Piecewise Polynomial Image Warping for HMD Distortion Correction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing head-worn and heads-up display systems face significant computational and memory resource challenges in pre-warping images to correct distortions caused by projection surfaces, particularly for high-resolution images, due to the large size of look-up tables required for accurate image warping.
Innovation Solution
Implementing a piecewise multivariate polynomial approximation of the per-pixel warping map, dividing the image warping field into a grid with polynomial approximations for each cell, reduces the computational and memory requirements by generating multiple approximations for each light source, allowing for efficient pre-warping of images.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a per-pixel warping map (look-up table) is used to correct image distortions, then the accuracy of distortion correction is improved, but the memory and computational resources required increase significantly
Solution Approach 1:
The patent divides the image warping field into a grid of cells, where each cell contains simplified warping parameters rather than per-pixel data. This segmentation reduces memory requirements while maintaining correction accuracy through piecewise polynomial approximation functions that operate on smaller, manageable regions of the image.
Solution Approach 2:
The patent transforms the storage requirement from per-pixel warping maps to polynomial approximation coefficients. By changing the parameter representation from detailed per-pixel displacement data to compact polynomial coefficients, the system achieves significant memory reduction while preserving distortion correction functionality through mathematical approximation.
2Measurement precision
If a per-pixel warping map is used to correct image distortions, then the accuracy of distortion correction is improved, but the computational resources required increase significantly
Solution Approach 1:
By dividing the warping field into cells with localized polynomial approximations, the patent reduces the computational complexity of applying warping corrections. Each cell's polynomial function can be evaluated independently and more efficiently than processing entire per-pixel lookup tables, reducing overall computational resource requirements.
Solution Approach 2:
The patent changes the computational approach from direct per-pixel lookup and manipulation to polynomial evaluation. This parameter transformation enables the use of efficient mathematical algorithms for calculating warped pixel positions, significantly reducing the computational power needed compared to traditional per-pixel warping map methods.
3Loss of information
If traditional per-pixel warping maps are used, then comprehensive warping information is available, but the size of the warping data structure becomes excessively large
Solution Approach 1:
The patent transforms the warping data structure from per-pixel displacement values to polynomial approximation coefficients. This parameter change compresses the data structure size dramatically while preserving warping information through mathematical models that can reconstruct the necessary transformation data on-demand during image warping operations.
Solution Approach 2:
Instead of storing complete per-pixel warping maps, the patent uses compact polynomial coefficient representations that act as compressed copies. These coefficient sets can generate the necessary warping information dynamically, providing a space-efficient alternative to storing full pixel-level warping data structures.
Data Source
AI summary
Techniques to pre-warp an image based on an image warping map comprising a number of cells where each cell corresponds to a polynomial approximation for a number of corresponding pixels to be warped are described. An image warping map can be generated by partitioning a per pixel warping map into cells and approximating the pixel movements of each cell with a polynomial function.