Single-Image Range Imaging via Fourier Spectrum Analysis
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Solution Overview
Problem
Existing optical imaging methods, such as stereographic imaging, require multiple image capture devices and complex computational processes to determine object distances accurately and efficiently, which is impractical for applications like power line detection and runway light detection.
Innovation Solution
A method utilizing a planar optical component with a transmittance varying as a function of two coordinates, featuring a two-dimensional Fourier transform with peaks on a circle, allows for single-image capture and precise distance calculation of multiple objects by superimposing and transforming reference and captured spectra, enabling distance determination without significant computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If stereographic imaging is used to determine object distances, then measurement precision is improved, but device complexity increases due to requiring multiple image capture devices and precise positioning
Solution Approach 1:
The patent segments the distance determination process by analyzing different spatial frequency components in the Fourier transform domain. Each concentric circle in the Fourier spectrum corresponds to objects at a specific distance range, allowing the system to separate and process distance information for multiple objects independently without requiring multiple capture devices.
Solution Approach 2:
The patent transitions from spatial domain imaging to frequency domain analysis by computing the Fourier transform of the captured image. This dimensional transformation allows distance information to be encoded in the radial frequency spectrum, where concentric circles represent different distance planes, enabling single-device range imaging through frequency-based separation.
2Measurement precision
If stereographic imaging with multiple devices is used, then measurement precision is improved, but computational complexity increases due to required image correlation processing
Solution Approach 1:
The patent extracts distance information directly from the Fourier transform spectrum of a single captured image. By identifying concentric circles in the frequency domain and measuring their radii, the system extracts distance data without performing complex correlation computations between multiple images, significantly reducing computational requirements while maintaining precision.
Solution Approach 2:
The patent replaces the mechanical/stereographic approach of using multiple physical cameras with a computational/optical approach using a single camera and Fourier transform processing. The distance measurement mechanism is substituted from geometric correlation of multiple images to spectral analysis of frequency components, simplifying the overall system complexity.
3Measurement precision
If stereographic imaging is used to capture moving objects, then measurement precision is improved, but loss of time increases due to requiring simultaneous capture from multiple angles
Solution Approach 1:
The patent merges the functions of multiple simultaneous capture devices into a single capturing device. By combining distance and positional information extraction through Fourier transform analysis of one image, the system eliminates the need for synchronized multi-device capture, reducing time loss while maintaining measurement precision for moving objects.
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 rapid and precise determination of object distances from a single image capture, eliminating the need for multiple devices and complex computations, while maintaining accuracy and simplicity in calculating distances for multiple objects simultaneously.
Implementation Method 1
having a two-dimensional Fourier transform T consisting of peaks located on a base circle of radius ρ∞
Implementation Method 2
planar optical component having a transmittance t which varies as a function of two coordinates in a plane of the component
Implementation Method 3
arranging an image sensor in a plane perpendicular to the axis Z, at a distance df from the component and on the side of the component which is opposite the field of view; using the sensor to capture an image formed by light originating from the objects through the component
Implementation Method 4
calculating a Fourier transform of the captured image, in order to obtain a spectrum Stot of spatial frequencies corresponding to peaks of the Fourier transform of the captured image
Data Source
AI summary
A method for range imaging allows determining respective distances to multiple objects, based on a single image. The image is captured through a component having a transmittance function of which the Fourier transform is inscribed on a circle within a plane of spatial frequencies. A Fourier transform of the captured image is calculated in order to obtain a total spectrum for the image content. The distance to each object is then calculated based on several homothetic superimpositions of a reference spectrum with the total spectrum, so that said reference spectrum coincides with a portion of the total spectrum each time.