iccv iccv2013 iccv2013-119 knowledge-graph by maker-knowledge-mining

119 iccv-2013-Discriminant Tracking Using Tensor Representation with Semi-supervised Improvement


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Author: Jin Gao, Junliang Xing, Weiming Hu, Steve Maybank

Abstract: Visual tracking has witnessed growing methods in object representation, which is crucial to robust tracking. The dominant mechanism in object representation is using image features encoded in a vector as observations to perform tracking, without considering that an image is intrinsically a matrix, or a 2nd-order tensor. Thus approaches following this mechanism inevitably lose a lot of useful information, and therefore cannot fully exploit the spatial correlations within the 2D image ensembles. In this paper, we address an image as a 2nd-order tensor in its original form, and find a discriminative linear embedding space approximation to the original nonlinear submanifold embedded in the tensor space based on the graph embedding framework. We specially design two graphs for characterizing the intrinsic local geometrical structure of the tensor space, so as to retain more discriminant information when reducing the dimension along certain tensor dimensions. However, spatial correlations within a tensor are not limited to the elements along these dimensions. This means that some part of the discriminant information may not be encoded in the embedding space. We introduce a novel technique called semi-supervised improvement to iteratively adjust the embedding space to compensate for the loss of discriminant information, hence improving the performance of our tracker. Experimental results on challenging videos demonstrate the effectiveness and robustness of the proposed tracker.

Reference: text


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 i a Abstract Visual tracking has witnessed growing methods in object representation, which is crucial to robust tracking. [sent-2, score-0.188]

2 The dominant mechanism in object representation is using image features encoded in a vector as observations to perform tracking, without considering that an image is intrinsically a matrix, or a 2nd-order tensor. [sent-3, score-0.195]

3 Thus approaches following this mechanism inevitably lose a lot of useful information, and therefore cannot fully exploit the spatial correlations within the 2D image ensembles. [sent-4, score-0.184]

4 In this paper, we address an image as a 2nd-order tensor in its original form, and find a discriminative linear embedding space approximation to the original nonlinear submanifold embedded in the tensor space based on the graph embedding framework. [sent-5, score-2.269]

5 We specially design two graphs for characterizing the intrinsic local geometrical structure of the tensor space, so as to retain more discriminant information when reducing the dimension along certain tensor dimensions. [sent-6, score-2.128]

6 However, spatial correlations within a tensor are not limited to the elements along these dimensions. [sent-7, score-0.944]

7 This means that some part of the discriminant information may not be encoded in the embedding space. [sent-8, score-0.485]

8 We introduce a novel technique called semi-supervised improvement to iteratively adjust the embedding space to compensate for the loss of discriminant information, hence improving the performance of our tracker. [sent-9, score-0.604]

9 Introduction Robust visual tracking is an essential component of many practical computer vision applications such as surveillance, vehicle navigation, and human computer interface. [sent-12, score-0.129]

10 Despite much effort resulting in many novel trackers, tracking generic objects remains a challenging problem . [sent-13, score-0.129]

11 partial occlusions, illumination changes, cluttered and moving backgrounds) appearance variations (see a more detailed discussion in [3 1]). [sent-22, score-0.038]

12 Many tracking systems construct an adaptive appearance model based on the collected image patches in previous frames. [sent-23, score-0.167]

13 This model is used to find the most likely image patch in the current frame. [sent-24, score-0.052]

14 There are many object representation methods proposed for visual tracking. [sent-26, score-0.044]

15 Some tracking approaches [21, 35] adopt holistic gray-scale image-asvector representation. [sent-27, score-0.129]

16 1 minimization based visual tracking approaches [17, 18, 3, 34, 33], which exploit the sparse representation of the image patch. [sent-29, score-0.173]

17 [8, 9] construct multiple basic appearance models by sparse principal component analysis (SPCA) of a set of feature templates (e. [sent-31, score-0.038]

18 These representation methods ignore that an image is intrinsically a matrix, or a 2nd-order tensor. [sent-34, score-0.152]

19 In [2, 10] only Haar-like features used, but great improvements are achieved by novel appearance models. [sent-37, score-0.038]

20 [12, 15] only use HOGs but apply novel appearance models to achieve good results. [sent-39, score-0.038]

21 [1] robustly combine multiple patch votes with each image patch represented by only gray-scale histogram features. [sent-41, score-0.104]

22 These representation methods have their own advantages for their specifically designed appearance models. [sent-42, score-0.082]

23 However, a lot ofuseful information is missed when extracting features. [sent-43, score-0.075]

24 image-as-matrix representation) can retain much more useful information because the original image data structure is preserved. [sent-46, score-0.046]

25 [29, 7, 27]) on tensor11556699 based subspace learning, particularly for face recognition. [sent-49, score-0.051]

26 Also, many previous visual tracking approaches use the tensor concept. [sent-50, score-0.917]

27 [13, 25, 24]) conduct PCA in the mode-k flattened matrix; others (e. [sent-53, score-0.077]

28 [26, 11]) adopt covariance tracking technique [19] in the mode-k flattened ma- trix. [sent-55, score-0.241]

29 Additionally, the dimension reduction based subspace learning methods used in [13, 25, 24] ignore a very important problem proposed in [27]. [sent-57, score-0.186]

30 The problem is that correlations within a tensor are not limited to the elements along certain tensor dimensions. [sent-58, score-1.732]

31 Some part of the discriminant information may not be encoded in the first few dimensions of the derived subspace. [sent-59, score-0.247]

