Projectile Tracking With Camera-Radar 3D Calibration
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Solution Overview
Problem
Existing camera calibration methods require decomposition into explicit intrinsic and extrinsic parameters, which is prone to reprojection errors and assumptions, limiting their accuracy and applicability to various lenses and tilts.
Innovation Solution
A camera system and method that calibrates without decomposing camera parameters, using a transformation matrix and affine corrections to implicitly adjust extrinsic parameters, allowing calibration with any lens or tilt, and tracks moving objects in motion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If camera parameters are decomposed into explicit intrinsic and extrinsic parameters, then the calibration process becomes more structured and easier to implement, but reprojection errors increase and measurement precision deteriorates
Solution Approach 1:
The patent merges intrinsic and extrinsic camera parameters into a unified transformation matrix that maps 3D world coordinates directly to 2D image coordinates without decomposition. This combined approach eliminates the reprojection errors that arise from separate parameter estimation and maintains high measurement precision while preserving calibration structure.
2Device complexity
If assumptions are made about intrinsic or extrinsic camera parameters (e.g., no lens distortion, no tilt), then the calibration complexity is reduced, but the applicability to diverse lenses and camera setups is limited
Solution Approach 1:
The patent creates a universal calibration framework using a transformation matrix that works with any lens type and camera orientation without requiring specific assumptions about intrinsic or extrinsic parameters. The method is adaptable to diverse camera setups including tilted cameras and various lens distortions, making it universally applicable across different imaging systems.
3Ease of operation
If decomposition into intrinsic and extrinsic parameters is performed, then the calibration can be done in standard steps, but the camera cannot work with any lenses or tilts without fine tuning
Solution Approach 1:
The patent combines intrinsic and extrinsic parameters into a single transformation matrix that directly maps 3D world points to 2D image points. This merged representation eliminates the need for decomposition steps while maintaining ease of operation, and simultaneously provides flexibility to work with any lens or camera tilt without fine-tuning.
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
Enables accurate measurement of moving objects without assumptions about intrinsic or extrinsic parameters, improving calibration accuracy and applicability to diverse setups.
Implementation Method 1
determining, with at least one radar, a radial velocity of the projectile
Data Source
AI summary
Disclosed are embodiments for determining the position and speed of a projectile in 3D world coordinates using a calibrated camera and radar. In some embodiments, a method comprises: capturing a sequential set of images of a projectile in motion; determining a radial velocity of the projectile; determining a set of two-dimensional (2D) image points representing respective locations of the projectile in the sequential set of images; determining respective depths of the 2D image points in their respective 2D image planes based on the 2D image points, time intervals between the captured 2D images, the radial velocity and a rotational part of a homographic transformation, the homographic transformation configured to project three-dimensional (3D) world coordinates to the 2D image planes; and determining a set of 3D world points of the projectile in the 3D world coordinates based on the 2D image points, the respective depths thereof and the homographic projection.