Fast Aerial Image Geolocalization Using the Projective-Invariant Contour Feature
Abstract
:1. Introduction
2. Materials and Methods
2.1. Projective-Invariant Contour Feature
2.1.1. Definition of the PICF
- (1)
- ;
- (2)
- , where is the angle of vector related to the X axis;
- (3)
- , if , then .
2.1.2. Equivariance of the PICF
2.1.3. The PICF Descriptor
- (1)
- Sample contour points: Divide the area centered at point into N areas with angle step ; for each area ; find the closest point to ; and take as the sample point on the contour in direction ; compute the relative coordinate of to point as ; if no point exists in the area, then set .
- (2)
- (3)
- Align contour points: Project all contour points with and , respectively, and get two transformed point sets and .
- (4)
- Compute the PICF descriptor: Convert the coordinates of the points in point sets to the polar coordinates, and sort the points with their angles in ascending order, then we get . For each area , compute the average distance of contour points in the area to the center point as: , where is the dimension of the descriptor, and ’. Finally, the two possible PICF descriptors of point in the point set P are obtained as: .
2.1.4. Discussion
2.2. Matching PICFs with Geometric Coherence
2.2.1. Geometric Coherence between PICF Correspondences
2.2.2. Refining Initial Matches with Geometric Coherence
Algorithm 1 PICF matching algorithm. |
|
2.3. PICF Based Fast Geolocalization
- (1)
- If the number of matching pairs is larger than (20 in this paper), an initial homography transformation is estimated with all the matching pairs using the RANSAC method and then refined with the plain ICP. The refined transformation is then verified with the alignment accuracy between the query road map and the reference road map.
- (2)
- If the obtained feature correspondences are less than or the first strategy fails to recover the right transformation, the obtained pairs are afterward sorted with their matching scores. Then, a homography transformation is estimated with a single correspondence and refined using all the road points in the query road map with a local-to-global iterative closest point algorithm. Furthermore, the refined transformation is then verified with the alignment accuracy. Each correspondence in the sorted pair set will be tested until a homography transformation that aligns the query road map and the reference one accurately enough is found. If our method fails to recover the correct transformation after all the correspondences obtained with the geometric-consistent matching algorithm, the left correspondences in the initial matching will be checked in the same manner.
2.3.1. Initial Homography Transformation Estimation from One Matching Pair
- (1)
- Compute matrix : ;
- (2)
- Compute vector : the homography transformation is approximated to a affinity, so we get ;
- (3)
- Compute the translation vector : since the contour center point is projected to , we get .
2.3.2. Transformation Refining
2.3.3. Transformation Validation
3. Results
3.1. Experiments on Synthetic Aerial Image Data Sets
3.2. Experiments on Real Aerial Image Data Sets
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
References
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Video Number | Localization | Maximum Altitude (m) | Trajectory Length (km) | Video Resolution |
---|---|---|---|---|
1 | Suizhou, Hubei | 1000 | 4.325 | 4096 × 2160 |
2 | Suizhou, Hubei | 1000 | 4.476 | 4096 × 2160 |
3 | Suizhou, Hubei | 1000 | 4.557 | 4096 × 2160 |
4 | Suizhou, Hubei | 1000 | 1.543 | 4096 × 2160 |
5 | Suizhou, Hubei | 1000 | 4.238 | 4096 × 2160 |
6 | Suizhou, Hubei | 1000 | 4.366 | 4096 × 2160 |
7 | Suizhou, Hubei | 1000 | 1.442 | 4096 × 2160 |
8 | Suizhou, Hubei | 1000 | 4.493 | 4096 × 2160 |
9 | Suizhou, Hubei | 1000 | 4.601 | 4096 × 2160 |
10 | Suizhou, Hubei | 1000 | 4.512 | 4096 × 2160 |
11 | Suizhou, Hubei | 1000 | 4.272 | 4096 × 2160 |
12 | Suizhou, Hubei | 1000 | 3.023 | 4096 × 2160 |
14 | Xian, Shanxi | 500 | 1.732 | 1920 × 1080 |
15 | Xian, Shanxi | 500 | 7.387 | 1920 × 1080 |
16 | Xian, Shanxi | 350 | 6.125 | 1920 × 1080 |
17 | Xian, Shanxi | 439 | 8.885 | 1920 × 1080 |
18 | Xian, Shanxi | 442 | 8.569 | 1920 × 1080 |
19 | Xian, Shanxi | 444 | 8.491 | 1920 × 1080 |
20 | Fengyang, Anhui | 400 | 4.831 | 3840 × 2160 |
21 | Fengyang, Anhui | 400 | 4.687 | 3840 × 2160 |
22 | Fengyang, Anhui | 400 | 2.032 | 3840 × 2160 |
Localization | Longitude Range | Latitude Range | Area |
---|---|---|---|
Suizhou, Hubei | [113.0000, 113.1792] | [32.0334, 31.6584] | 54.99 km × 37.97 km |
Xian, Shanxi | [108.9296, 109.1767] | [34.0707, 34.2053] | 22.46 km × 14.90 km |
Fengyang, Anhui | [117.4997, 117.8000] | [32.7357, 33.0812] | 28.30 km × 38.120 km |
Localization | Total Number of Mosaics | Number of Successful Geolocalized Mosaics | |
---|---|---|---|
2RIT | Ours | ||
Suizhou, Hubei | 21 | 14 | 16 |
Xian, Shanxi | 24 | 14 | 20 |
Fengyang, Anhui | 7 | 5 | 7 |
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Li, Y.; Wang, S.; He, H.; Meng, D.; Yang, D. Fast Aerial Image Geolocalization Using the Projective-Invariant Contour Feature. Remote Sens. 2021, 13, 490. https://doi.org/10.3390/rs13030490
Li Y, Wang S, He H, Meng D, Yang D. Fast Aerial Image Geolocalization Using the Projective-Invariant Contour Feature. Remote Sensing. 2021; 13(3):490. https://doi.org/10.3390/rs13030490
Chicago/Turabian StyleLi, Yongfei, Shicheng Wang, Hao He, Deyu Meng, and Dongfang Yang. 2021. "Fast Aerial Image Geolocalization Using the Projective-Invariant Contour Feature" Remote Sensing 13, no. 3: 490. https://doi.org/10.3390/rs13030490