Robust visual tracking based on a modified flower pollination algorithm

In this study, a target tracking algorithm based on the flower pollination algorithm (FPA) is proposed. This method solves the problem of robust visual target tracking in different complex tracking scenes with the good global and local optimisation ability of the FPA. Meanwhile, with the aim of solving the problem of invalid background feature interference and the loss of effective features caused by the fixed scale of tracking frame in traditional tracking methods, a scale adaptive adjustment model of tracking frame is proposed. Considering that the FPA has good global and local optimization ability at simultaneously, the position update equation of the FPA is introduced as the main optimization method of target tracking. In addition, considering that the traditional FPA is similar to classical swarm intelligence algorithm (such as the particle swarm optimization algorithm), it also faces the problems of a high probability of falling into local extrema, a low efficiency of late convergence speed and a high probability of early maturity. Therefore, this work proposes the GTFPA, an advanced FPA based on the gravitational search algorithm (GSA) and mutation mechanism via a trigonometric function. We qualitatively, quantitatively and statistically compare the proposed method with other classical general tracking methods through two datasets, OTB2015 and VOT2018, which contain hundreds of video sequences and more than ten tracking scenes and can effectively test the success rate, accuracy and stability of the trackers. The results of a large number of tracking experiments in a variety of complex tracking scenarios prove that the proposed GTFPA tracker performs well with regards to efficiency, accuracy and robustness.


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(MUSTer), a two-component approach consisting of shortand long-term memory storage for processing target visual memory. The MUSTer has a good tracking effect for solving scenes with complex backgrounds. Ref. [10] proposed the unified formulation for discriminative visual tracking (SRDCFdecon), which contains a unified learning formula for training the sample damage problem in tracking the detection paradigm. This method is universal and can be integrated into other discriminant tracking frameworks. Ref. [11] put forward the learning background-aware correlation filters (BACF), a background aware correlation filter based on HOG features, which can effectively simulate how the foreground and background of an object change over time. Ref. [12] proposed the large margin object tracker with circulant feature maps (LMCF), a new tracking approach that absorbs the strong resolution of structured output support vector machine (SVM) and accelerates the tracking speed significantly through correlation filtering. Ref. [13] presented a scale adaptive tracking algorithm based on a correlation filter tracking framework (SAMF). The SAMF performs very well in challenging tracking scenes such as scale variation and deformation. Ref. [14] proposed the discriminative scale space tracker (DSST), a robust scale estimation method based on detection and tracking framework, which is implemented by learning discriminant correlation filters based on the scale pyramid representation. Ref. [15] proposed a particle filter tracker advanced by the mean-shift algorithm (MSPF). The MSPF tracker is suitable for challenging tracking scenes involving fast motion and occlusion. Ref. [16] presented the spatial-temporal regularized correlation filter (DeepSTRCF) that can deal with the boundary effects of hand-crafted features and handle the inefficiency problem of the spatially regularized discriminative correlation filters. Ref. [17] proposed a correlation filter tracker improved by a convolutional operator (SiamVGG). The SiamVGG tracker can track fast-moving and motion blurred visual targets with high precision and efficiency. Ref. [18] put forward the a multi-cue analysis framework for robust visual tracking (MCCT), which combines various features of objects in multiple views and performs well in tracking precision and robustness.

B. Motivation
Most of the above tracking methods are suitable for specific tracking scenarios or they suffer from one or more defects in efficiency, accuracy, robustness, stability and so on. In order to solve the above defects, we identify two main improvement directions for visual tracking methods: search strategy and tracking frame scale adjustment strategy.

1) Search strategy
An effective search strategy is vital for improving the tracking efficiency of a visual target, and the flower pollination algorithm (FPA) has good global and local optimization ability simultaneously [19][20][21][22]. Therefore, this study introduces a position update equation of the FPA as the main optimization method of visual target tracking. However, the traditional FPA still faces the problems of a high probability of falling into local extrema, low convergence efficiency and a high risk of premature convergence [23][24][25][26]. Therefore, the main task of this study is to propose an improved flower pollination tracking method with high efficiency, high precision, good stability and universality for a variety of complex tracking environments.

