Coordinate Computation for Fisheye Lens Distortion Correction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for projecting images from a projection sphere to an image plane using super-wide angle optical systems, such as fisheye lenses, face challenges in achieving high precision while minimizing computational complexity, particularly near the zenith and rim of the projection sphere, due to varying bit precision requirements.
Innovation Solution
A coordinate computation device that transforms three-dimensional coordinates on a projection sphere to two-dimensional coordinates on a distorted image using a composite index combining the height and distance from the optical axis, allowing for precise computation with a small number of bits.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the zenith angle is used for computing image height, then the projection accuracy is improved, but the computational complexity increases due to trigonometric function calculations
Solution Approach 1:
The patent pre-computes and stores the relationship between zenith angles and image heights in a lookup table before actual projection operations. This allows the system to retrieve pre-calculated values instead of performing trigonometric calculations in real-time, thereby maintaining high projection accuracy while significantly reducing computational complexity during image transformation
Solution Approach 2:
The patent creates a simplified copy of the trigonometric relationship by storing computed values in a lookup table. This copy replaces the need for complex real-time trigonometric function evaluations, allowing the system to achieve the same projection accuracy with much simpler computational operations
2Device complexity
If the height is used instead of zenith angle, then the computational complexity is reduced, but the precision deteriorates in the vicinity of the zenith
Solution Approach 1:
The patent transforms the parameter representation by combining height and distance from optical axis into a composite index. This parameter transformation ensures that the composite index maintains sufficient variation even near the zenith, allowing precise computation throughout the entire projection sphere including regions where simple height or distance parameters would fail
Solution Approach 2:
The patent creates a composite index by combining multiple parameters (height and distance from optical axis) into a single unified parameter. This composite approach leverages the strengths of both individual parameters while compensating for their weaknesses, ensuring consistent precision across the entire projection sphere including the zenith region
3Device complexity
If the distance from optical axis is used, then the computational complexity is reduced, but the precision deteriorates in the vicinity of the rim
Solution Approach 1:
The patent transforms the parameter representation by combining height and distance from optical axis into a composite index. This parameter transformation ensures that the composite index maintains sufficient variation even near the rim, allowing precise computation throughout the entire projection sphere including regions where simple distance parameters would fail
4Measurement precision
If different bit precisions are used for different regions, then the computation precision is improved, but the device complexity increases
Solution Approach 1:
The patent applies local quality by using a composite index that automatically adapts to local requirements. The composite index structure inherently provides sufficient precision in all regions (zenith, rim, and intermediate areas) without requiring separate processing logic for different zones, thus achieving uniform high precision with simple consistent processing throughout
Data Source
Figure 1
Figure 2
Figure 3~4
AI summary
In an image processing for correcting a distorted image obtained by photography by use of a super-wide angle optical system such as a fisheye lens or an omnidirectional mirror, to obtain an image of a perspective projection method, a composite index (Rn) combining a height on the projection sphere with a distance from the optical axis is computed (301), and a distance (Rf) from an origin in the distorted image is computed (302), using the composite index (Rn). Further, two-dimensional coordinates (p, q) in the distorted image are computed (303), using the distance (Rf) from the origin, and a pixel value in an output image is determined using a pixel at a position in the distorted image specified by the two-dimensional coordinates, or a pixel or pixels neighboring the specified position. It is possible to perform the projection from the projection sphere to the image plane, that is, the computation of the coordinates on the coordinate plane, while restricting the amount of computation.