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CodLix LLC (Saint Petersburg, Russia) Southwest State University (Kursk, Russia)

Calculation of Optimal Parameters Calculation of Optimal Parameters for Aircraft Recognition on Remote Sensing Imagery for Aircraft Recognition on Remote Sensing Imagery by Contour Analysis by Contour Analysis

Authors: Miroshnichenko Sergei, Dremov Evgenii 2019

The Problem

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is to create a method for the aircraft recognition (not detection) on aerial and space imagery with the following features:

• 1. Use the object shape to recognize the object.
• 2. Be invariant to scaling and rotating of the recognized object

towards the reference instances.

• 3. Be capable to train on compact and nonuniform datasets.
• 4. Minimize the number of type I and II errors.

Related Work

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To reach affine transformation invariance a combination of few features and methods is used:

• Zernike moments and wavelet coefficients

Hsieh J W, Chen J M, Chuang C H and Fan K C 2005 Aircraft type recognition in satellite images Vision, Image and Signal Processing 152 307–315

• Radon transform, PCA and kNN classification

Liu G, Sun X, Fu K and Wang H 2013 Aircraft recognition in high-resolution satellite images using coarse-to-fine shape prior IEEE Geoscience and Remote Sensing Letters 10 573–577

• HOG, graph theory and an object reconstruction

Wu Q, Sun H, Sun X, Zhang D, Fu K and Wang H 2015 Aircraft recognition in high-resolution

• ptical satellite remote sensing images IEEE Geoscience and Remote Sensing Letters 12

112–116

Normalized Dot Product (NDP)

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1

( ( ), ( )) ( , , ) . | ( ) | | ( ) |

l i j n i j i j

n n l l l   



     



The NDP is: The positive NDP features:

• 1. NDP module is a similarity measure of two

contours within the range [0..1] .

• 2. Invariance to scaling.
• 3. Invariance to the rotation (only complex-valued).

The negative NDP features:

• 1. Not invariant to the change of the initial point.
• 2. Contours have to be equal in length.
• 3. Require to tune classification thresholds Ti.

: arg max( ( , ) ) , ( ) : max ( , ) .

i i i i i i i i

C i f T C i f T                   Γ Γ The classification rule is:

Training Dataset

B-1 B-52 C-5 C-37

C-130 C-135

S-3 P-3

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Training Dataset Details

Characteristics of contours in the training dataset Aircraft class B-1 B-52 C-5 C-37 C-130 C-135 P-3 S-3 Instances count 17 10 20 11 135 81 92 64 Mean items’ quantity 1132 1945 2404 1227 1570 1420 1458 1132 Items’ quantity histogram

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Training Classes Examples

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B-1 B-52

Test Dataset

B-1 B-52 C-5 C-37

C-130 C-135

S-3 P-3

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Test Dataset Details

Characteristics of contours in the test dataset Aircraft class B-1 B-52 C-5 C-37 C-130 C-135 P-3 S-3 Instances count 7 6 48 11 57 102 142 49 Mean items’ quantity 1263 1884 2441 1177 1483 1315 1345 1084 Items’ quantity histogram

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Initial Point Invariance

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The cross-correlation function (CCF) based on NDP is introduced to add invariance to the initial point’s shift:

   

 

0..

( , , ) max , , ,

s i j i j s l

l l  



    

is a contour obtained from by the cycle shift of its starting point to s elements.

( ) s j



j



0,2 0,4 0,6 0,8 1 52 104 156 208 260 312 364 416 468 520 572 624 676 728 780 832 884 936 988 1040 1092 1144 1196 1248 1300 1352

Instances Distance Measurement

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Within-class distances Between-class distances

Classification Thresholds Graphs

Total relative measurement error dependence from the classification threshold for classes C-130 and P-3. Total relative measurement error dependence from the classification threshold for classes B-1 and B-52. 12

Items Quantity Effect (C-135/B-52)

More type I errors 13 More type II errors

Items Quantity Graphs (B-1,B-52)

Total relative measurement error dependence from the B-1 vector-contour's items quantity. Total relative measurement error dependence from the B-52 vector-contour's items quantity. 14

Total relative measurement error dependence from the C- 130 vector-contour's items quantity. Total relative measurement error dependence from the P-3 vector-contour's items quantity. 15

Items Quantity Graphs (C-130,P-3)

Optimal Classification Threshold and Items’ Quantity Values per Class

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The proposed optimal items’ quantity calculation method was experimentally compared to the heuristic methods including the use of: (a) the minimal items’ quantity of the certain class’s instances to minimize the type II error; (b) the maximal items’ quantity of the certain class’s instances to minimize the type I error; (c) the recognized object’s items quantity to retain its actual level of details. Table 5. Optimal values of the vector-contour’s items quantity. Row name Total relative error, % Class index 1 2 3 4 5 6 7 8 Mean error through all classes Class name B-1 B-52 C-5 C-37 C-130 C-135 P-3 S-3 Heuristic (a) 12,18 20,00 38,66 0,09 13,68 7,59 11,97 8,38 14,07 Heuristic (b) 12,18 13,33 26,29 0,09 21,23 3,70 10,00 3,97 11,35 Heuristic (c) 11,49 8,89 19,29 0,15 11,42 2,53 7,32 2,58 7,96 Proposed method 9,42 0,00 2,13 0,00 6,51 0,23 4,18 0,76 2,90 17

Optimal Items’ Quantity Value vs Heuristics

Similarity Functions

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 

1( ,

) max , , .

i ik i k

f l      Γ

 

2 1

1 ( , ) , , .

i

N i ik i k i

f l N 



   



Γ

• 1. Maximum CCF for a vector-contour

and one of the reference instances

• 2. The mean CCF value for the whole class

Modified Similarity Function

To reduce of errors number we modified the classification rule to combine the functions, integrate their merits and mutually compensate shortcomings. The modified classification rule then becomes the following:

2 1 2 1

: arg max( ( , ) ) , ( ) : arg max( ( , ) ) , max ( , ) : max ( , ) .

i i i i i i i i i i i i i i i i

C i f T C C i f T i f T i f T                                 Γ Γ Γ Γ

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Future Work

• 1. Develop a CNN-based segmentation method to detect aircraft edges

invariantly to:

• camouflage
• poor contrast with the underlying surface
• illuminated and shaded areas
• close-lying airfield equipment.
• 2. Get higher edges precision enough to recognize fighter class aircraft.

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Thank You for Attention!

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