Focal Length Estimation Using Polynomial Models for Image Stitching
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Solution Overview
Problem
Current image stitching techniques require a minimum of 4 point correspondences to estimate focal length, which is inefficient and prone to errors due to the rapid decrease in the probability of choosing correct correspondences as sample size increases.
Innovation Solution
The technique employs a polynomial model to estimate focal length using only 2 pairs of corresponding points when focal lengths are the same and 3 pairs when they are different, establishing and solving polynomial equations to determine the focal length associated with each image.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If 4 point correspondences are used for focal length estimation in RANSAC loop, then measurement precision is maintained, but productivity decreases and reliability worsens due to rapid probability decrease of choosing correct correspondences
Solution Approach 1:
The patent changes the mathematical model from traditional linear estimation to polynomial relationship modeling. By establishing that corresponding points satisfy a polynomial equation involving focal length, the method enables solving for focal length using only 2 point correspondences instead of 4, thereby improving efficiency while maintaining precision.
Solution Approach 2:
Instead of using multiple random samples and voting mechanisms as in traditional RANSAC, the patent inverts the approach by directly solving the polynomial equation formed by minimal point correspondences. This inversion allows deterministic solution with 2 points rather than probabilistic sampling with 4+ points.
2Measurement precision
If 4 point correspondences are used for focal length estimation, then measurement precision is maintained, but device complexity increases due to additional computational steps
Solution Approach 1:
The patent transforms the computational problem by changing from linear algebra operations on 4 points to polynomial equation solving on 2 points. The polynomial relationship between corresponding points and focal length enables this simplification, reducing both computational steps and complexity while preserving accuracy.
3Measurement precision
If larger sample size is used in RANSAC loop, then measurement precision might improve, but reliability decreases rapidly as probability of choosing correct correspondences decreases
Solution Approach 1:
The patent uses exactly the minimal number of point correspondences (2 or 3) needed to solve the polynomial equation, avoiding the excessive sampling required by traditional RANSAC. This partial action approach achieves reliable results with minimal data, eliminating the probability degradation issue.
Data Source
AI summary
A focal length estimation technique is presented that estimates the focal length used to capture each of a pair of overlapping images taken by a camera rotating about its center. When it is known that the focal length is the same for both images, it is estimated using just two pairs of corresponding points between the images. When it is either unknown whether the focal lengths are the same or it is known that they vary, the focal length of each image is estimated using just three pairs of corresponding points between the images.