# Online Visual Tracking of Weighted Multiple Instance Learning via Neutrosophic Similarity-Based Objectness Estimation

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Problem Formulation

#### 3.1. System Overview

**H**

_{k}. For each frame, we chose the updated

**H**

_{k}as the new classifier for tracking. For a new arriving frame, the above procedures were repeated.

#### 3.2. Objectness Measure

_{w}can be calculated by:

**S**(

**T**

_{i}) is the superpixel set obtained by the literature [21], with the segmentation parameter tuple

**T**

_{i}. For each superpixel s, $\left|s\backslash {O}_{W}\right|$ computes its area outside O

_{w}and $\left|s\cap {O}_{W}\right|$ calculates its area inside O

_{w}. From Equation (1), we can get determine that a superpixel contributes less when it straddles the window O

_{w}. The superpixels inside the window O

_{w}contribute the most. $ss({O}_{W},{T}_{i})$ achieves to 1 when there is not any superpixel straddling the window O

_{w}.

**T**

_{i}is also an important parameter.

**T**

_{i}is a set of parameters that can affect the segmentation result greatly. Different segmentation algorithms always relate to different parameters. For the efficient graph-based image segmentation algorithm [21] employed in this work, each tuple ${T}_{i}=\left\{\sigma ,k,m\right\}$ contained three parameters including $\sigma $ (used to smooth the input image before segmenting it), k (value for the threshold function), and m (minimum component size enforced by post-processing). As shown in Figure 2, when we use the same segmentation algorithm [21] but employ different segmentation parameter tuples, the segmentation results are quite different. In addition, with the three different segmentation results, the corresponding superpixel sets are also quite different from each other. From Equation (1), we can find that the calculation of SS-based objectness highly depends on the shape and distribution of the superpixels in the image. To apply the objectness measure for weighting the training samples, we then proposed a neutrosophic set-based scheme to handle such a problem.

#### 3.3. Neutrosophic Set-Based Segmentation Parameter Selection

_{i}can be represented as:

_{Cj}(A

_{i}) denotes the degree to which the alternative A

_{i}satisfies the criterion C

_{j}, I

_{Cj}(A

_{i}) indicates the indeterminacy degree to which the alternative A

_{i}satisfies or does not satisfy the criterion C

_{j}, F

_{Cj}(A

_{i}) indicates the degree to which the alternative A

_{i}does not satisfy the criterion C

_{j}, ${T}_{Cj}({A}_{i})\in \left[0,1\right]$, ${I}_{Cj}({A}_{i})\in \left[0,1\right]$, ${F}_{Cj}({A}_{i})\in \left[0,1\right]$.

_{j}. The cosine similarity score between A

_{i}and A* is defined by [35]:

_{j}is the weight for each criterion, and ${w}_{j}\in \left[0,1\right]$, ${\sum}_{j}{w}_{j}}=1$. Both the cosine and tangent measures have been successfully employed for medical diagnoses [24] and some visual analysis missions [7,26]. In this work, the neutrosophic similarity score was utilized for fusing information, and these two measures were tested separately in the experimental section.

**T**

_{k}, the corresponding membership functions T

_{O}(

**T**

_{k}) (truth), I

_{O}(

**T**

_{k}) (indeterminacy), and F

_{O}(

**T**

_{k}) (falsity) were defined as:

_{l*}is the rectangular window corresponding to the object location and

**T**

_{i}is the the i-th segmentation parameter tuple. As shown in Figure 3, ${O}_{j}(r)$ is a square window centered at the j-th pixel of the C uniform sampled pixels on the boundary of the square window with the edge length of 2r+1(pixel) centered at l

^{*}, the distribution of ${O}_{j}(r)$ is symmetric, l

^{*}is the center of the object location, and ${O}_{j}(r)$ has the same size as the objects.

**T**

_{i}and the ideal choice:

**T**

_{sel}. For the cosine and tangent measures, the selections may be different from each other.

#### 3.4. Neutrosophic Set-Based Superpixel Filter

_{l}is the rectangular window, which corresponds to the object location calculated by the afore-trained classifier before the modification, suppose

**S**(

**T**

_{sel}) is the superpixel set obtained by the literature [21] with the selected segmentation tuple

**T**

_{sel}, and s

_{i}is the i-th superpixel included in

**S**(

**T**

_{sel}).

