Comparison of Three Weak Small Moving Target Detection Methods based on Time Domain Filtering

The weak small moving target detection method based on time domain filtering can be seen as a background suppression method in time domain. In this paper, aiming at three commonly used time domain filtering methods – the time domain average filtering, the time domain median filtering, and the time domain minimum value filtering, we analyze the weak small targets detection performance of them by observing their images after filtering. The experimental results show that although the time domain minimum value filtering method in target brightness is the highest, but produces the more false alarm points, and the number of false alarm areas using the time domain average filtering method is obviously less than using the time domain median filtering method and the time domain minimum value filtering method. The performance using the time domain average filtering method is better than the other two, so the time domain average filtering method is more suitable for weak small moving target detection than the time domain median filtering methods and the time-domain minimum value filtering method.


Introduction
Background filtering and suppression actually uses a variety of the image preprocessing algorithms to enhance the target and suppress the background of infrared image.In this way, the SNR of image is improved.The background of infrared image is generally considered as spatial correlation, stability in the time domain and on the low frequency part of the image in frequency domain.The target is generally considered irrelevant to the background; it occupies the high frequency part of the image in the frequency domain [1].Therefore, we can detect the target directly from the image except the background.We also can predicate the background firstly, and then eliminate the image background to calculate the residual image.Image preprocessing methods mainly includes the time domain filtering method, the spatial domain filtering method and the transform domain filtering method.
The time domain filtering method estimates global motion parameters for registration to the background before the time domain filtering, Bin Wu et al. put forward the infrared background suppression algorithm based on third order cumulates [2]; Yan Xing et al. put forward the frame of nonlinear filtering algorithm; reference [3] proposed a multiple frames integrated detection algorithm in time domain based on the point estimation.Due to the need for three dimensional signal processing, the computational complexity of these methods is very large, and they would occupy lots of storage space.It is difficult to accurately estimate the global motion parameters of the non-stationary background.Therefore, they are mainly used to inhibit the short-time stationary background.
The spatial domain filtering method has good real-time performance and it easy to implement, so it is widely used in practical engineering [4].Hat transform method is a kind of practical nonlinear background prediction technology [5].In order to enhance the adaptability of the algorithm, some scholars introduced the adaptive filter technology to image preprocessing, such as the two-dimensional minimum mean square error filter [6], the minimum mean square support vector machine [7], Karman filters [8] and Wiener filters [9], etc. Ming Li put forward a three-dimensional bidirectional filter to inhibit the complex background [10].Ch.O. Goo put forward a kind of infrared small target detection method based on variable structure tensor [11]; Siguang Zhong et al. used gradient operator to describe the target area of the "gray singularity" to implement the background suppression [12]; Biyin Zhong et al. set up first-order field spatial distribution model of infrared dim-small target image, and used the neat filter to realize background suppression adaptive and target enhancement [4,13]; Yanhua Wang and others used anisotropic diffusion filter to separate the target and gradient feature of background to improve the image of the SNR [14]; Jin Liu et al. put forward a kind of infrared background prediction and suppression algorithm based on improved M estimate of the current residual error [15]; Jin Qin put forward weak small targets detection method based on the optical flow estimation and adaptive background suppression [16]; Riming Liu et al. proposed an adaptive region growing algorithm that could automatic extract the small target from infrared image [17].Without the statistical properties of the backgrounds and assumption of the gray feature, the structures of these methods are very simple, and widely used in engineering application.However, they would residue much strong background texture, and it is not enough to improve the SNR of image as for detecting the weak small target in complex background.
The transform domain filtering method firstly maps the image to transform domain, and then detects the target in the transform domain.Yang Yong et al. used Butterworth high-pass filter in the preprocessing of infrared dim-small target image [18]; Thayaparan T. et al. found the frequency domain algorithm based on the fast Fourier transform [19].But these methods are not suitable for the weak small target detection in the low SNR infrared image.S. Liu and Z. Cao proposed an improved visual attention algorithm to detect SAR image target in complex environments [20]; M. S. Islam and U. Chong presented an improvement in moving target detection based on Hough Transform and Wavelet [21]; Zhicheng Wang et al. proposed a detection method of fusion the infrared small target based on support vector machine in the wavelet domain [22].The performance of these methods mainly depends on the design of wavelet basis.Liu Riming and others extracted high order statistical characteristic of the image by Fukunaga -Koontz nuclear transformation to implement the background suppression and enhancement the target [23].Yong Yang et al. used two-dimensional general S transformation to obtain the information of background [24].In order to solve the structured background suppression, Xiang Zhang et al. put forward an infrared weak small target background suppression method based on dual tree complex wavelet transform [25].Yiquan Wu et al. put forward a test method of inhibition the original image, based on nonnegative matrix decomposition and independent component analysis and complex contoured transform [26].Y. Wu, and D. Yin put forward a kind of background prediction test method based on the next sampling transform and fuzzy c-means clustering multi-model least squares support vector machine (SVM) [27].All in all, the transform domain filtering method need to implement two transformations, so its computational complexity generally become larger and its real-time is reduced.

