cvpr cvpr2013 cvpr2013-267 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Dong Wang, Huchuan Lu, Ming-Hsuan Yang
Abstract: In this paper, we propose a generative tracking method based on a novel robust linear regression algorithm. In contrast to existing methods, the proposed Least Soft-thresold Squares (LSS) algorithm models the error term with the Gaussian-Laplacian distribution, which can be solved efficiently. Based on maximum joint likelihood of parameters, we derive a LSS distance to measure the difference between an observation sample and the dictionary. Compared with the distance derived from ordinary least squares methods, the proposed metric is more effective in dealing with outliers. In addition, we present an update scheme to capture the appearance change of the tracked target and ensure that the model is properly updated. Experimental results on several challenging image sequences demonstrate that the proposed tracker achieves more favorable performance than the state-of-the-art methods.
Reference: text
sentIndex sentText sentNum sentScore
1 edu Abstract In this paper, we propose a generative tracking method based on a novel robust linear regression algorithm. [sent-6, score-0.366]
2 Based on maximum joint likelihood of parameters, we derive a LSS distance to measure the difference between an observation sample and the dictionary. [sent-8, score-0.222]
3 Compared with the distance derived from ordinary least squares methods, the proposed metric is more effective in dealing with outliers. [sent-9, score-0.506]
4 In addition, we present an update scheme to capture the appearance change of the tracked target and ensure that the model is properly updated. [sent-10, score-0.248]
5 Experimental results on several challenging image sequences demonstrate that the proposed tracker achieves more favorable performance than the state-of-the-art methods. [sent-11, score-0.192]
6 Introduction Visual tracking plays a critical role in computer vision that finds many practical applications (e. [sent-13, score-0.178]
7 Although significant progress has been made in the past decades, developing a robust tracking algorithm is still a challenging problem due to numerous factors such as partial occlusion, illumination variation, pose change, complex motion, and background clutter. [sent-16, score-0.343]
8 Generative methods focus on searching for the regions which are the most similar to the tracked targets, while discriminative methods cast tracking as a classification problem that distinguishes the tracked targets from the surrounding backgrounds. [sent-22, score-0.412]
9 In this work, we propose a robust generative tracker which is able to handle partial occlusion and other challenging factors effectively. [sent-23, score-0.426]
10 , a set of basis vectors from a subspace or a series of templates) to describe the tracked target. [sent-27, score-0.221]
11 A given candidate sample is linearly represented by the dictionary, and the representation coefficient and reconstruction error are computed, from which the corresponding likelihood (belonging to the object class) is determined. [sent-28, score-0.197]
12 [20] propose an incremental visual tracking (IVT) method which represents the tracked target by a low dimensional PCA subspace (a set of PCA basis vectors) and assumes that the error is Gaussian distributed with small variances (i. [sent-30, score-0.537]
13 Therefore, the representation coefficient can be obtained by a simple projection operator, which is equivalent to the ordinary least squares solution under the assumption that the dictionary atoms are orthogonal. [sent-33, score-0.528]
14 The reconstruction error is computed by the objective function of the ordinary least squares methods. [sent-34, score-0.43]
15 While the IVT method is effective to handle appearance change caused by illumination variation and pose variation, it is not robust to some challenging factors (e. [sent-35, score-0.169]
16 , partial occlusion and background clutter) due to the following two reasons. [sent-37, score-0.139]
17 First, ordinary least squares methods have been shown to be sensitive to outliers due to the formulation based on reconstruction error with Gaussian noise assumption. [sent-38, score-0.629]
18 Second, the IVT method uses new observations to update the observation model without detecting outliers and processing them accordingly. [sent-39, score-0.243]
19 Other recent tracking algorithms [16, 12] based on the Gaussian noise assumption or the ordinary least squares methods have similar problems as the IVT method. [sent-40, score-0.66]