_{si}and h

_{si}are the width and height, respectively, of the tight rectangular bounding box of the super pixel s

_{i}, w

_{ol}and h

_{ol}are the width and height corresponding to the object window O

_{l},

**x**

_{si}is the centroid location of s

_{i}, l is the center of the O

_{l}, and D is half the length of the O

_{l}diagonal. The function f(x) in T

_{sd}(i) is defined as:

_{sd}(i) when the width or the height of s

_{i}is larger or smaller than the w

_{ol}or h

_{ol}. As seen in Figure 4, when x > 1, the response of f(x) decreases slowly in the intervals of [1,1.2] and [1.6,1.8], but decreases sharply during the interval of [1.2,1.6]. The reason for such a design is that we wanted to keep the information of those superpixels with a relative similar size to the object, and try to discard the superpixels with a much larger width or height than the object. As shown in Figure 4, the response has decreased at the value of less than 0.1 when x equals 1.6. However, we choose a different solution when x < 1. The response of f(x) decreases much slower than in the interval of x > 1, because a small superpixel may be one of the real parts of the object. We tried to keep the information of such superpixels.

_{i}and the ideal superpixel:

**H**

_{i}is the filter response for the superpixel s

_{i}, γ is a threshold parameter, and ls(i) is the cosine or tangent similarity score calculated by Equation (17) or Equation (18).

**S**(

**T**

_{sel}) is the superpixel set obtained by using the selected segmentation parameter tuple

**T**

_{sel}and O

_{W}is a rectangular window with the same size as the object.

#### 3.5. Object Localization

**H**

_{k}. All the windows whose center is located within the circle area for searching are employed as candidates, suppose sr denotes the searching radius. The scale of each window is the same as the tracked object. The

**H**

_{k}response of each candidate window finally forms the classification map.

**H**

_{k}. We calculated the Neut-Objectness confidence map by using the similar manner of the calculation of the classification confidence map, but the response of the filtered objectness measure is employed instead of the

**H**

_{k}response. Let l

_{nss}denote the center location of the candidate window with a maximum value within the Neut-Objectness confidence map, and the corresponding response is nss(O

_{w}(l

_{nss}),

**T**

_{sel}). The fused object location is calculated by

**H**

_{k}(l

_{nss}) is the response of

**H**

_{k}for the window centered at l

_{nss}, λ is the ratio parameter, and τ

_{1}and τ

_{2}are threshold parameters for λ,τ

_{1},τ

_{2}∈[0,1].

**H**

_{k}response at the corresponding location achieves a relative high value. Such a method can effectively remove the interference, which may be caused by an objectness estimation that is not stable enough.

#### 3.6. Weighted Multiple Instance Learning

**X**

^{+}during the learning process. The weight of the j-th positive instance in

**X**

^{+}is obtained by using the filtered objectness measure:

_{Wj}is the window corresponding to the j-th instance in

**X**

^{+}. Then, the positive bag probability is computed by [15,17]:

_{1j}, and x

_{1j}denotes the j-th instance in the positive bag.

_{ij}to be positive is defined as [13]:

_{1j}denotes the j-th instance in the positive bag, x

_{0j}denotes the j-th instance in the negative bag, and σ is the sigmoid function, $\sigma \left(x\right)=1/1+{e}^{-x}$.

**H**

_{k}in Equation (24) is defined as:

_{ij}) is a set of Haar-like features corresponding to the weak classifier h

_{k}(x

_{ij}), f(x

_{ij}) = (f

_{1}(x),…,f

_{K}(x))

^{T}. We assume the features in f(x

_{ij}) are independent and assume uniform prior p(y = 0) = p(y = 1) as MIL tracker [13]. Then, the h

_{k}(x

_{ij}) is described as [13]:

_{k}(

^{.}) is also defined as a Gaussian function as the MIL tracker, that is:

_{j}is the weight of the j-th positive instance defined in Equation (22), y

_{i}is the label of the training bag, y

_{i}equals to 1 when the bag is positive, and y

_{i}is set as 0 when the bag is negative.

**H**

_{k}. In the WMIL tracker, a more efficient criterion was proposed. Similar rules are employed here. The scheme for selecting K weak classifier is given below [15].

