Projection Transformation Parameter Estimation with Quadratic Surface Constraints
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for calculating projection transformation parameters can result in erroneous calculations leading to deformations of convex quadrilaterals into non-convex forms, even when error-free correspondence points are used.
Innovation Solution
A device and method that include detecting correspondence points, fitting a quadratic surface to these points, and calculating a projection transformation matrix while maintaining the properties of the quadratic surface, ensuring the transformation results in a convex quadrilateral.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If planar projection transformation parameters are calculated using minimum four pairs of image correspondence points, then calculation efficiency is improved, but erroneous correspondence points cannot be completely eliminated leading to non-convex quadrilateral deformations
Solution Approach 1:
The patent applies preliminary action by fitting a quadratic surface to correspondence points before calculating projection transformation parameters. This preprocessing step establishes geometric constraints that prevent erroneous transformations. The quadratic surface fitting is performed in advance to identify and eliminate correspondence points that would lead to non-convex quadrilateral deformations, ensuring reliable transformation results while maintaining calculation efficiency.
2Reliability
If RANSAC method is used to eliminate erroneous correspondence points, then transformation accuracy is improved, but correspondence points that satisfy mathematical equations cannot be removed
Solution Approach 1:
The patent changes the parameter verification approach from normal direction checking to quadratic surface property checking. Instead of verifying whether normal directions match (which can be ambiguous), the method transforms the problem into verifying whether correspondence points satisfy quadratic surface equations. This parameter change provides clearer geometric constraints that effectively distinguish correct from erroneous correspondence points without increasing method complexity.
3Reliability
If normal direction verification is used to identify correct correspondences, then erroneous points are reduced, but some directions may match by coincidence leading to undetected errors
Solution Approach 1:
The patent applies spheroidality by replacing linear normal direction verification with quadratic surface fitting. The quadratic surface introduces curvature-based geometric constraints that provide more robust error detection. By fitting a quadratic surface to correspondence points and verifying whether transformed points satisfy the surface equation, the method achieves higher measurement precision in detecting erroneous correspondences while maintaining reliability in identifying correct transformations.
Data Source
AI summary
A projection transformation parameter for guaranteeing a deformation to a convex quadrilateral can be calculated even when one or more of correspondence points are errors. A projection transformation parameter estimation device according to an embodiment includes a correspondence point detection unit (1) configured to detect information about a correspondence between two pieces of input data, a quadratic surface calculation unit (2) configured to fit a quadratic surface to the information about the correspondence for one or both of the two pieces of the input data, and a projection transformation matrix calculation unit (3) configured to calculate a projection transformation parameter between the two pieces of the input data by using the information about the correspondence with a constraint condition specifying that a property of the quadratic surface is maintained even after projection transformation.