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A novel visual tracking method using bat algorithm Ming-Liang Gao n, Jin Shen, Li-Ju Yin, Wei Liu, Guo-Feng Zou, Hai-Tao Li, Gui-Xia Fu School of Electrical & Electronic Engineering, Shandong University of Technology, Zibo 255049, China
art ic l e i nf o
a b s t r a c t
Article history: Received 8 October 2015 Received in revised form 13 November 2015 Accepted 22 November 2015 Communicated by: Prof. R. Tadeusiewicz
Bat algorithm (BA) is a new meta-heuristic optimization algorithm that is inspired by the echolocation characteristics of bats with varying pulse rates of emission and loudness. BA has been proven to be a powerful tool in solving a wide range of global optimization problems. In this study, visual tracking is considered to be a process of searching for target by various bats in sequential images. A BA-based tracking architecture is proposed and the sensitivity and adjustment of the parameters in BA are studied experimentally. To demonstrate the tracking ability of the proposed tracker, comparative studies of tracking accuracy and speed of the BA-based tracker with three representative trackers, namely, particle filter, meanshift and particle swarm optimization are presented. Comparative results show that the BAbased tracker outperforms the other three trackers. & 2015 Elsevier B.V. All rights reserved.
Keywords: Visual tracking Bat algorithm Parameter sensitivity Comparative study
1. Introduction In recent years, a large body of researches on visual tracking have been published in the literature [1–3]. The reason is that visual tracking has found its way into many real-world applications, including visual surveillance [4], traffic flow monitoring [5], video compression [6], human-computer interaction [7], and so on. However, visual tracking is still a challenging task because it often suffers from difficulties in handling complex factors in real world scenarios, e.g. partial occlusion, shape deformation, illumination variation, camera motion, etc. Object tracking in image can be regarded as a process of searching for the most similar candidate region of the target by an efficient target representation [8]. Therefore, a robust appearance model and an efficient search strategy are of crucial importance for a tracker. Recently, great efforts have been spent on appearance model building. The appearance model generally consists of two components, namely visual representation and statistical modeling [3]. Visual representation focuses on how to construct robust object descriptors using different types of visual features and it is commonly divided into global visual representation [9, 10] and local visual representation [11,12]. Statistical modeling concentrates on how to build effective mathematical models for object identification using statistical learning technique which can be classified into three categories, including generative [13,14], discriminative [15,16], and hybrid generative-discriminative [17,18]. n
Corresponding author. E-mail address:
[email protected] (M.-L. Gao).
However, compared with the appearance model, there are fewer attentions paid on the search strategies. In tracking process, target can be located by searching and measuring every possible candidate in the state vector. This exhaustive search is often timeconsuming because the state-space for visual tracking is very large. Therefore, an effective target search strategy for state estimation is essential to reduce the scope of the target’s state. In general, there are two well known search strategies, namely, probabilistic methods and deterministic methods [19]. Probabilistic methods regard tracking process as a state solving problem under the Bayesian framework, modeling uncertainty and propagating the conditional densities through the tracking process. Particle filter is a typical method of these methods [20]. Deterministic methods locate targets in each frame by iteratively searching for a region which maximizes the similarity measure between this region and the target window. A representative deterministic method is meanshift [21]. Essentially speaking, visual tracking can be interpreted as an optimization problem [8]. The observation distance between the target and candidate forms the similarity function and locating the target in video can be interpreted as maximizing the similarity function in the candidate solution. In this sense, many researchers start to solve visual tracking problems using optimization algorithms with more “intelligent” searching strategies. For example, Zhang et al. proposed a tracking algorithm based on particle swarm optimization [22]. In their work, the parameters that control the movement of the particles in the swarm were updated dynamically depending on the fitness values of the particles. Experimental results showed that the proposed tracker was more robust and effective than particle filter and unscented particle filter. Fourie et al. designed a visual tracking system based on
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Please cite this article as: M.-L. Gao, et al., A novel visual tracking method using bat algorithm, Neurocomputing (2015), http://dx.doi. org/10.1016/j.neucom.2015.11.072i
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2. Bat algorithm for visual tracking 2.1. Bat algorithm The bat-inspired meta-heuristic optimization algorithm, namely bat algorithm, was recently proposed by Yang [24] based on the echolocation of micro-bats. In the standard bat algorithm, the echolocation characteristics of bats are idealized as three rules [24]. (1) All bats use echolocation to sense distance, and they also “know” the difference between food/prey and background barriers in some magical way; (2) Bats fly randomly with velocity vi at position xi with a fixed frequencyand loudness to search for prey. They can automatically adjust the wavelength (or frequency) of their emitted pulses and adjust the rate of pulse emission depending on the proximity of the target. (3) Although the loudness can vary in many ways, it is assumed that the loudness varies from a large (positive) A0 to a minimum constant value Amin . (4) For each bat (sayi), its position xt1 and velocityvt1 are defined i i in a d-dimensional search space, and they are updated subsequently during the iterations. The new solutions xti and velocities vti at time step t are calculated using a global search strategy by
Fig. 1. Pseudo-code of bat algorithm.