_{j}and w

_{m}are the weights of the corresponding samples, and they are calculated by Equation (22).

Algorithm 1 Online neutrosophic similarity-based objectness tracking with weighted multiple instance learning algorithm (NeutWMIL) |

Initialization: (1) Initialize the region of the tracked object in the first frame. (2) Initialize the MIL-based classifier H_{k} by employing the training bags surrounding the object location.Online tracking: (1) Select suitable segmentation parameter tuple T_{sel} by utilizing the method of neutrosophic set-based segmentation parameter selection.(2) Read a new frame of the video sequence. (3) Calculate the superpixel set for the current frame with the selected tuple T_{sel}.(4) Compute the estimation of the filtered objectness surrounding the location obtained by the afore-trained classifier H_{k}, and get the final object location l^{*} in this frame by Equation (21).(5) Compute the neutrosophic set-based weight by Equation (22). (6) Crop M positive instances within the circular region centering at to form a positive bag, then crop L negative instances from an annular region to form a negative bag. (7) Update the parameters of W weak classifiers by Equation (28). (8) Select K weak classifiers by Equation (30) and form the current classifier H_{k}.(9) Go to step (1) until the end. |

## 4. Experiments

#### 4.1. Parameter Setting

**H**

_{k}maintained K = 15 weak classifiers. Three segmentation parameter tuples were chosen—${T}_{1}=\left\{0.4,450,150\right\}$, ${T}_{2}=\left\{0.5,500,200\right\}$, and ${T}_{3}=\left\{0.6,550,250\right\}$. When we performed the tuple selection algorithm, the parameter r defined in Equation (6) was set to 8, and C was set to 4, which means the four corners of the square window with an edge length of 17 pixels were considered for evaluating the indeterminate estimation. For the neutrosophic set-based superpixel filter, when calculating the similarity score of each superpixel by Equations (17)–(18), we set w

_{cint}= w

_{csd}= w

_{tint}= w

_{tsd}= 0.5, which meant each criterion was treated equally. The threshold parameter $\gamma $ in Equation (19) decided how many superpixels could pass the filter. To fully use the superpixel information and to filter the noisy superpixel in the meantime, a near median value 0.4 was set to $\gamma $. For the object location step, the location estimated by the trained classifier was more robust than the filtered objectness-based result statistically. However, when a relatively high response of the filtered objectness was received, as well as the response of the classifier, the objectness results were usually robust enough, and a more accurate result could be achieved by fusing these two kinds of results. By considering this, for the parameters in Equation (21), we set ${\tau}_{1}=0.3$ and ${\tau}_{2}=0.3$, and then the fusing ratio $\lambda $ is set to 0.3. Finally, all parameters were kept constant for all the experiments.

#### 4.2. Evaluation Criteria

_{i}corresponds to the ground truth. Giving a threshold u, we can say the result is correct if p

_{i}> u. Suppose FNs is the number of the frames, then the success ratio is calculated by:

