# American Institute of Mathematical Sciences

August  2020, 3(3): 141-155. doi: 10.3934/mfc.2020021

## A fast matching algorithm for the images with large scale disparity

 1 Computer Science Department, Curtin University, Perth, Australia 2 Automation College, Shenyang Aerospace University, Liaoning, China

* Corresponding author: Shichu Chen

Received  October 2019 Revised  March 2020 Published  June 2020

With the expansion of application areas of unmanned aerial vehicle (UAV) applications, there is a rising demand to realize UAV navigation by means of computer vision. Speeded-Up Robust Features (SURF) is an ideal image matching algorithm to be applied to solve the location for UAV. However, if there is a large scale difference between two images with the same scene taken by UAV and satellite respectively, it is difficult to apply SURF to complete the accurate image matching directly. In this paper, a fast image matching algorithm which can bridge the huge scale gap is proposed. The fast matching algorithm searches an optimal scaling ratio based on the ground distance represented by pixel. Meanwhile, a validity index for validating the performance of matching is given. The experimental results illustrate that the proposed algorithm performs better performance both on speed and accuracy. What's more, the proposed algorithm can also obtain the correct matching results on the images with rotation. Therefore, the proposed algorithm could be applied to location and navigation for UAV in future.

Citation: Shichu Chen, Zhiqiang Wang, Yan Ren. A fast matching algorithm for the images with large scale disparity. Mathematical Foundations of Computing, 2020, 3 (3) : 141-155. doi: 10.3934/mfc.2020021
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A region of intensities can be calculated in three additions on integral image
Left to right: templates of Gaussian second order partial derivative $L_{yy}$ and $L_{xy}$ separately; Approximations of corresponding box filters $D_{yy}$ and $D_{xy}$ respectively
Filters $D_{yy}$ (above) and $D_{xy}$ (below) with two size: $9\times 9$ templates (left) and $15\times 15$ templates (right)
Filters and octaves permutation
Scale space
$3\times 3 \times 3$ neighbourhood non-maximum suppression
Haar wavelet templates in $x$ and $y$ directions
A sliding sector to find out dominant orientation
Descriptor and sub-region divisions
Different local characteristics
Flowchart of fast matching algorithm
(b) and (d) is the UAV image A; (a) and (c) are the matched tiles with Image A via Ao' method and the proposed method respectively
(b) and (d) is the UAV image B; (a) and (c) are the matched tiles with Image B via Ao' method and the proposed method respectively
(b) and (d) is the UAV image C; (a) and (c) are the matched tiles with Image A via Ao' method and the proposed method respectively
(b) and (d) is the UAV image D; (a) and (c) are the matched tiles with Image A via Ao' method and the proposed method respectively
Diagram of the angle between $\overline{AB}$ and Google map direction
The matching results for Image B with rotations
The matching results for Image C with rotations
Pseudo-code of fast matching algorithm
 Algorithm: Fast matching algorithm for images with large scale disparity Input: UAV aerial image $I_{UAV}$, satellite tiles $Tile_{i}$, $i=1$, 2, ..., n and $C = 2$. Output: Best matching tile $Tile_{b}$ with $I_{scaled}$. 1: $\alpha_{best} = \frac{D_{UAV}}{D_{Tile}} \times C$; 2: Reduce $I_{UAV}$ with $\alpha_{best}$ to get $I_{scaled}$; 3: Let $Value_{i}$ represent the corresponding matching performance between $I_{scaled}$ and $Tile_{b}$; 4: for $i:=1$ to $n$ do 5: Double the size of $Tile_{i}$; 6: Do the matching between the doubled $Tile_{i}$ and $I_{scaled}$; 7: Matching performance is valued by $Value_{i}$ 8: end for 9: $b=argmax_{i} {Value_{i}}$ and $Tile_{b}$ is the best matching tile with $I_{scaled}$. Stop.
 Algorithm: Fast matching algorithm for images with large scale disparity Input: UAV aerial image $I_{UAV}$, satellite tiles $Tile_{i}$, $i=1$, 2, ..., n and $C = 2$. Output: Best matching tile $Tile_{b}$ with $I_{scaled}$. 1: $\alpha_{best} = \frac{D_{UAV}}{D_{Tile}} \times C$; 2: Reduce $I_{UAV}$ with $\alpha_{best}$ to get $I_{scaled}$; 3: Let $Value_{i}$ represent the corresponding matching performance between $I_{scaled}$ and $Tile_{b}$; 4: for $i:=1$ to $n$ do 5: Double the size of $Tile_{i}$; 6: Do the matching between the doubled $Tile_{i}$ and $I_{scaled}$; 7: Matching performance is valued by $Value_{i}$ 8: end for 9: $b=argmax_{i} {Value_{i}}$ and $Tile_{b}$ is the best matching tile with $I_{scaled}$. Stop.
Comparisons on time-consuming and numbers of matched pairs
 Image No. Matching time (second) Numbers of matched pairs Image A using fast method 23.1 7 Image A using Ao's method 738.1 3 Image B using fast method 23.0 6 Image B using Ao's method 703.7 3 Image C using fast method 24.1 6 Image C using Ao's method 749.9 7 Image D using fast method 23.3 7 Image D using Ao's method 697.5 9
 Image No. Matching time (second) Numbers of matched pairs Image A using fast method 23.1 7 Image A using Ao's method 738.1 3 Image B using fast method 23.0 6 Image B using Ao's method 703.7 3 Image C using fast method 24.1 6 Image C using Ao's method 749.9 7 Image D using fast method 23.3 7 Image D using Ao's method 697.5 9
Comparisons of real scene direction with calculated scene rotation direction
 Image No. Real image direction (degree) Calculated image direction (degree) 15 16.44 30 29.57 Image B 45 49.10 60 59.82 75 76.25 90 93.21 110 109.07 120 117.15 Image C 130 130.09 140 138.96 150 149.41 160 159.54
 Image No. Real image direction (degree) Calculated image direction (degree) 15 16.44 30 29.57 Image B 45 49.10 60 59.82 75 76.25 90 93.21 110 109.07 120 117.15 Image C 130 130.09 140 138.96 150 149.41 160 159.54

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