32 This may lead to subspace learning degradations and result in tracking distractions. [sent-60, score-0.215]

33 [27] propose to rearrange elements in the tensor to solve the subspace learning degradation problem, the exhaustive element rearranging makes it unsuitable for real-time tracking. [sent-64, score-1.011]

34 Inspired by these findings, we propose a new discriminant tracking approach which adopts a 2nd-order tensor (image-as-matrix) representation. [sent-65, score-1.146]

35 Then, we embed the target and background tensor samples into two specially designed graphs, so that the object can be effectively separated from the background in the graph embedding framework for dimension reduction. [sent-67, score-1.201]

36 It is noted that, this approach can be extended by using higher-order tensor representation (e. [sent-68, score-0.832]

37 3rd-order tensor with a feature vector for each pixel, see [25, 24, 26, 11] for more details), although we only use gray-scale image-as-matrix representation. [sent-70, score-0.788]

38 Because the correlations within a 2nd-order tensor are not limited to the elements along particular columns and rows, the discriminative embedding space derived from dimension reduction may not encode enough of the discriminant information. [sent-71, score-1.489]

39 We improve the classification accuracy of our tensor representation based tracking approach by using the available unlabeled tensor samples. [sent-72, score-1.851]

40 By this improvement, we can adjust the discriminative embedding space so that most of the discriminant information is encoded in it. [sent-74, score-0.589]

41 At each iteration, a number of unlabeled tensor samples are selected and used to learn a new discriminative embedding space. [sent-76, score-1.207]

42 The learned embedding spaces from different iterations and the one trained using only the labeled samples are combined linearly to form a final adjusted embedding space which encodes most of the discriminant information. [sent-77, score-0.706]

43 That is to say, we make use of the unlabeled samples in an inductive fashion, which is very different from most semi-supervised tracking approaches (e. [sent-78, score-0.306]

44 [6, 10, 12]), in which all the unla- beled samples are used for training without selection. [sent-80, score-0.086]

45 The new semi-supervised improvement technique adopts a novel strategy to address the two questions: 1) how to select the unlabeled samples; 2) what class labels should be assigned to the selected unlabeled samples. [sent-81, score-0.324]

46 It is also very different from some margin improving techniques, where the unlabeled samples with the highest classification confidences are selected and the class labels that are predicted by the current classifier are assigned to them, as in Selftraining [20], ASSEMBLE [4]. [sent-82, score-0.25]

47 These techniques may increase the classification margin, but they do not provide any novel information to adjust the discriminative embedding space. [sent-83, score-0.342]

48 We plug the margin improving technique ASSEMBLE into our system and make a direct comparison with our method in Section 3. [sent-84, score-0.142]

49 We elaborate the important components of the proposed approach in this section, in particular the tensor based linear embedding and derivation of the proposed semi-supervised improvement technique. [sent-88, score-1.07]

50 Before all of these, we first review some terminology for tensor operations. [sent-89, score-0.854]

51 Terminology for tensor operations A tensor is a higher order generalization of a vector (1storder tensor) and a matrix (2nd-order tensor). [sent-92, score-1.576]

52 A tensor is a multilinear mapping over a set of vector spaces. [sent-93, score-0.823]

53 ×mn order tensor is denoted as A ∈ Rm1 ×m2 , and its eorledmeren tetns are represented by ai1,. [sent-97, score-0.788]

54 The inner product of two nth-order tensors is defined as ? [sent-101, score-0.062]

55 , and the distance bettwheee nno rAm a onfd A AB i ss ? [sent-131, score-0.066]

56 2,n adn-dor tdheer dtiesntsaoncr case, ttwhee norm aisn cda Blled is st ? [sent-138, score-0.139]

57 T nhoer mm iosd cea-llke dv tehceto Frrso are uths en rcomlu amndn vectors o ? [sent-145, score-0.044]

58 The inverse operation osf rmomode fl-kat flattening i tse nmsoorde A-k. [sent-153, score-0.112]

59 folding, which restores the original tensor A from A(k) . [sent-154, score-0.829]

60 ×mn 11557700 Figure 1: Block diagram of the proposed tracker. [sent-161, score-0.028]

61 MA(k) , sfooll boew ceodm by mtedod beyk folding. [sent-188, score-0.044]

62 Note that for tensors and matrices of the appropriate sizes, A U V = A ×n V U and (pAro p×r tUe) s i×z V, A A= ×A ×U ( ×VUV). [sent-189, score-0.062]

63 M =or eA d ×etaiVls o ×f the tensor algebra are given =in A[23×]. [sent-190, score-0.816]

64 Tensor based linear embedding Previous work has demonstrated that the image variations of many objects can be modeled by low dimensional linear spaces. [sent-193, score-0.238]

65 However, the typical algorithms either only consider an image as a high dimensional vector, or can not fully detect the intrinsic local geometrical and discriminative structure of the collected image patches in the tensor form. [sent-194, score-0.94]

66 Then, a particular question arises: how to find an effective linear embedding space approximation to the original nonlinear submanifold embedded in the tensor space. [sent-195, score-1.199]

67 Graph embedding for dimension reduction [28, 22] provides us an innovation to this question in the sense of local isometry. [sent-196, score-0.381]

68 Generally case: We express the training sample set in the tensor form as {Xi ∈ Rm1 , i= 1, 2, . [sent-197, score-0.788]

69 We build two graphs: an Mintrinsi⊆c graph G and a penalty graph Gp to model the local geometrical dan ad pdeinscalrtiymin gartaipvhe sGtructure of M. [sent-206, score-0.142]

70 edtr Wcalp bned th deis edge weight tmruactrtuicrees ooff ? [sent-208, score-0.083]


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