Image Registration Using Random Projections
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Solution Overview
Problem
Conventional image registration methods face high computational complexity, especially with large high-resolution images, leading to costly computations and potential losses in accuracy and robustness due to truncated search strategies.
Innovation Solution
The method employs Johnson-Lindenstrauss dimension reduction using random projections to reduce image patches from a d-dimensional space to a k-dimensional space, allowing for efficient similarity measures and incorporating accelerated search techniques like approximate nearest neighbor formulations, while maintaining accuracy and robustness.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional image registration methods are used to align images, then accurate feature correspondence can be achieved, but computational complexity becomes prohibitively high
Solution Approach 1:
The patent applies dimensionality reduction by projecting image patches from high-dimensional space (d dimensions) to lower-dimensional space (k dimensions) using random projections. This transforms the computational problem from O(Tn²d) complexity to O(Tn² log n) complexity, making the registration process computationally feasible while preserving the essential feature correspondence relationships needed for accurate alignment.
Solution Approach 2:
The patent extracts and processes only the most critical components of the image data by dividing images into patches and selecting representative features for comparison. This extraction approach focuses computational resources on the most informative regions and features, reducing overall computational complexity while maintaining registration accuracy.
2Productivity
If computational complexity is reduced to make registration faster, then processing speed improves, but accuracy and robustness are lost
Solution Approach 1:
The patent changes the dimensional parameter of the data representation from d dimensions to k dimensions (where k < d) through random projection. This parameter transformation reduces computational complexity from O(Tn²d) to O(Tn² log n) while the Johnson-Lindenstrauss lemma guarantees that the essential geometric relationships and feature correspondences are preserved, maintaining registration accuracy.
Solution Approach 2:
The patent introduces random projection as an intermediary transformation step between the original image patches and the comparison process. This intermediary operation in lower-dimensional space acts as a computationally efficient mediator that preserves the necessary information for accurate registration without requiring full high-dimensional comparisons.
3Loss of information
If full high-resolution images are processed for registration, then complete feature information is captured, but computation time increases significantly
Solution Approach 1:
The patent segments the full high-resolution images into multiple smaller patches, which are then independently processed through dimensionality reduction. This segmentation allows the computational burden to be distributed and managed more efficiently, capturing complete feature information across all patches while reducing the computational time required compared to processing the entire image as a single unit.
Data Source
AI summary
According to some aspects, a computer-implemented method of registering a first image and a second image is provided. The method comprises computer-implemented acts of logically dividing the first image into a first plurality of regions, logically dividing the second image into a second plurality of regions, projecting the first plurality of regions and the second plurality of regions into a lower dimensional space using random projections, determining, for each of the projected first plurality of regions, at least one of the projected second plurality of regions that is closest according to first criteria, and determining a transform that brings each of the projected first plurality of regions into a closest correspondence with the respective at least one of the projected second plurality of regions according to second criteria, the transform indicating the registration of the first image and the second image. According to some aspects, at least one computer readable medium encoding instructions that when executed perform such a method and/or a system for providing such a method is provided.