Spherical Harmonic Descriptors for 3D Object Identification
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Solution Overview
Problem
Current methods lack effective and efficient means to identify and differentiate controlled objects (COs) produced through additive manufacturing, particularly in detecting counterfeit or regulated items like weapons, which poses legal and regulatory challenges.
Innovation Solution
The use of confidentiality preserving descriptors (CPDs) based on spherical harmonic transformations and discriminative band comparisons enables accurate identification of three-dimensional objects by encoding their shape into low-dimensional representations, allowing for efficient detection and comparison of key features.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If manual validation methods are used to identify controlled objects, then the process is simple to implement, but the identification accuracy and efficiency are insufficient
Solution Approach 1:
The patent replaces manual validation methods with an automated computer-based system that uses spherical harmonic transformations and discriminative band comparisons. This substitution of mechanical/manual processes with computational algorithms achieves high identification accuracy while maintaining manageable system complexity through efficient mathematical operations.
Solution Approach 2:
The patent transforms three-dimensional object data into spherical harmonic coefficients, changing the parameter representation from spatial coordinates to frequency-domain coefficients. This parameter transformation enables accurate object identification through mathematical operations on the transformed data, resolving the contradiction between accuracy and complexity.
2Productivity
If feature-based CPDs are used for object identification, then the processing speed is fast, but the identification accuracy is insufficient for complete object restoration
Solution Approach 1:
The patent uses discriminative band comparisons that operate on a subset of spherical harmonic coefficients rather than requiring complete object restoration. This partial action approach achieves sufficient identification accuracy for detecting controlled objects while maintaining fast processing speeds, resolving the contradiction between speed and accuracy.
3Measurement precision
If spherical harmonic transformations are applied to map digital representations onto a sphere, then the object identification accuracy is improved, but the computational complexity increases
Solution Approach 1:
The patent segments the spherical harmonic coefficients into different frequency bands and processes them separately using discriminative band comparisons. This segmentation reduces computational complexity by avoiding the need to process all coefficients simultaneously, while still achieving high identification accuracy through selective band analysis.
Data Source
AI summary
According to examples, a method comprises obtaining a digital representation of a three-dimensional object, mapping the digital representation on to a sphere of a pre-determined radius and generating a descriptor of the digital representation based on a spherical harmonic decomposition of an output of the mapping.