20 1 tracker that uses a series of target templates and trivial templates to model the tracked target, where the target templates are used to describe the object class to be tracked and trivial templates are used to deal with outliers (e. [sent-43, score-0.987]
21 For tracking, a candidate sample can be sparsely represented by both tar- get and trivial templates, and its corresponding likelihood is determined by the reconstruction error with respect to target templates. [sent-46, score-0.26]
22 1 tracker in terms of both speed and accuracy by using accelerated proximal gradient algorithm [5], replacing raw pixel templates with orthogonal basis vectors [24, 26, 25], modeling the similarity between different candidates [31], to name a few. [sent-49, score-0.345]
23 Although these algorithms consider outliers by using additional trivial templates, this formulation can be generalized with better understanding. [sent-50, score-0.151]
24 In this work, we show that the linear regression with the Gaussian-Laplacian noise assumption is more effective in dealing with outliers for object tracking. [sent-51, score-0.348]
25 In addition, from the viewpoint of linear regression, it is not suitable to estimate the likelihood based on the reconstruction error with respect to target templates. [sent-52, score-0.167]
26 We present a novel distance function to compute the distance between a candidate and the object class. [sent-53, score-0.146]
27 In this paper, we present a generative tracking algorithm based on linear regression. [sent-54, score-0.243]
28 First, we introduce a novel linear regression method, Least Soft-thresold Squares (LSS), which assumes that the error vectors follow the i. [sent-56, score-0.148]
29 Second, we present an efficient iter- ation method to solve the LSS problem and propose a LSS distance to measure the dissimilarity between the observation vector and the dictionary. [sent-59, score-0.134]
30 We note that the LSS method is related to the robust regression with the Huber loss function and is effective in detecting outliers. [sent-60, score-0.157]
31 Compared with the least squares distance, the LSS distance is more effective in measuring the distance between the observation vector and the dictionary when outliers occur. [sent-61, score-0.671]
32 Third, we design a generative tracker by using the LSS method, where the dictionary consists of PCA basis vectors. [sent-62, score-0.324]
33 The observation likelihood of each candidate is computed based on the LSS distance. [sent-63, score-0.202]
34 Furthermore, we update the tracker by using an effective update scheme. [sent-64, score-0.271]
35 Numerous experiments on challenging image sequences with comparisons to state-ofthe-art tracking methods demonstrate the effectiveness of the proposed model and algorithm. [sent-65, score-0.219]
36 The coefficient x can be obtained by maximizing the posteriori probability p (x|y), which is also equivalent to maximizing the joint likelihood probability p (x, y). [sent-82, score-0.165]
37 Thus, the likelihood of the estimator (the joint probability of the error term e) is p (e) = fθ (ei). [sent-92, score-0.123]
38 1), the MLE solution is equivalent to the ordinary le? [sent-102, score-0.135]
39 If the error e follows the Laplacian distribution (ei ∈ L (0, σL)2), the MLE solution is equivalent to least absolute deviations (LAD) solution, x? [sent-120, score-0.145]
40 However, it is difficult to be solved by using either the simplex-based methods [6] or the iteratively reweighted least squares methods [22]. [sent-126, score-0.321]
41 y = Ax + n + s, (4) where the Gaussian component models small dense noise and the Laplacian one aims to handle outliers 3. [sent-136, score-0.199]
42 , decomposing the noise into sparse and non-sparse ones [3, 8] for achieving robust motion estimation) have appeared in computer vision community. [sent-146, score-0.197]
43 In this work, the proposed algorithm focuses on not only handling occlusion but also deriving a novel distance metric to compare the target candidate and the target template under the outlier condition, which will be presented later. [sent-148, score-0.376]
44 Because of this, we treat the Laplacian noise term s as missing values with the same Laplacian prior, and therefore we can maximize the joint likelihood p (y, x, s) instead. [sent-173, score-0.204]
45 Least Soft-thresold Squares Regression To maximize the joint likelihood of Eq. [sent-197, score-0.117]
