Free Form MTF Algorithm for Distorted Optical Edge Analysis
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Solution Overview
Problem
The ISO 12233 standard fails to provide accurate modulation transfer function (MTF) estimates, especially for highly distorted images, as it relies on straight edges and becomes inaccurate or unable to produce results in cases of significant distortion, such as those captured by wide field of view cameras with barrel distortion.
Innovation Solution
A novel method, referred to as the free form (FF) MTF algorithm, performs edge detection on image rows, calculates varying degree polynomials to fit edge points, selects an appropriate polynomial to represent the edge, and estimates MTF, allowing for accurate calculations even from distorted images.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the ISO 12233 standard method is used to determine MTF, then the measurement process is simple and straightforward, but the measurement precision deteriorates under highly distorted image conditions
Solution Approach 1:
The patent applies polynomial curves to fit distorted edge points instead of requiring straight edges. The method models the curved/distorted edge geometry using mathematical polynomials, allowing accurate MTF measurement even when the edge appears curved or distorted in the image, thus resolving the contradiction between maintaining measurement simplicity and achieving accuracy under distortion.
Solution Approach 2:
The patent transforms the measurement approach by changing from fixed straight-edge assumptions to variable polynomial degree fitting. By adjusting the polynomial degree parameter to match the distortion level, the method adapts to different image conditions while maintaining measurement accuracy, effectively resolving the trade-off between simplicity and precision.
2Measurement precision
If polynomial fitting of varying degrees is performed to fit edge points, then the MTF measurement precision improves for distorted images, but the computational complexity increases
Solution Approach 1:
The patent implements a systematic approach of calculating polynomials of multiple degrees and selecting the appropriate one based on fit quality metrics. This partial action principle allows the method to compute only as much complexity as needed - using lower degree polynomials for simple cases and higher degrees only when distortion requires it, thus balancing computational resources with measurement precision.
3Adaptability or versatility
If edge detection is performed on distorted images, then the MTF can be measured for wide field of view cameras, but the measurement reliability decreases due to distortion
Solution Approach 1:
The patent changes the fundamental parameter assumption from 'edges must be straight' to 'edges can be modeled by polynomials of varying degrees'. This parameter change enables the method to adapt to distorted images from wide field of view cameras while maintaining measurement reliability through polynomial fitting that captures the distorted geometry accurately.
Data Source
AI summary
A method of determining a modulation transfer function (MTF) for an image includes receiving an image captured through the optical system, performing edge detection on columns or rows in the image to calculate a plurality of edge points, calculating a plurality polynomials to fit to the calculated edge points, each of the plurality of polynomials varying in degree, selecting a polynomial from the plurality of polynomials to represent the detected edge, and estimating the MTF based on the selected polynomial.