Lookup Table Curvature Interpolation for Precise Sparse Mapping
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing image processing techniques using lookup tables (LUTs) face challenges in achieving precise values without excessive memory usage, particularly when performing linear interpolation for complex functions, which may not be sufficiently accurate and resource-intensive.
Innovation Solution
Implementing curvature interpolation that uses adjacent entries in the LUT to determine output values, minimizing error through coefficients derived from a curve that fits the output values, thereby reducing computational resources and improving precision.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If linear interpolation is used to obtain intermediate values from a lookup table, then memory usage is reduced, but precision of the obtained values deteriorates for complex functions
Solution Approach 1:
The patent applies curvature interpolation instead of linear interpolation to account for the non-linear relationship between input and output values in complex functions. By fitting a curve (e.g., quadratic or cubic) through known LUT entries and using its derivatives to calculate intermediate values, the method captures the curvature of the function, thereby improving precision while maintaining reduced memory usage.
2Measurement precision
If a lookup table includes an entry for every possible value of the function, then precision is improved, but memory usage increases tremendously
Solution Approach 1:
The patent uses a sparse lookup table with fewer entries than would be needed for complete coverage, combining these partial entries with curvature interpolation to achieve high precision. Instead of storing every possible value, the method strategically stores key points and uses mathematical interpolation to derive intermediate values, balancing memory efficiency with precision.
3Use of energy by moving object
If linear interpolation is used to achieve sufficient precision, then computational resources are reduced, but precision is insufficient for complex functions
Solution Approach 1:
The patent employs curvature-based interpolation methods that use fitted curves and their derivatives to compute intermediate values. This approach maintains computational efficiency by avoiding exhaustive calculations while achieving higher precision than linear interpolation for complex, non-linear functions through intelligent use of mathematical relationships.
Data Source
AI summary
Circuitry may include a memory that stores a plurality of entries respectively mapping a defined input value to a defined output value. The circuitry may also include processing circuitry that receives an input value having a value between first and second defined input values, determines coefficients defining a curvature between first and second defined output values corresponding to the first and second defined input values, and determines an output value based on the input value and the curvature defined by the coefficients.