improved harmony search (IHS) algorithm [23]. In their work, the target location was obtained using IHS algorithm. Experimental results showed that IHS was able to track poorly modeled targets in real time. Recently, Gao et al. proposed a cuckoo search (CS) based tracker [8]. In their work, the relationship between optimization and visual tracking was studied comparatively and tracking experiments show that the proposed tracker performed well in various challenging tracking examples. It is well-known that bat is an extremely powerful animal with strong search abilities in nature. Inspired by the echolocation characteristics of bats with varying pulse rates of emission and loudness, Yang proposed a new meta-heuristic algorithm, namely the bat algorithm (BA) [24]. Preliminary studies indicated that BA had superior performance over genetic algorithms and particle swarm optimization for various standard test functions [24]. Since the emergence of this algorithm, it has been applied to a wide range of optimization applications including artificial neural network [25], scheduling [26], electricity market [27], etc. In this study, visual tracking is considered to be a process of searching for target by various bats in sequential images. A tracking framework based on BA is proposed and the parameters’ sensitivity and adjustment in BA are studied experimentally. Meanwhile, to demonstrate the tracking ability of BA-based tracker, the tracking performances of the proposed tracker, PSO, particle filter and meanshift in various challenging examples are studied comparatively. The rest of the paper is organized as follows: in Section 2, the basic concepts and procedure of BA are discussed and a BA-based visual tracking architecture is presented. In Section 3, the parameters’ sensitivity and adjustment of BA in the tracking system are analyzed. In Section 4, comparative studies of tracking performance are carried out and the results are analyzed and discussed. In Section 5, the paper is concluded and future work that stems from this study is directed.
f i ¼ f min þ ðf max f min Þβ
ð1Þ
vti ¼ vti 1 þ ðxti 1 x Þf i
ð2Þ
xti ¼ xti 1 þ vti
ð3Þ
where β A ½0; 1 is a random vector drawn from a uniform distribution. x is the current global best solution found so far, which is located after comparing all the solutions among all the n bats at the current iteration. The values of the frequency f min and f max depend on the domain size of the problem of interest. For the local search part, once a solution is selected from among the current best solutions, a new solution for each bat is generated locally using random walk, as given by xnew ¼ xold þ εAt
ð4Þ
where ε A ½ 1; 1 is a random number, xold is the solution in the current optimization solution set, and At ¼ o Ati 4 is the average loudness of all the bats at time step t. The loudness Ai and the pulse rate ri are updated to reflect that if the target is found the bats decrease the loudness and increase the pulse rate by Ati þ 1 ¼ ωAti ; rti þ 1 ¼ r0i ½1 expð γ tÞ
ð5Þ
is the initial pulse rate, ω is the pulse frequency where increasing coefficient and γ is the pulse amplitude attenuation coefficient. For any 0 o ω; γ o1, we have r0i
Ati -0; rti -r0i ; as
t-1
ð6Þ
The basic steps of BA are summarized as the pseudo code shown in Fig. 1 [24]. 2.2. Bat algorithm-based tracking system Suppose there is target in the image being searched. And a group of target candidates are randomly generated in the image. The aim of BA-based tracker is to find the “best” candidate using the bat algorithm. Based on this, a BA-based tracking framework is designed as shown in Fig. 2.
Please cite this article as: M.-L. Gao, et al., A novel visual tracking method using bat algorithm, Neurocomputing (2015), http://dx.doi. org/10.1016/j.neucom.2015.11.072i
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Fig. 2. BA-based tracking framework.
Fig. 4. Comparison of tracking performance with different population size n. Fig. 3. Challenging tracking problem used for parameters’ sensitivity and adjustment.
