A Novel Error Criterion of Fundamental Matrix Based on Principal Component Analysis
Estimating the fundamental matrix (FM) using the known corresponding points is a key step for three-dimensional (3D) scene reconstruction, and its uncertainty directly affects camera calibration and point-cloud calculation. The symmetric epipolar distance is the most popular error criterion for esti...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Remote Sensing |
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| Online Access: | https://www.mdpi.com/2072-4292/14/21/5341 |
| _version_ | 1797466577819402240 |
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| author | Yuxia Bian Shuhong Fang Ye Zhou Xiaojuan Wu Yan Zhen Yongbin Chu |
| author_facet | Yuxia Bian Shuhong Fang Ye Zhou Xiaojuan Wu Yan Zhen Yongbin Chu |
| author_sort | Yuxia Bian |
| collection | DOAJ |
| description | Estimating the fundamental matrix (FM) using the known corresponding points is a key step for three-dimensional (3D) scene reconstruction, and its uncertainty directly affects camera calibration and point-cloud calculation. The symmetric epipolar distance is the most popular error criterion for estimating FM error, but it depends on the accuracy, number, and distribution of known corresponding points and is biased. This study mainly focuses on the error quantitative criterion of FM itself. First, the calculated FM process is reviewed with the known corresponding points. Matrix differential theory is then used to derive the covariance equation of FMs in detail. Subsequently, the principal component analysis method is followed to construct the scalar function as a novel error criterion to measure FM error. Finally, three experiments with different types of stereo images are performed to verify the rationality of the proposed method. Experiments found that the scalar function had approximately 90% correlation degree with the Manhattan norm, and greater than 80% with the epipolar geometric distance. Consequently, the proposed method is also appropriate for estimating FM error, in which the error ellipse or normal distribution curve is the reasonable error boundary of FM. When the error criterion value of this method falls into a normal distribution curve or an error ellipse, its corresponding FM is considered to have less error and be credible. Otherwise, it may be necessary to recalculate an FM to reconstruct 3D models. |
| first_indexed | 2024-03-09T18:41:45Z |
| format | Article |
| id | doaj.art-15fb325e0832482ea14c90e4134ac7f8 |
| institution | Directory Open Access Journal |
| issn | 2072-4292 |
| language | English |
| last_indexed | 2024-03-09T18:41:45Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj.art-15fb325e0832482ea14c90e4134ac7f82023-11-24T06:37:27ZengMDPI AGRemote Sensing2072-42922022-10-011421534110.3390/rs14215341A Novel Error Criterion of Fundamental Matrix Based on Principal Component AnalysisYuxia Bian0Shuhong Fang1Ye Zhou2Xiaojuan Wu3Yan Zhen4Yongbin Chu5College of Resources and Environment, Chengdu University of Information Technology, Chengdu 610000, ChinaCollege of Resources and Environment, Chengdu University of Information Technology, Chengdu 610000, ChinaSichuan Zhihui Geographic Information Technology Co., Ltd., Chengdu 610000, ChinaCollege of Resources and Environment, Chengdu University of Information Technology, Chengdu 610000, ChinaCollege of Earth Science and Technology, Southwest Petroleum University, Chengdu 610000, ChinaCollege of Resources and Environment, Chengdu University of Information Technology, Chengdu 610000, ChinaEstimating the fundamental matrix (FM) using the known corresponding points is a key step for three-dimensional (3D) scene reconstruction, and its uncertainty directly affects camera calibration and point-cloud calculation. The symmetric epipolar distance is the most popular error criterion for estimating FM error, but it depends on the accuracy, number, and distribution of known corresponding points and is biased. This study mainly focuses on the error quantitative criterion of FM itself. First, the calculated FM process is reviewed with the known corresponding points. Matrix differential theory is then used to derive the covariance equation of FMs in detail. Subsequently, the principal component analysis method is followed to construct the scalar function as a novel error criterion to measure FM error. Finally, three experiments with different types of stereo images are performed to verify the rationality of the proposed method. Experiments found that the scalar function had approximately 90% correlation degree with the Manhattan norm, and greater than 80% with the epipolar geometric distance. Consequently, the proposed method is also appropriate for estimating FM error, in which the error ellipse or normal distribution curve is the reasonable error boundary of FM. When the error criterion value of this method falls into a normal distribution curve or an error ellipse, its corresponding FM is considered to have less error and be credible. Otherwise, it may be necessary to recalculate an FM to reconstruct 3D models.https://www.mdpi.com/2072-4292/14/21/5341fundamental matrixerrorcovariancematrix differential theoryprincipal component analysisManhattan norm |
| spellingShingle | Yuxia Bian Shuhong Fang Ye Zhou Xiaojuan Wu Yan Zhen Yongbin Chu A Novel Error Criterion of Fundamental Matrix Based on Principal Component Analysis Remote Sensing fundamental matrix error covariance matrix differential theory principal component analysis Manhattan norm |
| title | A Novel Error Criterion of Fundamental Matrix Based on Principal Component Analysis |
| title_full | A Novel Error Criterion of Fundamental Matrix Based on Principal Component Analysis |
| title_fullStr | A Novel Error Criterion of Fundamental Matrix Based on Principal Component Analysis |
| title_full_unstemmed | A Novel Error Criterion of Fundamental Matrix Based on Principal Component Analysis |
| title_short | A Novel Error Criterion of Fundamental Matrix Based on Principal Component Analysis |
| title_sort | novel error criterion of fundamental matrix based on principal component analysis |
| topic | fundamental matrix error covariance matrix differential theory principal component analysis Manhattan norm |
| url | https://www.mdpi.com/2072-4292/14/21/5341 |
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