3D Bounding Volume Estimation from 2D Polygon Projection
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Solution Overview
Problem
Existing 3D object recognition methods, particularly those based on machine learning, are complex, costly, and lack interpretability, making them unsuitable for applications in autonomous vehicles where accountability is crucial, and require extensive manual annotation of training data.
Innovation Solution
A computer-implemented method using a mathematical optimization procedure with a target function comprising fewer than 100,000 terms to ascertain a three-dimensional bounding volume, such as a bounding box, by receiving two-dimensional minimum bounding polygon data and applying a projection matrix, and optimizing position, size, and orientation through separate target functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If machine learning methods are used for 3D object recognition, then recognition accuracy is improved, but system complexity and training data requirements increase
Solution Approach 1:
The patent replaces complex machine learning systems with a mathematical optimization approach using projection geometry and linear algebra. Instead of training neural networks, the invention uses a camera calibration matrix and projection equations to directly compute 3D bounding volumes from 2D image data, eliminating the need for statistical learning while maintaining recognition accuracy
Solution Approach 2:
The invention creates a mathematical model that copies the geometric projection relationship between 3D space and 2D image plane. By establishing a projection matrix that replicates the camera's optical projection, the system can transform 2D image coordinates into 3D spatial coordinates without requiring training data, thus reducing system complexity while preserving recognition capability
2Measurement precision
If machine learning methods are used for 3D object recognition, then recognition accuracy is improved, but cost and time consumption increase
Solution Approach 1:
The patent performs preliminary camera calibration to obtain the camera calibration matrix before actual 3D recognition tasks. This pre-computed projection matrix enables direct transformation from 2D to 3D coordinates during operation, eliminating the need for time-consuming training processes while maintaining accurate recognition performance
Solution Approach 2:
The invention substitutes the training-based machine learning approach with a deterministic mathematical optimization method. By using projection geometry and algebraic optimization, the system achieves 3D bounding volume estimation without iterative training, significantly reducing time consumption while preserving recognition accuracy
3Measurement precision
If black box machine learning models are used, then recognition performance is improved, but interpretability and accountability decrease
Solution Approach 1:
The patent replaces opaque neural network models with transparent mathematical optimization based on projection geometry. The explicit use of camera calibration matrices and projection equations allows direct interpretation of how 2D image coordinates map to 3D spatial coordinates, providing full interpretability and accountability for the recognition results
Solution Approach 2:
The invention transforms the problem from learning complex nonlinear parameters in neural networks to optimizing explicit geometric parameters (projection matrix, bounding volume dimensions, position, and orientation). This parameter transformation makes the system interpretable while maintaining recognition performance through mathematically rigorous optimization
Data Source
AI summary
A computer-implemented method for ascertaining a three-dimensional bounding volume, preferably a bounding box, for an object displayed on first data, the first data having at least three spatial dimensions, information data of a two-dimensional minimum bounding polygon being received for the object displayed on second data, a projection matrix, which defines a mapping of a three-dimensional data point of the first data onto a two-dimensional data point in the second data being received, and the three-dimensional bounding volume of the object being ascertained with the aid of a mathematical optimization procedure and a target function, the target function comprising fewer than 100,000 terms. The invention also relates to a device for processing data, which comprises computer components for carrying out the above method, as well as a computer program product, comprising commands, which, when the program is executed by a computer, prompt the latter to carry out the above method.