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A Method for Solving Ill-Conditioned Nonlinear Least Squares Problems and Its Application in Image Distortion Correction Using Self-Calibration.
- Source :
-
Axioms (2075-1680) . Mar2024, Vol. 13 Issue 3, p209. 16p. - Publication Year :
- 2024
-
Abstract
- In this study, the ill-conditioning of the iterative method for nonlinear models is discussed. Due to the effectiveness of ridge estimation for ill-conditioned problems and the lack of a combination of the H-K formula with the iterative method, the improvement of the LM algorithm is studied in this paper. Considering the LM algorithm for ill-conditioned nonlinear least squares, an improved LM algorithm based on the H-K formula is proposed for image distortion correction using self-calibration. Three finite difference methods are used to approximate the Jacobian matrix, and the H-K formula is used to calculate the damping factor in each iteration. The Brown model, quadratic polynomial model and Fourier model are applied to the self-calibration, and the improved LM algorithm is used to solve the model parameters. In the simulation experiment of space resection of a single image, we evaluate the performance of the LM algorithm based on the gain ratio (LMh) and the improved LM algorithm based on the H-K formula (LMHK), and the accuracy of different models and algorithms is compared. A ridge trace analysis is carried out on the damping factor to illustrate the effects of the improved algorithm in handling ill-conditioning. In the second experiment, the improved algorithm is applied to measure the diameter of a coin using a single camera. The experimental results show that the improved LM algorithm can reach the same or higher accuracy as the LMh algorithm, and it can weaken the ill-conditioning to a certain extent and enhance the stability of the solution. Meanwhile, the applicability of the improved LM algorithm in self-calibration is verified. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 13
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Axioms (2075-1680)
- Publication Type :
- Academic Journal
- Accession number :
- 176270558
- Full Text :
- https://doi.org/10.3390/axioms13030209