Rotation-Invariant Point Set Mapping Evaluation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing image registration methods face challenges in accurately aligning spatial point sets, especially when objects undergo relative motions or are partially occluded, as they rely on assumptions of global affine transformations and are not rotation invariant, leading to suboptimal results in complex scenarios.
Innovation Solution
A system and method for evaluating a one-to-one mapping between two spatial point sets in nD, involving the generation of mapped agreeable (n+1)-combinations, computation of affine transformations, and calculation of local distance measures based on the difference of left sub-matrices, to provide a rotation-invariant evaluation of point set mappings.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If global affine transformation methods are used for image registration, then the registration process is simple and fast, but the accuracy deteriorates when objects undergo relative motions or are partially occluded
Solution Approach 1:
The patent divides the global affine transformation into multiple local affine transformations, each defined by a subset of corresponding points. This segmentation allows the method to adapt to local variations in the image data while maintaining the computational efficiency of affine transformations, thereby resolving the contradiction between speed and accuracy.
Solution Approach 2:
The patent applies different affine transformations to different regions (local areas) of the image rather than using a single global transformation. This local quality approach enables accurate alignment in each local region even when objects undergo relative motions or occlusions, while the overall process remains computationally efficient.
2Device complexity
If existing distance measures are used for evaluating point set mappings, then the evaluation is computationally simple, but the reliability deteriorates when rotation invariance is required
Solution Approach 1:
The patent changes the parameters used in distance measures from simple Euclidean distances to affine-invariant distances that incorporate rotation information. This parameter change maintains computational simplicity while achieving rotation invariance, as the new parameters are designed to be invariant under affine transformations including rotations.
3Reliability
If feature-based registration is used to handle large deformations, then the method is effective for complex scenarios, but the process complexity increases when used as a pre-processing step
Solution Approach 1:
The patent segments the complex feature-based registration process into simpler local affine transformation evaluations, reducing the overall process complexity while maintaining effectiveness for large deformations through the cumulative effect of multiple local transformations.
Data Source
AI summary
A computer implemented method for evaluating a one-to-one mapping between a first spatial point set and a second spatial point set in nD comprising the steps of receiving a first and a second spatial point sets in nD and a one-to-one mapping between the two spatial point sets; generating a pair of mapped agreeable (n+1)-combinations in the first point set; computing two affine transformations that transform the pair of mapped agreeable (n+1)-combinations to correspondents in the second point set; computing the difference of the left sub-matrices of the two affine transformations; and computing a local distance measure based on the difference of the left sub-matrices of the two affine transformations.