#### 4.3. Quantitative Analysis

#### 4.4. Qualitative Analysis

#### 4.4.1. MountainBike, Sylvester, Rubik, and Gym

#### 4.4.2. Couple, BlurBody, Basketball, and Doll

#### 4.4.3. David, Tiger1, Biker, Tiger2, and Soccer

#### 4.5. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Yilmaz, A.; Javed, O.; Shah, M. Object tracking: A survey. ACM Comput. Surv.
**2006**, 38, 13. [Google Scholar] [CrossRef] - Yang, H.; Shao, L.; Zheng, F.; Wang, L.; Song, Z. Recent advances and trends in visual tracking: A review. Neurocomputing
**2011**, 74, 3823–3831. [Google Scholar] [CrossRef] - Comaniciu, D.; Ramesh, V.; Meer, P. Kernel-based object tracking. IEEE Trans. Pattern Anal. Mach. Intell.
**2003**, 25, 564–577. [Google Scholar] [CrossRef] - Ross, D.; Lim, J.; Lin, R.-S.; Yang, M.-H. Incremental learning for robust visual tracking. Int. J. Comput. Vis.
**2008**, 77, 125–141. [Google Scholar] [CrossRef] - Leichter, I. Mean shift trackers with cross-bin metrics. IEEE Trans. Pattern Anal. Mach. Intell.
**2011**, 34, 695–706. [Google Scholar] [CrossRef] [PubMed] - Vojir, T.; Noskova, J.; Matas, J. Robust scale-adaptive mean-shift for tracking. Pattern Recogn. Lett.
**2014**, 49, 250–258. [Google Scholar] [CrossRef] - Hu, K.; Ye, J.; Fan, E.; Shen, S.; Huang, L.; Pi, J. A novel object tracking algorithm by fusing color and depth information based on single valued neutrosophic cross-entropy. J. Intell. Fuzzy Syst.
**2017**, 32, 1775–1786. [Google Scholar] [CrossRef] [Green Version] - Hu, K.; Fan, E.; Ye, J.; Fan, C.; Shen, S.; Gu, Y. Neutrosophic similarity score based weighted histogram for robust mean-shift tracking. Information
**2017**, 8, 122. [Google Scholar] [CrossRef] - Hu, K.; Fan, E.; Ye, J.; Pi, J.; Zhao, L.; Shen, S. Element-weighted neutrosophic correlation coefficient and its application in improving camshift tracker in rgbd video. Information
**2018**, 9, 126. [Google Scholar] [CrossRef] - Grabner, H.; Grabner, M.; Bischof, H. Real-Time Tracking Via On-Line Boosting; Chantler, M., Fisher, B., Trucco, M., Eds.; BMVA Press: Graz, Austria, 2006; pp. 6.1–6.10. [Google Scholar]
- Grabner, H.; Leistner, C.; Bischof, H. Semi-Supervised On-Line Boosting for Robust Tracking; European Conference on Computer Vision (ECCV); Forsyth, D., Torr, P., Zisserman, A., Eds.; Springer Berlin Heidelberg: Marseille, France, 2008; pp. 234–247. [Google Scholar]
- Babenko, B.; Ming-Hsuan, Y.; Belongie, S. Visual tracking with online multiple instance learning. In Proceedings of the IEEE Conference on Computer Vision Pattern Recognition (CVPR) 2009, Miami, FL, USA, 20–25 June 2009; pp. 983–990. [Google Scholar]
- Babenko, B.; Ming-Hsuan, Y.; Belongie, S. Robust object tracking with online multiple instance learning. IEEE Trans. Pattern Anal. Mach. Intell.
**2011**, 33, 1619–1632. [Google Scholar] [CrossRef] - Kaihua, Z.; Lei, Z.; Ming-Hsuan, Y. Real-time object tracking via online discriminative feature selection. IEEE Trans. Image Process.
**2013**, 22, 4664–4677. [Google Scholar] - Zhang, K.; Song, H. Real-time visual tracking via online weighted multiple instance learning. Pattern Recogn.
**2013**, 46, 397–411. [Google Scholar] [CrossRef] - Abdechiri, M.; Faez, K.; Amindavar, H. Visual object tracking with online weighted chaotic multiple instance learning. Neurocomputing
**2017**, 247, 16–30. [Google Scholar] [CrossRef] - Yang, H.; Qu, S.; Zhu, F.; Zheng, Z. Robust objectness tracking with weighted multiple instance learning algorithm. Neurocomputing
**2018**, 288, 43–53. [Google Scholar] [CrossRef] - Hu, K.; Zhang, X.; Gu, Y.; Wang, Y. Fusing target information from multiple views for robust visual tracking. IET Comput. Vis.
**2014**, 8, 86–97. [Google Scholar] [CrossRef] - Alexe, B.; Deselaers, T.; Ferrari, V. What is an object? In Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, CA, USA, 13–18 June 2010; pp. 73–80. [Google Scholar]
- Alexe, B.; Deselaers, T.; Ferrari, V. Measuring the objectness of image windows. IEEE Trans. Pattern Anal. Mach. Intell.
**2012**, 34, 2189–2202. [Google Scholar] [CrossRef] [PubMed] - Felzenszwalb, P.F.; Huttenlocher, D.P. Efficient graph-based image segmentation. Int. J. Comput. Vision
**2004**, 59, 167–181. [Google Scholar] [CrossRef] - Smarandache, F. Neutrosophy: Neutrosophic Probability, Set and Logic; American Research Press: Rehoboth, MA, USA, 1998; p. 105. [Google Scholar]
- Peng, X.; Dai, J. A bibliometric analysis of neutrosophic set: Two decades review from 1998 to 2017. Artif. Intell. Rev.
**2018**, 52, 1–57. [Google Scholar] [CrossRef] - Ye, J.; Fu, J. Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function. Comput. Methods Programs Biomed.
**2016**, 123, 142–149. [Google Scholar] [CrossRef] [Green Version] - Guo, Y.; Sengur, A. A novel 3d skeleton algorithm based on neutrosophic cost function. Appl. Soft Comput. J.
**2015**, 36, 210–217. [Google Scholar] [CrossRef] - Guo, Y.; Şengür, A.; Ye, J. A novel image thresholding algorithm based on neutrosophic similarity score. Meas. J. Int. Meas. Confed.
**2014**, 58, 175–186. [Google Scholar] [CrossRef] [Green Version] - Guo, Y.; Şengür, A.; Akbulut, Y.; Shipley, A. An effective color image segmentation approach using neutrosophic adaptive mean shift clustering. Meas. J. Int. Meas. Confed.
**2018**, 119, 28–40. [Google Scholar] [CrossRef] [Green Version] - Guo, Y.; Xia, R.; Şengür, A.; Polat, K. A novel image segmentation approach based on neutrosophic c-means clustering and indeterminacy filtering. Neural Comput. Appl.
**2017**, 28, 3009–3019. [Google Scholar] [CrossRef] - Rashno, A.; Koozekanani, D.D.; Drayna, P.M.; Nazari, B.; Sadri, S.; Rabbani, H.; Parhi, K.K. Fully automated segmentation of fluid/cyst regions in optical coherence tomography images with diabetic macular edema using neutrosophic sets and graph algorithms. IEEE Trans. Biomed. Eng.
**2018**, 65, 989–1001. [Google Scholar] [CrossRef] [PubMed] - Ashour, A.S.; Guo, Y.; Kucukkulahli, E.; Erdogmus, P.; Polat, K. A hybrid dermoscopy images segmentation approach based on neutrosophic clustering and histogram estimation. Appl. Soft Comput.
**2018**, 69, 426–434. [Google Scholar] [CrossRef] [Green Version] - Guo, Y.; Şengür, A. A novel image segmentation algorithm based on neutrosophic similarity clustering. Appl. Soft Comput. J.
**2014**, 25, 391–398. [Google Scholar] [CrossRef] [Green Version] - Fan, E.; Xie, W.; Pei, J.; Hu, K.; Li, X. Neutrosophic hough transform-based track initiation method for multiple target tracking. IEEE Access
**2018**, 6, 16068–16080. [Google Scholar] [CrossRef] - Wang, H.; Smarandache, F.; Zhang, Y.; Sunderraman, R. Single valued neutrosophic sets. Multispace Multistructure
**2010**, 4, 410–413. [Google Scholar] - Ye, J. Single valued neutrosophic cross-entropy for multicriteria decision making problems. Appl. Math. Model.
**2014**, 38, 1170–1175. [Google Scholar] [CrossRef] - Ye, J. Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int. J. Fuzzy Syst.
**2014**, 16, 204–211. [Google Scholar]