46 sa]sed = oarng tmhei standard least squares criterion and an ? [sent-206, score-0.289]
47 As our algorithm consists of two main components: ordinary least squares and soft-thresholding operation, we denote it as the Least Soft-threshold Squares Regression method. [sent-240, score-0.395]
48 Remark 1: The proposed least soft-threshold squares regression is equivalent to robust regression with the Huber loss function: x = argmxin? [sent-254, score-0.525]
49 We note the approach to compute robust regression with the Huber loss function is less efficient than the proposed method as the former is generally solved by using the iteratively reweighted least squares scheme which requires solving a weighted least squares problem (i. [sent-261, score-0.733]
50 Robust line fitting by using the least soft-threshold squares (LSS) regression. [sent-268, score-0.289]
51 Figure 1 shows an example of fitting a straight line when small Gaussian noise and outliers occur simultaneously. [sent-269, score-0.199]
52 ; z10], A = [z, 1] and x = [a; b], we use the proposed least soft-threshold squares (LSS) method to estimate the parameter x. [sent-281, score-0.289]
53 The matrix A is known as dictionary or basis matrix, and the vector ai is called an atom or basis vector. [sent-295, score-0.16]
54 For some vision applications (such as tracking), it requires not only to estimate the coefficient accurately but also to define a distance between a noisy observation and the dictionary or the subspace. [sent-296, score-0.238]
55 The distance is usually defined to be inversely proportional to the maximum joint likelihood with respect to the coefficient x, d∝(y −;lAog)mxaxp(y,x) (10) = −logmxaxp(y|x)p(x). [sent-298, score-0.182]
56 Take the ordinary least squares method for example (i. [sent-299, score-0.395]
57 Figure 2 illustrates a toy example of good and bad candidates for template matching with partial occlusion. [sent-337, score-0.21]
58 In Table 2, we report the OLS distance and the LSS distance between the template and different candidates. [sent-340, score-0.147]
59 ) template as t, the good candidate as yG and the bad candidate as yB respectively. [sent-348, score-0.218]
60 In this example, dOLS (yB ; t) is smaller than dOLS (yG; t), which means the bad candidate is picked if the OLS distance is used. [sent-349, score-0.155]
61 On the other hand, the good candidate is selected (dLSS (yG; t) < dLSS (yB ; t)) when the proposed LSS distance is used. [sent-350, score-0.1]
62 Thus, we note that the proposed LSS distance is better than the OLS distance for handling outliers (e. [sent-351, score-0.204]
63 A toy example of good and bad candidates for template matching. [sent-373, score-0.148]
64 Least Soft-thresold Squares Tracking In this paper, visual tracking is treated as a dynamic Bayesian inference task with a hidden Markov model. [sent-375, score-0.178]
65 , yt} up to the t-th frame, the aim is to estimate the target state variable xt by using the maximum a posteriori estimation, x? [sent-379, score-0.209]
66 p(xt|xt−1)p(xt−1|y1:t−1)xt−1, (16) where p (xt |xt−1) is the motion model that describes the state transition between consecutive frames, and p (yt |xt) is the observation model that estimates the likelihood of an observed image patch belonging to the object class. [sent-384, score-0.183]
67 Observation Model: In this paper, we assume that the tracked target object is generated by a PCA subspace (spanned by U and centered at μ) with i. [sent-388, score-0.212]
68 d GaussianLaplacian noise, y = μ + Uz + n + s, (17) where y denotes an observation vector, U represents a matrix of column basis vectors, z indicates the coefficients of basis vectors, n is the Gaussian noise component and s is the Laplacian noise component. [sent-390, score-0.366]
69 d Gaussian-Laplacian noise assumption, the distance between the vector y and the subspace (U, μ) is the least softthreshold squares distance, d(y;U,μ) = mz,isn21 ? [sent-393, score-0.461]
70 Thus, for each observation yi corresponding to a predicted state xi, we firstly solve the following optimization problem, ? [sent-398, score-0.134]
71 Then we reconstruct the observation vector 222333777533 by replacing the outliers with its corresponding parts of the mean vector μ, yri=? [sent-476, score-0.2]
72 , PCA basis vectors U and the mean vector μ) by using an incremental principal component analysis (PCA) method [20]. [sent-495, score-0.141]
73 Experiments The proposed tracker is implemented in MATLAB and runs at 4 frames per second on a PC with Intel i7-3770 CPU (3. [sent-497, score-0.151]