As shown in Fig. 2, the target is chosen by the user or detected by some specific object detectors in the first frame. Then, the state vector is initialized. The state vector in this work is defined as x ¼ ðx; y; sÞ, where ðx; yÞ is the target's location in pixel coordinates and s denotes the scale parameter that controls the size of the object. Once target is selected and state vector is initialized, new candidates’ state vectors are generated by a dynamic model. Considering that the target’s state between adjacent frames is small, a random walk model can meet the tracking requirements. In this work, the values of the frequency f min and f max of the state vector x ¼ ðx; y; sÞ are set as f min ¼ ½ 20; 20; 0:8 and f max ¼ ½20; 20; 1:2.
An observation model based on the state vector is established to describe the appearance and the state of the object. As known to all, a good observation model is crucial to a tracker, but it is not easy to choose a certain observation model for all tracking scenarios. In this work, we are more concerned with the search performance, so we selected a widely used kernel based spatial color histogram [21] as the observation model. The kernel-based spatial color histogram is denoted by: ðuÞ p^ c ðX k Þ ¼ C
M X c ci 2 k δ bðci Þ u ; u ¼ 1; U U U; m r i¼1
ð7Þ
where δ is the Kronecker delta function. The function b : R2 f1:::mgassociates to the pixel at location ci and the index bðci Þ of its bin in
Please cite this article as: M.-L. Gao, et al., A novel visual tracking method using bat algorithm, Neurocomputing (2015), http://dx.doi. org/10.1016/j.neucom.2015.11.072i
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the quantized feature space. r ¼ ðhx ; hy Þ denotes the width and height of the target’s rectangle. kðxÞ is a isotropic kernel assigning smaller weight M P k ‖c r ci ‖2 is the normalto pixels farther from the center. C ¼ 1= i¼1
ization constant. When the state vector is described, a similarity measurement is adopted to measure the similarity between the target and the candidates. In this work Bhattacharyya distance is utilized to measure the similarity between two histograms. It is defined as N pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X Bðh1 ; h2 Þ ¼ 1 h1 ðiÞh2 ðiÞ
ð8Þ
i ¼ 1
where N is the number of bins in the histograms and h1 and h2 are the histograms being compared.
Fig. 5. A performance comparison using different values of ω and γ.
After that, the bat algorithm is adopted to select the candidate solution. This process is carried out by maximizing the similarity function. Every time the optimizer is queried for the target location, the frame is displayed to indicate the location of the target. The whole loop continues until no more frames are available.
3. Parameters' sensitivity and adjustment It is worth mentioning that parameter tuning often seems a self-contradicting problem in optimization algorithms. The speed and accuracy should be considered simultaneously during the parameter tuning. As aforementioned, there are three parameters, namely n (population size), ω(pulse frequency increasing coefficient) and γ (pulse amplitude attenuation coefficient) to be finetuned in BA algorithm. We tested the tracking performance using a series of different parameter values on a challenging tracking example with 200 frames as shown in Fig. 3. The target in Fig. 3 is suffered from various challenging factors, e.g. scale variation, fast motion, in-plane rotation, out-of-plane rotation and low resolution. All those challenging factors will provide ample local distractors that can cause the tracker to lose the target. The optimization process was terminated using three termination conditions as mentioned in Ref. [23]. We first analysis the population size n. The population size was varied from 5 to 50, with each a space 5. The performance is evaluated using two measures, number of lost targets (Lost targets), i.e. the number of frames where the overlap region between its bounding box and the ground-truth is less than 50%, and time complexity, i.e. the average time costs (ms). Fig. 4 shows the performance comparison using different values of n. Fig. 4 shows that there is a general trend that when the population size n o20, the number of lost targets decreases along with the increases of n, and meanwhile the time cost raises. This
Fig. 6. A snapshots of the tracking examples. (a) Girl (b) Dog (c) Bird (d) Couple(e) David (f) MountainBike (g) Surfer (h) Basketball. Table 1 Description of the tracking examples. Video
Frame numbers
Challenging factors
Girl Dog Bird Couple David MountainBike Surfer Basketball
500 126 98 139 251 227 200 71
Scale variation, occlusion, deformation, motion blur, out-of-plane rotation Scale variation, deformation, out-of-plane rotation Occlusion, deformation, fast motion, in-plane rotation, out-of-plane rotation Scale variation, deformation, out-of-plane rotation, fast motion, background clutters Occlusion, out-of-plane rotation, deformation, background clutters In-plane rotation, out-of-plane rotation, background clutters Scale variation, fast motion, in-plane rotation, out-of-plane rotation, low resolution Motion blur, fast Motion, background Clutters
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Fig. 7. Tracking accuracy comparisons of different trackers for the examples. (a) Girl (b) Dog (c) Bird (d) Couple (e) David (f) MountainBike (g) Surfer (h) Basketball.