**Figure 2.**Segmentation results with different segmentation parameter tuples. ${T}_{1}=\left\{0.4,450,150\right\}$, ${T}_{2}=\left\{0.5,250,400\right\}$, ${T}_{3}=\left\{0.6,550,250\right\}$.

**Figure 6.**Success and center position error plots of tested sequences MountainBike, Sylvester, Rubik, and Gym.

**Figure 7.**Success and center position error plots of tested sequences Couple, BlurBody, Basketball, and Doll.

**Figure 8.**Success and center position error plots of tested sequences David, Tiger1, Biker, Tiger2, and Soccer.

**Figure 9.**Sampled tracking results for tested sequences MountainBike (

**a**), Sylvester (

**b**), Rubik (

**c**), and Gym (

**d**).

**Figure 10.**Sampled tracking results for tested sequences Couple (

**a**), BlurBody (

**b**), Basketball (

**c**), and Doll (

**d**).

**Figure 11.**Sampled tracking results for tested sequences David (

**a**), Tiger1 (

**b**), Biker (

**c**), Tiger2 (

**d**), and Soccer (

**e**).

Sequence | IV | SV | OCC | DEF | MB | FM | IPR | OPR | OV | BC | LR | FNs | NC |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Freeman1 | Y | Y | Y | 326 | 3 | ||||||||

