3D Point Cloud Visibility Using Differentiable Radial Transformation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for determining point cloud visibility are computationally intensive and lack differentiability, making them unsuitable for optimization processes or learning models.
Innovation Solution
A method that computes visibility of points in a point cloud using a radial transformation function and differentiable convex hull approximation, enabling efficient and parallelizable computation of visibility indicators.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If surface reconstruction methods are used to determine visibility, then visibility determination accuracy is improved, but computational complexity and processing time increase significantly
Solution Approach 1:
The patent extracts the essential visibility determination task from the complex surface reconstruction process. Instead of reconstructing complete surfaces and calculating normals for each point, the method directly determines visibility by checking if transformed points lie on the convex hull boundary, thereby removing unnecessary computational steps while maintaining accuracy.
Solution Approach 2:
The patent creates a simplified representation of the visibility problem by transforming points radially and checking their positions relative to the convex hull. This copying approach replaces the complex surface reconstruction with a simpler geometric problem that yields the same visibility information without the computational burden.
2Measurement precision
If traditional visibility methods are used, then visibility can be determined, but the methods lack differentiability and cannot be utilized in optimization processes or learning models
Solution Approach 1:
The patent replaces the mechanical/discrete visibility determination methods with a differentiable mathematical formulation. By using smooth radial transformation functions and differentiable convex hull approximation, the method substitutes non-differentiable geometric algorithms with continuous mathematical operations that can be differentiated and used in gradient-based optimization and learning models.
3Measurement precision
If a large number of points are sampled on the object surface, then visibility metric accuracy is improved, but computational time and processing resources increase
Solution Approach 1:
The patent changes the parameter space by applying radial transformation to map points onto a unit sphere. This transformation consolidates the visibility determination into a problem of finding convex hull vertices in transformed space, which can be solved efficiently regardless of the original number of sampled points, thereby maintaining accuracy while improving computational efficiency.
Data Source
AI summary
A method and system are provided for determining visibility of points in 3D point clouds without requiring surface reconstruction. The method applies a differentiable radial transformation to transform points in a manner that maps visible points to extreme positions, followed by a novel differentiable computation to identify these extreme points. Unlike previous approaches, the method's end-to-end differentiability enables direct optimization of viewpoint positions and integration with machine learning systems while maintaining theoretical correctness guarantees. The method is computationally efficient through parallel implementation and robust to varying point densities and noise. Applications include optimal viewpoint selection, visibility-based path planning, and 3D scene understanding tasks that benefit from differentiable visibility determination.