2) Scale adjustment strategy of tracking frame
The scale of the tracking frame of the traditional visual target tracker is fixed in the whole tracking process [27][28].
On this basis, it cannot adapt to the change of target scale, and can easily mix too many invalid features or lose some effective features, which affects the accuracy and efficiency of the tracking process [29][30][31]. Therefore, it is essential to study and propose a model in which the scale of the tracking frame can be adjusted adaptively with the actual situation of the target.

C. Contribution
The main research innovations and contributions of this work are as follows:  This new method helps solve the common problems of the standard FPA, including the high probability of falling into local extrema, low convergence efficiency in the later stage of iteration and sample degradation. Thus, the efficiency and accuracy of the target tracking process based on the FPA are greatly optimized.
3) The dynamic adjustment mechanism of the conversion probability of the FPA algorithm is established. In this study, a conversion probability adjustment mechanism based on an exponential function is proposed, so that the conversion probability decreases dynamically with the iteration of the algorithm. This mechanism not only ensures that the FPA tracker can fully explore the search space in the early stages and increase the accuracy of the global optimal value, but also ensures that the algorithm can accelerate the convergence speed in the later stage of iteration.
Through the comparison of qualitative, quantitative and statistical experiments on OTB2015 and VOT2018, it can be seen that the newly proposed GTFPA tracking algorithm performs well in efficiency, accuracy and robustness, and the visual tracking results under eight typical tracking scenarios show that the tracking frame of GTFPA algorithm can always closely fit the tracked object and has good tracking accuracy and stability.

A. MATHEMATICAL MODEL OF TARGET STATE
The mathematical model of the target state is as follows: The target observation equation is as follows: where t r represents the distance coordinates, t  represents the phase coordinates and t v refers to the Gaussian white noise similar to t f .

B. MATHEMATICAL MODEL OF TARGET APPEARANCE
The appearance model of a certain image area j is represented by the characteristic probability density function of this area, which is expressed as follows: where

C. FITNESS FUNCTION
The fitness function value ) ( j X fitness of image region j in the target tracking optimization problem in this study is defined as the similarity function value between image block Xj and real target region Xc (the optimal solution found in the last frame). The Bhattacharyya function ) ( j X  is used to determine the similarity between different image blocks [32].
The fitness function can be expressed as follows:

D. SCALE ADAPTIVE ADJUSTMENT METHOD OF TRACKING FRAME
The scale  of the tracking frame of the traditional trackers is fixed in the whole tracking process and therefore cannot easily adapt to the change of the target scale. It is also simple to mix too many invalid features or lose some effective features, which affects the accuracy and efficiency of the algorithm. Therefore, we propose a tracking frame scale adaptive adjustment model, which is expressed as follows: represents the position of the target center at where t i x is the pollen i of the t generation, t j x and t k x represent pollen j and k, respectively, randomly selected from different flowers of the same plant during the local search, which can enhance the diversity of the population. And p is the transformation probability of the global and local searches, ,  represents the step size adjustment factor for Author Name: Preparation of Papers for IEEE Access (February 2017) VOLUME XX, 2017 5 the search process and parameter L represents pollination intensity, which follows the Levy distribution and its expression is as follows [34]: represents the standard gamma function, and  takes the value 1.5 [34].
where k i x represents the position of individual i on the k-th dimension.
According to the law of universal gravitation, the interaction force between individuals i and individual j in the k-dimensional space at time t is defined as: refers to the inertial mass acting on where T is the maximum number of iterations, 0 The larger the individual's inertial mass ) (t M i is, the greater its gravitational pull on other individuals, the more likely it is to move to the center of the sample set, and the closer its position is to the optimal solution. ) (t M i is updated as follows: where, randj is a random number in [0,1], nbest is the number of individuals with high quality at time t. The acceleration of In the process of iteration t, the updating formula of individual velocity and position is as follows: where randi is a random number between [0,1].