Mountain-Bike | Y | Y | Y | 228 | 3 | ||||||||

Vase | Y | Y | Y | 271 | 3 | ||||||||

Sylvester | Y | Y | Y | 1345 | 3 | ||||||||

Rubik | Y | Y | Y | Y | 1997 | 4 | |||||||

Gym | Y | Y | Y | Y | 767 | 4 | |||||||

Football | Y | Y | Y | Y | 362 | 4 | |||||||

Boy | Y | Y | Y | Y | Y | 602 | 5 | ||||||

Couple | Y | Y | Y | Y | Y | 140 | 5 | ||||||

BlurBody | Y | Y | Y | Y | Y | 334 | 5 | ||||||

Basketball | Y | Y | Y | Y | Y | 725 | 5 | ||||||

Doll | Y | Y | Y | Y | Y | 3872 | 5 | ||||||

FleetFace | Y | Y | Y | Y | Y | Y | 707 | 6 | |||||

Coke | Y | Y | Y | Y | Y | Y | 291 | 6 | |||||

David | Y | Y | Y | Y | Y | Y | Y | 471 | 7 | ||||

ClifBar | Y | Y | Y | Y | Y | Y | Y | 472 | 7 | ||||

Tiger1 | Y | Y | Y | Y | Y | Y | Y | 354 | 7 | ||||

Biker | Y | Y | Y | Y | Y | Y | Y | 142 | 7 | ||||

Tiger2 | Y | Y | Y | Y | Y | Y | Y | Y | 365 | 8 | |||

Soccer | Y | Y | Y | Y | Y | Y | Y | Y | 392 | 8 |

**Table 2.**The average center location errors (in pixels) for the compared trackers (bold red fonts indicate the best performance, while the italic blue fonts indicate the second best ones).

Sequence | Neut-WMIL | Neutan-WMIL | ON-WMIL | WMIL | MIL | OAB | SemiB |
---|---|---|---|---|---|---|---|

Freeman1 | 14.30 | 16.70 | 17.80 | 15.64 | 17.06 | 66.12 | 54.69 |

MountainBike | 7.89 | 15.02 | 29.80 | 120.05 | 8.07 | 12.96 | 44.39 |

Vase | 21.97 | 21.53 | 22.62 | 21.08 | 15.04 | 34.58 | 32.05 |

Sylvester | 7.75 | 8.79 | 8.96 | 18.37 | 17.49 | 12.18 | 22.75 |

Rubik | 14.49 | 41.30 | 80.97 | 84.44 | 22.56 | 33.74 | 53.82 |

Gym | 11.47 | 29.60 | 62.04 | 123.95 | 20.71 | 15.24 | 23.60 |

Football | 12.86 | 12.54 | 16.79 | 14.38 | 11.66 | 171.91 | 96.91 |

Boy | 7.54 | 7.38 | 19.63 | 7.88 | 108.24 | 3.43 | 56.03 |

Couple | 9.70 | 7.88 | 35.68 | 35.92 | 34.80 | 33.86 | 102.71 |

BlurBody | 33.91 | 36.44 | 35.07 | 85.45 | 81.99 | 59.44 | 108.71 |

Basketball | 10.76 | 10.22 | 17.69 | 25.65 | 107.05 | 145.94 | 158.50 |

Doll | 28.18 | 82.91 | 47.29 | 74.80 | 70.37 | 127.33 | 52.73 |

FleetFace | 29.66 | 50.11 | 69.94 | 109.24 | 50.68 | 44.27 | 69.49 |

Coke | 23.54 | 32.47 | 43.24 | 46.60 | 113.62 | 17.64 | 50.93 |

David | 18.97 | 38.47 | 46.67 | 20.22 | 24.34 | 71.55 | 55.41 |

ClifBar | 17.85 | 9.65 | 10.50 | 20.08 | 23.47 | 32.87 | 74.98 |

Tiger1 | 14.52 | 13.94 | 25.10 | 73.96 | 84.24 | 42.01 | 60.78 |

Biker | 10.30 | 11.51 | 36.35 | 20.15 | 27.54 | 92.87 | 93.26 |

Tiger2 | 17.28 | 19.19 | 50.53 | 40.29 | 21.93 | 58.31 | 68.10 |

Soccer | 28.35 | 88.16 | 57.80 | 101.44 | 51.88 | 99.71 | 92.07 |

average | 17.06 | 27.69 | 36.72 | 52.98 | 45.64 | 58.80 | 68.59 |

**Table 3.**The average overlap ratio for the compared trackers (bold red fonts indicate the best performance, while the italic blue fonts indicate the second best ones).