74 For each sequence, × the location of the tracked target is manually labeled in the first frame. [sent-501, score-0.173]
75 As a trade-off between effectiveness and speed, 600 particles are adopted and our tracker is incrementally updated every 5 frames. [sent-503, score-0.151]
76 The challenging factors of these sequences include partial occlusion, illumination variation, pose change, background clutter and motion blur. [sent-517, score-0.202]
77 We evaluate the proposed tracker against eleven state-of-the-art algorithms, including the FragT [1], IVT [20], MIL [4], VTD [15], TLD [14], APGL1 [5], MTT [3 1], LSAT [17], SCM [32], ASLSA [13] and OSPT [26] trackers. [sent-518, score-0.151]
78 Given the tracking result (bounding box) of each frame RT and the corresponding ground truth bounding box RG, the overlap score is defined as score = Table 4 reports the average overlap rates, where larger average scores mean more accurate results. [sent-525, score-0.178]
79 Qualitative Evaluation Severe Occlusion: We test several sequences (Occlusion1, Occlusion2, Caviar1, Caviar2, Caviar3, DavidOutdoor) with heavy or long-time partial occlusion, scale change and rotation. [sent-529, score-0.135]
80 This can be attributed to two reasons: (1) the proposed LSS distance takes outliers (e. [sent-531, score-0.158]
81 , occlusion) into account explicitly; and (2) the update scheme is able to avoid degrading the observation model by removing the outliers from new observed samples. [sent-533, score-0.243]
82 The IVT method is sensitive to partial occlusion (Occlusion2, Caviar1, Caviar3, DavidOutdoor) since the OLS distance is not effective to handle outliers. [sent-535, score-0.219]
83 Illumination Change: Figure 3 (d) shows the tracking results in the sequences (DavidIndoor, Car4, Singer1) with significant illumination variation, scale change and pose change. [sent-538, score-0.283]
84 Due to the use of incremental PCA algorithm, the proposed tracker achieves good performance in dealing with the appearance change caused by light change. [sent-542, score-0.274]
85 Background Clutter: Figure 3 (e) demonstrates the tracking results in the Car11, Deer and Football sequences with background clutter. [sent-544, score-0.219]
86 These videos also pose other challenging factors including illumination variation (Car11), fast motion (Deer) and partial occlusion (Football). [sent-545, score-0.238]
87 As the proposed LSS distance encourages good matching results when outliers occur, our tracker performs better than other methods in these videos (e. [sent-546, score-0.309]
88 Fast Motion: Figure 3 (f) illustrates the tracking results on the Jumping, Owl and Face sequences. [sent-549, score-0.178]
89 It is difficult to predict the locations of the tracked objects when they undergo abrupt motion. [sent-550, score-0.131]
90 Furthermore, the appearance change caused by motion blur poses great challenges for capturing the tracked targets accurately and updating the observation models properly. [sent-551, score-0.288]
91 Conclusion In this paper, we propose a Least Soft-thresold Squares (LSS) regression method that assumes the noise is Gaussian-Laplacian distributed, and apply it to object tracking. [sent-563, score-0.171]
92 We derive a LSS distance to measure the difference between an observation sample and the dictionary. [sent-565, score-0.134]
93 The LSS distance is effective in handling outliers and therefore provides an accurate match, which facilitates object tracking (e. [sent-566, score-0.37]
94 In addition, we develop a robust generative tracker based on the proposed LSS method and a simple update scheme. [sent-569, score-0.298]
95 Both quantitative and qualitative evaluations on challenging image sequences show that the proposed tracker performs favorably against several state-of-the-art algorithms. [sent-570, score-0.192]
96 Visual tracking via adaptive structural local sparse appearance model. [sent-669, score-0.178]
97 222333777755 (a) Tracking results on sequence Oc lusion1 and Oc lusion2 with heavy oc lusion and in-plane rotation. [sent-677, score-0.102]
98 (b) Tracking results on sequence Caviar1 and Caviar2 with partial oc lusion and scale change. [sent-678, score-0.164]
99 Robust tracking using local sparse appearance model and k-selection. [sent-733, score-0.178]
100 The estimation of laplace random vectors in additive white gaussian noise. [sent-774, score-0.097]
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