Basic Principles
The weak small moving target detection method based on the time domain filtering can be seen as a background suppression method in time domain.In this paper, aiming at three commonly used time domain filtering methods -the time domain average filtering, the time domain median filtering, and the time domain minimum value filtering, we compare their performance by using them to detect the weak small target in IR images.

The Time Domain Average Filtering
The time domain average filtering uses the average of the pixel (i, j) in the time window K as its background prediction value.The residual signal fr (i, j, k) of the pixel (i, j) after average filtering can be represented as follows.
The steps of time domain average filtering are described as follows.
1. Read K frames of infrared images into memory, and store in imk (k=1, 2, …, K). 2. Put imk combined by function imaddd(), stored in matrix I, and make matrix I divided by K, then we get the matrix J, which contains the time domain average of each point.
3. Make each frame of image minus the mean value matrix, and then get the residual signal.4. Select an appropriate threshold for binarization.5.The points which gray values are greater than threshold are candidate targets, and then the others are background points.

The Time Domain Median Filtering
The time domain median filtering uses the median of the pixel (i, j) in the time window K as its background prediction value.The residual signal fr (i, j, k) of the pixel (i, j) after median filtering can be represented as follows.
The steps of the time domain median filtering are similar to the steps of the time domain average filtering.Only the step (2) need to be changed to remove the gray value of each pixel in the array, then get the median of each point by function median(a), which deposited in corresponding position of the matrix b which has the same size to the image matrix.

The Time Domain Minimum Value Filtering
The time domain minimum value filtering uses the minimum value of the pixel (i, j) in the time window K as its background prediction value.The residual signal fr (i, j, k) of the pixel (i, j) after median filtering can be represented as follows.
The steps of the time domain minimum value filtering and the time domain average filtering are almost similar.Only the step (2) need to be changed to remove the gray value of each pixel in the array, then get the median of each point by function min(a), which deposited in corresponding position of the matrix b which has the same size to the image matrix.

Experimental Results and Analysis
The experimental results for the first frame image in infrared sequence images using the time domain average filtering, the time domain median filtering, and the timedomain minimum value filtering are shown in Figure 1.
As shown in Figure 1, the three time domain filtering methods can detect the target, but they all produce some false alarm points.These false alarm points are generally produced by cloud edge or random noise.
In Figure 1b, 1c and 1d, the false alarm points using the time domain average filtering are mainly produced by cloud edge, and the number of the false alarm areas using the time domain average filtering is obviously less than the other two methods.
Seen in Figure 1c and 1d, the number of the false alarm areas using the time domain median filtering is similar to he number of the false alarm areas using the time-domain minimum value filtering, but the number of the false alarm pixels using the time domain median filtering is obviously less than the number of the false alarm pixels using the time-domain minimum value filtering.Only considering the false alarm points by using the three time domain filtering methods, it is not enough to judge which method is the best one of them.We want to find more information using the three dimensional histograms.The three dimensional histograms of the binary images by using three time domain filtering methods are shown in Figure 2.
The three dimensional histogram of the binary image by suing the time domain average filtering method is shown in Figure 2a.It shows that the ordinate of the target is around 44, and the ordinates of false alarm points remain 10 -15.
As shown in the three dimensional histogram of the binary image by suing the time domain median filtering method (seen in Figure 2b), the ordinate of the target is about 47, and the ordinates of most of the false alarm points maintain 20-30.
As shown in the three dimensional histogram of the binary image by suing the time domain minimum value filtering method (seen in Figure 2c), the ordinate of the target is around 62, and the ordinates of most of the false alarm points remain 35-47.Furthermore, the number of false alarm points by using the time domain minimum filter ing method is more than the other two.In short, comprehensive consideration, the time domain average filtering method is more suitable for weak small moving target detection than the time domain median filtering methods and the time-domain minimum value filtering method.

Conclusion
In this paper, we introduce three time domain filtering methods, and apply the three time domain filtering methods in weak small moving target detection.By comparing the number of the false alarm points and the three dimensional histograms by using the three time domain filtering methods to detect the weak small target in infrared image, we can see that although the time domain minimum value filtering method is the highest in target brightness, but it produces the biggest number of the false alarm points.The performance of the time domain average filtering method is better than the other two, so it is the most appropriate method to detect weak small moving target in the time domain filtering.

Figure 1 .
Figure 1.The results of the three time domain filtering methods: (a) the original infrared image, (b) the binary image by using the time domain average filtering, (c) the binary image by using the time domain median filtering, (d) the binary image by using the time domain minimum filtering.

Figure 2 .
The three dimensional histograms of the binary images by using three time domain filtering methods: (a) get the binary image of the three dimensional histogram, (b) median filter to get the binary image of the three dimensional histogram, (c) the minimum filter to get the binary image of the three dimensional histogram.Unauthenticated Download Date | 6/23/19 3:19 AM