means that the increasing population size enhances the tracking accuracy and meanwhile makes the tracker more time-consuming. However, it can be seen from Fig. 4 that when the population size n 4 20, the lost targets is relatively stable, but the time cost continues to grow. Comprehensive considering the tracking accuracy and speed, the best value of the population size n ¼ 20.
Next, ω and γ are investigated by dividing the range [0.1, 0.9] into equal parts, with each a space 0.1, respectively. During the testing process, the speed which is noted by average generations till convergence is calculated. A contour plot comparing the speed for various values of ω and γ is shown in Fig.5. It can be seen from Fig.5 that when ω and γ
Please cite this article as: M.-L. Gao, et al., A novel visual tracking method using bat algorithm, Neurocomputing (2015), http://dx.doi. org/10.1016/j.neucom.2015.11.072i
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Fig. 8. Tracking results.
are located in the interval of ½ω 4 ¼ 0:8; γ 4 ¼ 0:75, the speed is faster compared with other cases. Therefore, the overall optimal values are set to be ω ¼ 0:8 and γ ¼ 0:8 in this work.
4. Experiments and discussions In order to demonstrate the tracking ability of BA, the proposed method was compared with three representative tracking
Please cite this article as: M.-L. Gao, et al., A novel visual tracking method using bat algorithm, Neurocomputing (2015), http://dx.doi. org/10.1016/j.neucom.2015.11.072i
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methods including particle filter (PF, probabilistic-based method), meanshift (MS, deterministic-based method) and particle swarm intelligence (PSO, optimization-based method). To carry on the comparison, some videos from Ref. [2] are selected and used for evaluation. (note: the tracking examples are available on the website http://visual-tracking.net). A few snapshots from the video clips are shown in Fig. 6. The targets in these examples are suffered from various challenging factors as depicted in Table 1. To make a fair comparison, the same target model (kernel-based spatial color histogram) and motion model (random walk model) were used. For PF, the particle number was set as 500. For BA, we utilized the parameter values found by the sensitivity analysis of Sect. 3. In PSO algorithm, we used the same population size and the same termination conditions as those used in BA. The acceleration constants φ1 and φ2 in PSO were set adaptively according to Ref. [22]. To evaluate the tracking accuracy of the trackers, the videos were manually labeled by identifying the center of the tracked target in each frame visually. Then, the Euclidean distance between the true center and the center estimated by the trackers was calculated and used as accuracy metric and the comparisons results are shown in Fig. 7. In Fig.7(a)–(h), the black, red, green and blue lines represent the tracking accuracy of the BA, MS, PF and PSO for the tracking examples, respectively. It can be seen from Fig. 7(a) to (h) that the BA-based tracker performs well in all the challenging scenarios. It can successfully track the target during the entire tracking process. The PSO-based tracker failed to track the target in the “Girl” and “Basketball” videos. The MS and PF based trackers may perform well in some specific tracking examples, but they fail to track the target in most challenging examples. Examples that illustrate the differences in accuracy are shown in Fig. 8. In order to analyze the time complexity, the average time costs of the four trackers in the tracking process are calculated and the comparative results are shown in Table 2. It can be seen from Table 2 that in some tracking examples (e.g. “Girl”, “Couple”, “Surfer” and “Basketball”), the average time cost of BA is a little more than meanshift, but in other examples it is fewer than meanshift. As mentioned in Section3, the time cost of the two optimization based trackers, namely, BA and PSO are determined by three termination conditions and Table 2 shows that the convergence speed of BA based tracker is faster than PSO based tracker. This is in conformity with the Yang’s statements in Ref. [24]. Generally, the average time cost of BA is smaller than PF based tracker with 500 particles (except for “Couple” example). Theoretically speaking, the BA-based tracker has many advantages. Firstly, BA makes better use of the most recent observational information compared with particle filter. In particle filter, the observational information is only used to evaluate the particles and the location of the particles in the search space is not changed. In contrast, BA is a swarm intelligence algorithm and every single bat in the population exchange information frequently based on the current observational information during the movement. Secondly, compared with meanshift algorithm, BA is more robust to local distractors. Meanshift is a gradient-based optimization algorithm and it is computationally efficient. However, it can easily converge to a local maximum caused by the background distractors, clusters, occlusions, and quick moving objects. By contrast, The agents in BA have two search capabilities namely local search and global search. It can automatically switch from global search to local search by tuning relevant parameters which enables BA explore more efficiently on the global scale, and more robust to local distractors. Thirdly, compared with PSO, the math model of BA is more general and reasonable. As pointed out by Yang in Ref. [24], PSO is just a special case of BA by setting Ai ¼ 0 and ri ¼ 1 in Eq. (5). The fine adjustment of the parameters Ai and ri makes BA a potentially more powerful and promising algorithm than PSO.
