Cubic Polynomial Correction via 2D Lookup Table
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Solution Overview
Problem
High-speed imaging systems, such as X-ray CT scanners, face challenges in correcting nonlinearities due to cubic polynomials, requiring extensive computational resources and memory for real-time correction, which is impractical for high-speed applications.
Innovation Solution
A method to reduce cubic polynomials to a two-dimensional lookup table using timing and dimensionless shape parameters, allowing for rapid correction of nonlinearities using hardware less capable than a general-purpose CPU, by structuring a two-dimensional table to accommodate all cubic polynomials with 1% accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a three-dimensional numerical table is used to invert homogeneous cubic polynomials with arbitrary coefficients, then correction accuracy is improved, but memory storage requirements increase to many megabytes and access speed decreases
Solution Approach 1:
The patent transforms the three-dimensional lookup table (requiring many megabytes) into a two-dimensional table by introducing a timing parameter dimension. The cubic polynomial inversion is mapped to a 2D table indexed by normalized output value and timing parameter, reducing memory requirements to tens of kilobytes while maintaining 1% correction accuracy.
2Adaptability or versatility
If general processing units are used to solve cubic equations tens of thousands of times per second, then computational flexibility is improved, but processing speed is insufficient for high-speed imaging systems generating tens of millions of pixel values per second
Solution Approach 1:
The patent pre-computes and stores the inversion results of cubic polynomials in a two-dimensional lookup table during system initialization or calibration. During real-time operation, the system simply performs table lookups based on measured output values and timing parameters, avoiding complex real-time cubic equation solving and achieving processing speeds compatible with high-speed imaging systems.
3Quantity of substance
If a two-dimensional table is used to tabulate all cubic polynomials, then memory storage is reduced to tens of kilobytes, but table lookup speed and accuracy must be optimized
Solution Approach 1:
The patent introduces a timing parameter as an additional dimension for indexing the lookup table, and uses normalized output values as the second index. This parameter transformation allows the compact two-dimensional table to represent the full range of cubic polynomial inversions while maintaining 1% accuracy through proper normalization and indexing strategies.
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 efficient correction of nonlinearities in high-speed imaging systems, reducing memory requirements and computational complexity, allowing for accurate and rapid processing of millions of pixel values per second.
Implementation Method 1
a grouping of imaging inspection devices positioned on the frame and adapted for directing beams onto the articles
Data Source
AI summary
An imaging inspection machine for inspecting objects located within articles, with the imaging inspection machine having an inspection location for articles having a quantity of objects located along a path of travel through an inspection location located within the imaging inspection machine. Imaging inspection devices are positioned on the frame and adapted for directing beams through articles as articles move through the inspection location within the imaging inspection machine. As a result of inspecting the articles, output signals are applied to a processing and analysis assembly which performs only simple table lookups into an appropriately formed table and one multiplication for each pixel to correct nonlinearities matched by a cubic polynomial.