 1:
The patent introduces a differentiable rendering pipeline as an intermediary between the 3D mesh and derivative computation. This pipeline uses continuous differentiable functions (such as soft-max weighting and differentiable occlusion handling) to bridge the discontinuous occlusion boundaries, enabling accurate gradient flow without requiring complex custom derivative calculations at boundary regions
Solution Approach 2:
The patent replaces traditional mechanical mesh processing approaches (which involve explicit boundary detection and handling) with a field-based differentiable rendering system. This substitution uses continuous mathematical fields and differentiable operations to naturally handle occlusion boundaries, eliminating the need for discrete boundary processing and its associated computational overhead
2Measurement precision
If contemporary methods are used for derivative computation, then measurement precision can be improved, but ease of manufacture deteriorates due to implementation difficulty
Solution Approach 1:
The differentiable rendering pipeline serves multiple functions simultaneously: it performs standard rendering, handles occlusion boundaries, and provides differentiable outputs for gradient computation. This multi-functionality eliminates the need for separate custom derivative calculation routines, simplifying implementation while maintaining accuracy
Solution Approach 2:
The patent transforms the discrete, non-differentiable rendering parameters into continuous differentiable parameters. By using soft-max weighting functions and continuous occlusion handling, the system maintains measurement precision while enabling straightforward implementation through standard differentiable operations rather than complex boundary case handling
3Productivity
If splat-based differentiable rendering is used, then productivity is improved through computational efficiency, but manufacturing precision may worsen without proper weighting mechanisms
Solution Approach 1:
The patent implements feedback through differentiable weighting mechanisms that continuously adjust splat contributions based on occlusion and visibility information. This feedback loop ensures that computationally efficient splat operations maintain rendering accuracy by dynamically weighting contributions according to scene geometry and occlusion relationships
Solution Approach 2:
The system uses dynamic weighting of splats based on continuous differentiable functions that adapt to scene conditions. Rather than static blending, the weighting mechanisms dynamically adjust contributions according to occlusion boundaries and view-dependent factors, maintaining precision while benefiting from efficient splat-based rendering
Data Source
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AI summary
Systems and methods of the present disclosure are directed to a method that can include obtaining a 3D mesh comprising polygons and texture/shading data. The method can include rasterizing the 3D mesh to obtain a 2D raster comprising pixels and coordinates respectively associated with a subset of pixels. The method can include determining an initial color value for the subset of pixels based on the coordinates of the pixel and the associated shading/texture data. The method can include constructing a splat at the coordinates of a respective pixel. The method can include determining an updated color value for a respective pixel based on a weighting of the subset of splats to generate a 2D rendering of the 3D mesh based on the coordinates of a pixel and a splat.