3D Trajectory Estimation from 2D Camera Images
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Solution Overview
Problem
Current methods for estimating the 3D trajectory of a projectile, such as a ball, from 2D camera images are limited, particularly as they require specialized radar equipment or dual camera systems, while single lens cameras are widely available but lack effective methods for this purpose.
Innovation Solution
A method using optimization techniques to fit a trajectory model to observed pixel locations from single or multiple 2D camera images, combining physics models of projectile motion with camera projection transforms to estimate initial conditions and calculate a 3D trajectory, which can be extended indefinitely, incorporating forces like gravity and drag, and spin effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If specialized radar equipment or dual camera systems are used to estimate 3D trajectory, then measurement precision is improved, but device complexity and cost increase
Solution Approach 1:
The patent replaces expensive, complex radar equipment and dual camera systems with inexpensive single lens cameras. The solution uses widely available consumer-grade cameras instead of specialized measurement equipment, achieving comparable trajectory estimation accuracy through software-based optimization rather than hardware complexity
Solution Approach 2:
The patent substitutes physical measurement systems (radar waves, stereo vision hardware) with a computational approach using optimization techniques. The mechanical/optical measurement problem is transformed into a mathematical optimization problem that fits a trajectory model to observed pixel locations, replacing complex physical systems with algorithmic processing
2Device complexity
If single lens cameras are used, then device complexity is reduced, but the ability to estimate 3D trajectory is lost
Solution Approach 1:
The patent changes the approach from using multiple cameras (spatial redundancy) to using a single camera with optimized parameter estimation. By formulating the problem as an optimization task that estimates initial conditions (position, velocity, spin) and fits them to a physics-based trajectory model, the system extracts maximum information from 2D pixel sequences to reconstruct 3D motion
Solution Approach 2:
The patent introduces a trajectory model and optimization algorithm as an intermediary between the simple single camera input and the complex 3D trajectory output. This intermediary layer processes the 2D image data through physics-based motion models to generate accurate 3D trajectory estimates, bridging the gap between limited input and comprehensive output
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 estimation of a 3D trajectory from 2D camera images using single lens cameras, allowing for the calculation of metrics like carry distance, and is applicable to various projectiles, including balls, without the need for specialized equipment.
Implementation Method 1
Forces may include for example, without limitation, any or all of gravity
Implementation Method 2
Forces may include for example, without limitation, any or all of gravity, drag
Implementation Method 3
Forces may include for example, without limitation, any or all of gravity, drag, and Magnus effect force due to spin
Data Source
AI summary
A method that estimates the 3D trajectory of a projectile, such as a golf ball or baseball, by analyzing a sequence of images from a single-lens, 2D camera. Image analysis may be used to locate the projectile in the camera images, using motion detection and filters for the projectile's expected size and shape. A physics model may be used to calculate the projectile's trajectory as a function of its initial position and velocity (for example, just after impact with a golf club or bat). A camera projection transform may map this trajectory into predicted pixel locations, which may be compared to the observed projectile locations in the camera images. The projectile's trajectory may be estimated by finding initial conditions that minimize differences between observed and predicted pixel locations, using a nonlinear least squares solver for example. The method may be extended to multiple cameras.