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Table 2 Average time cost of the four trackers for the examples. Video
Girl Dog Bird Couple David MoutainBike Surfer Basketball
Time cost (ms) BA
MS
PF
PSO
43.6 5.86 12.4 25.6 16.2 12.1 34.2 10.2
34.5 12.4 22.2 7.6 21.5 17.9 10.3 3.7
85.3 18.84 30.2 14.0 51.5 24.3 23.2 15.4
55.7 7.5 11.7 27.1 18.95 13.8 40.3 15.3
5. Conclusions and future work Visual tracking is one of the most important tasks in computer vision and it is crucial to many vision problems and applications. Although many attentions have been paid on the studies of appearance model, the attention paid on the target search strategy is not so much. In this work, visual tracking is considered to be a process of searching for target by various bats in sequential images and a BAbased tracking architecture is given. The parameters’ sensitivity and adjustment of the BA in tracking system are analyzed. To demonstrate the tracking ability of the proposed tracker, comparative studies of tracking accuracy and speed of the BA-based tracker with three representative trackers, namely, particle filter, meanshift, particle swarm optimization are presented. Comparative results show that the BA-based tracker outperforms the other trackers. To the author's knowledge this is the first time that BA has been adapted for use in a visual tracking system and our initial results showed it to be a potential powerful tracking method. Future work is expected on more efficient feature selection methods and multiple targets tracking in the BA-based tracking system.
Acknowledgments Many thanks to the anonymous reviewers for their valuable comments that helped to improve this paper. Many thanks to Dr. Ming-Hsuan Yang from University of California at Merced for providing the tracking databases in this work. This work is supported by the Promotive Research Fund for Young and Middleaged Scientists of Shandong Province (No. BS2014DX009), Natural Science Foundation of Shandong Province (Nos. ZR2014FL027, ZR2015FL029, ZR2015FL034 and ZR2012FL22), and the National Natural Science Foundation of China (No. 51407112).
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Ming-Liang Gao received his Ph.D. in communication and information systems from Sichuan University, Chengdu, China, in 2013. His main research interests include meta-heuristic optimization, analysis of motion, and visual tracking.
Jin Shen received his Ph.D. in optical engineering from University of Shanghai for Science and Technology, Shanghai, China, in 2003. Currently, he is a professor in the School of Electrical and Electronic Engineering, Shandong University of Technology, Zibo, China. His main research interests include weak signal detection and dynamic light scattering nanoparticles measurement technology.
Li-Ju Yin received her Ph.D. in electronic science and technology from Nanjing University of Science and Technology, Nanjing, China, in 2012. Her main research interests include photo-electronic imaging and image processing..
Wei Liu received his Ph.D. in theory of electrical engineering and new technology from the Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing, China, in 2006. His research interests include measurement control and instrumentation manufacture.
Guo-Feng Zou received his Ph.D. in pattern recognition and intelligent system from the Harbin Engineering University, Harbin, China, in 2013. His main research interests include visual tracking, face recognition, and abnormal activity recognition.
Hai-Tao Li received his Ph.D. in theory of electrical engineering and new technology from the Southwest Jiaotong University, Chengdu, China, in 2012. His research interests include pulsed power technology and its applications.
Gui-Xia Fu received her Ph.D. in pattern recognition and intelligent system from the Harbin Engineering University, Harbin, China, in 2014. Her main research interests include object tracking and robot navigation.
Please cite this article as: M.-L. Gao, et al., A novel visual tracking method using bat algorithm, Neurocomputing (2015), http://dx.doi. org/10.1016/j.neucom.2015.11.072i