Sequence | Neut-WMIL | Neutan-WMIL | ON-WMIL | WMIL | MIL | OAB | SemiB |
---|---|---|---|---|---|---|---|

Freeman1 | 0.299 | 0.281 | 0.243 | 0.281 | 0.260 | 0.201 | 0.170 |

MountainBike | 0.705 | 0.607 | 0.554 | 0.380 | 0.701 | 0.621 | 0.258 |

Vase | 0.314 | 0.312 | 0.308 | 0.307 | 0.312 | 0.275 | 0.236 |

Sylvester | 0.696 | 0.675 | 0.657 | 0.547 | 0.514 | 0.612 | 0.478 |

Rubik | 0.553 | 0.457 | 0.191 | 0.236 | 0.490 | 0.385 | 0.288 |

Gym | 0.474 | 0.366 | 0.172 | 0.074 | 0.399 | 0.438 | 0.269 |

Football | 0.574 | 0.583 | 0.412 | 0.508 | 0.604 | 0.237 | 0.149 |

Boy | 0.662 | 0.670 | 0.375 | 0.591 | 0.296 | 0.780 | 0.272 |

Couple | 0.594 | 0.617 | 0.462 | 0.456 | 0.486 | 0.279 | 0.078 |

BlurBody | 0.525 | 0.496 | 0.506 | 0.298 | 0.281 | 0.375 | 0.193 |

Basketball | 0.655 | 0.667 | 0.502 | 0.529 | 0.213 | 0.037 | 0.048 |

Doll | 0.356 | 0.164 | 0.275 | 0.141 | 0.231 | 0.051 | 0.270 |

FleetFace | 0.568 | 0.552 | 0.459 | 0.305 | 0.579 | 0.560 | 0.415 |

Coke | 0.521 | 0.448 | 0.277 | 0.234 | 0.047 | 0.551 | 0.176 |

David | 0.407 | 0.309 | 0.234 | 0.395 | 0.346 | 0.212 | 0.238 |

ClifBar | 0.426 | 0.508 | 0.467 | 0.403 | 0.373 | 0.264 | 0.224 |

Tiger1 | 0.657 | 0.671 | 0.517 | 0.128 | 0.168 | 0.526 | 0.303 |

Biker | 0.437 | 0.445 | 0.246 | 0.246 | 0.259 | 0.241 | 0.244 |

Tiger2 | 0.610 | 0.571 | 0.309 | 0.292 | 0.505 | 0.250 | 0.202 |

Soccer | 0.321 | 0.101 | 0.204 | 0.145 | 0.221 | 0.103 | 0.101 |

average | 0.52 | 0.47 | 0.37 | 0.32 | 0.36 | 0.35 | 0.23 |

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**MDPI and ACS Style**

Hu, K.; He, W.; Ye, J.; Zhao, L.; Peng, H.; Pi, J.
Online Visual Tracking of Weighted Multiple Instance Learning via Neutrosophic Similarity-Based Objectness Estimation. *Symmetry* **2019**, *11*, 832.
https://doi.org/10.3390/sym11060832

**AMA Style**

Hu K, He W, Ye J, Zhao L, Peng H, Pi J.
Online Visual Tracking of Weighted Multiple Instance Learning via Neutrosophic Similarity-Based Objectness Estimation. *Symmetry*. 2019; 11(6):832.
https://doi.org/10.3390/sym11060832

**Chicago/Turabian Style**

Hu, Keli, Wei He, Jun Ye, Liping Zhao, Hua Peng, and Jiatian Pi.
2019. "Online Visual Tracking of Weighted Multiple Instance Learning via Neutrosophic Similarity-Based Objectness Estimation" *Symmetry* 11, no. 6: 832.
https://doi.org/10.3390/sym11060832