3D Target Orientation Estimation Using Spherical Projection
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Solution Overview
Problem
True 3D target recognition is a computationally expensive task due to its nine degrees of freedom, making existing methods inefficient for accurate orientation and translation alignment of 3D data sets.
Innovation Solution
The method splits the algorithm into two stages for orientation and translation, using translation invariant 3D signatures derived from Fourier transforms, and represents data on a sphere or axisymmetric surface to reduce complexity, with optic flow refinement for precise alignment.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If true 3D matching is performed with nine degrees of freedom, then measurement precision and reliability are improved, but computational complexity and processing time increase significantly
Solution Approach 1:
The patent segments the nine-degree-of-freedom matching problem into two independent stages: orientation matching (3 rotational parameters) and translation matching (3 translational parameters). This segmentation reduces the computational complexity from O(n^9) to O(n^3) + O(n^3), making the system feasible for real-time applications while maintaining measurement precision through systematic decomposition of the matching process
Solution Approach 2:
The patent transforms the 3D target recognition problem into a 2D problem by projecting LIDAR data onto the surface of a sphere. This dimensionality reduction converts complex 3D orientation matching into 2D spherical coordinate matching, significantly reducing computational complexity while preserving essential geometric relationships through spherical projection mathematics
2Productivity
If 3D data is represented on a sphere, then rotational invariance and computational efficiency are improved, but data representation complexity increases
Solution Approach 1:
The patent maps 3D LIDAR data points onto a spherical surface using spherical coordinates (latitude, longitude, radius), transforming the problem from Euclidean 3D space to spherical manifold. This enables rotational invariance because rotations in 3D space correspond to simple coordinate transformations on the sphere, improving processing speed while the mathematical framework handles representation complexity systematically
Solution Approach 2:
The patent explicitly adopts spherical geometry to represent 3D data, utilizing the inherent rotational symmetry of the sphere. By representing target orientations and positions on a spherical manifold, the system achieves natural rotational invariance where rotating the target corresponds to rotating the spherical coordinate system, eliminating the need for complex rotation calculations in Cartesian coordinates
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly reduces computational complexity and enhances the reliability of 3D target recognition by efficiently estimating orientation and translation, leading to robust and accurate comparisons between 3D target and reference data sets.
Implementation Method 1
The translation invariant signature is preferably obtained by calculating the modulus of the 3D transform of the data set. The transform is preferably the Fourier Transform or an FFT
Data Source
AI summary
A method of target recognition performs a 3D comparison of target and reference data. Translation invariant signatures are derived from the two data sets, and an estimate of the orientation of the target with respect to the reference is obtained. Rotational alignment and comparison can then be achieved. The 3D data sets can be represented on an axi-symmetric surface such as a sphere and rotational convolution, over a discrete set of selected rotation angles can be performed. Optic flow can be used to derive the estimate of orientation or the target relative to the reference, in terms of a displacement field.