2) IMPROVED LOCAL SEARCH OF MUTATION OPERATION BASED ON TRIGONOMETRIC FUNCTION
Since the FPA algorithm mainly focuses on the local search in the late iteration, and the similarity of pollens increases, which leads to the loss of diversity of pollen population, the algorithm is prone to premature convergence and then falls into local optima [36][37]. In order to improve the population diversity in the late iteration of the algorithm, a stochastic perturbation factor should be added to the standard local search formula for flower pollination. Meanwhile, in order to avoid random disturbance affecting convergence efficiency too randomly, this study proposes an improved local search method for flower pollination based on variation operation performed by a trigonometric function, as shown in the following formula:

3) DYNAMIC CONVERSION PROBABILITY
The FPA randomly selects the global search or local search according to the conversion probability p, whose value will affect the evolution direction and optimization performance of the algorithm [39]. If p is too small, the algorithm is difficult to converge due to the large number of global search operations. If the value of p is too large, the algorithm can easily fall into local optima because it performs more local searches [40][41]. In conclusion, in the standard FPA, the conversion probability p is fixed. However, in the actual optimization process, p plays a key role in adjusting the local search and global searches, which affects the balance of global or local search weight. In order to make the initial iteration more inclined to the global search, the value of p should be slightly larger at the beginning. On the contrary, local searches should be more prevalent at the end of the iteration, so p should take a smaller value at the end of the iteration. Therefore, the fixed conversion probability of standard FPA algorithm needs to be reformed.

7) Calculate the transformation probability p according
to Equation (19) and judge whether to carry out the global or local search, which are executed according to Formula (17) or Formula (18) respectively, according to p . 8) Calculate the fitness value, update the global optimal solution, and update the optimal target location ; 9) Judge whether the end condition of the algorithm is met. If so, exit and output the optimal solution; otherwise, repeat steps 3) to 9).
The flow chart of the target tracking algorithm based on the GTFPA algorithm is shown in Figure 1.

IV. EXPERIMENTAL ANALYSIS
We used MATLAB to implement the proposed tracker on a machine equipped with an Intel Core i-7-4790 CPU @ 3.60GHz with 32 GB RAM. Set the maximum iteration number T as 500, the sample number S as 70, initial conversion probability p as 0.642 and initial universal gravitation parameter G0 as 100. The proposed GTFPA tracking method achieves an average tracking speed of 27 frames per second (FPS). For experimental verification, we employ OTB2015 [42] and VOT2018 [43], which contain hundreds of video sequences and more than ten tracking scenes and can effectively test the success rate, accuracy and stability of the trackers. We evaluate the tracking accuracy, efficiency, and adaptability of the tracker in different tracking scenarios by carrying out qualitative and quantitative comparison between our tracker with nine classical generative trackers in OTB2015 including the ECO [7], C-COT [8], MUSTer [9], SRDCFdecon [10], BACF [11], LMCF [12], SAMF [13], DSST [14] and MSPF [15]. We evaluate the robustness and stability of these trackers by carrying out statistical comparison between our tracker with eight state-of-the-art tracking methods in VOT2018 including DeepSTRCF [16], SiamVGG [17], ECO, GTFPA, MCCT [18], C-COT, Staple, SRDCF [44] and DSST.

A. QUALITATIVE COMPARISONS
In this section, we evaluated the tracking tracking performance of GTFPA in three aspects: precision, efficiency and adaptability to different tracking scenarios. We selected eight challenging tracking scenes including illumination variation, motion blur, deformation, complex background, occlusion, rotation, scale variation and low resolution. As

B. QUANTITATIVE COMPARISONS
To further evaluate the tracking performance of GTFPA comprehensively, we quantitatively compare our tracker with the classical trackers in OTB-2015 via success rate (the percentage of successful frames) and precision rate (the ratio of tracking frames whose center position error is smaller than a given threshold). As illustrated in Tables 1 and 2

C. STATISTICAL COMPARISON
To evaluate the robustness and stability of the GTFPA, we carry out a statistical comparison with the VOT2018 database.
This section introduces some new tracking methods that perform very well in VOT2018, including DeepSTRCF [16], SiamVGG [17] and MCCT [18] for better evaluation of the GTFPA. In statistical comparison, we compare the GTFPA with these classical generative trackers in three aspects: average overlap (EAO), accuracy (Acc.) and robustness (R. for short, measured by failure rate). As illustrated in Table 3, GTFPA ranked second in EAO, fourth in ACC, and third in R.Ail. It turns out that GTFPA is more competitive in robustness and stability than other classical generative trackers. As shown in Table 4, the tracking speed of the GTFPA is 27 frames per second, ranking in the third place.
The tracking efficiency of the GTFPA is not obviously inferior to other classical generative trackers.

V. CONCLUSION
This study proposed a robust visual tracking algorithm based on the FPA. Specifically, in this study, a tracking frame In future work, more robust features could be employed. Issues related to automatic detection and target behavior analysis are also of concern.