nips nips2012 nips2012-360 knowledge-graph by maker-knowledge-mining

360 nips-2012-Visual Recognition using Embedded Feature Selection for Curvature Self-Similarity

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Author: Angela Eigenstetter, Bjorn Ommer

Abstract: Category-level object detection has a crucial need for informative object representations. This demand has led to feature descriptors of ever increasing dimensionality like co-occurrence statistics and self-similarity. In this paper we propose a new object representation based on curvature self-similarity that goes beyond the currently popular approximation of objects using straight lines. However, like all descriptors using second order statistics, ours also exhibits a high dimensionality. Although improving discriminability, the high dimensionality becomes a critical issue due to lack of generalization ability and curse of dimensionality. Given only a limited amount of training data, even sophisticated learning algorithms such as the popular kernel methods are not able to suppress noisy or superﬂuous dimensions of such high-dimensional data. Consequently, there is a natural need for feature selection when using present-day informative features and, particularly, curvature self-similarity. We therefore suggest an embedded feature selection method for SVMs that reduces complexity and improves generalization capability of object models. By successfully integrating the proposed curvature self-similarity representation together with the embedded feature selection in a widely used state-of-the-art object detection framework we show the general pertinence of the approach. 1

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 de Abstract Category-level object detection has a crucial need for informative object representations. [sent-4, score-0.464]

2 This demand has led to feature descriptors of ever increasing dimensionality like co-occurrence statistics and self-similarity. [sent-5, score-0.266]

3 In this paper we propose a new object representation based on curvature self-similarity that goes beyond the currently popular approximation of objects using straight lines. [sent-6, score-0.883]

4 Consequently, there is a natural need for feature selection when using present-day informative features and, particularly, curvature self-similarity. [sent-10, score-0.77]

5 We therefore suggest an embedded feature selection method for SVMs that reduces complexity and improves generalization capability of object models. [sent-11, score-0.581]

6 By successfully integrating the proposed curvature self-similarity representation together with the embedded feature selection in a widely used state-of-the-art object detection framework we show the general pertinence of the approach. [sent-12, score-1.224]

7 Starting with brightness values of image pixels and simple edge histograms [10] descriptors evolved and more sophisticated features like shape context [1] and wavelets [23] were suggested. [sent-14, score-0.263]

8 The probably most widely used and best performing image descriptors today are SIFT [18] and HOG [4] which model objects based on edge orientation histograms. [sent-15, score-0.314]

9 Furthermore it is noticeable that all descriptors that model the object boundary rely on image statistics that are primarily based on edge orientation. [sent-18, score-0.358]

10 However, it was shown in different studies within the perception community that besides orientation also curvature is an important cue when performing visual search tasks. [sent-20, score-0.622]

11 In our earlier work [21] we extended the modeling of object boundary contours beyond the widely used edge orientation histograms by utilizing curvature information to overcome the drawbacks of straight line approximations. [sent-21, score-1.224]

12 However, curvature can provide even more information about the object boundary. [sent-22, score-0.668]

13 By computing co-occurrences between discriminatively curved boundaries we build a curvature self-similarity descriptor that provides a more detailed and accurate object description. [sent-23, score-0.929]

14 While it was shown that self-similarity and co-occurrence lead to very robust and highly discriminative object representations, these second order image statistics are also pushing feature spaces to extremely 1 high dimensions. [sent-24, score-0.377]

15 Since the amount of training data stays more or less the same, the dimensionality of the object representation has to be reduced to prevent systems to suffer from curse of dimensionality and overﬁtting. [sent-25, score-0.377]

16 [5], for instance, suggested an approach that results in a 160000 dimensional descriptor which was evaluated on the ETHZ shape dataset which contains on average 30 positive object instances per category. [sent-28, score-0.433]

17 To exploit the full capabilities of high-dimensional representations applied in object detection we developed a new embedded feature selection method for SVM which reliable discards superﬂuous dimensions and therefore improves object detection performance. [sent-29, score-1.074]

18 The paper is organized as follows: First we will give a short overview on embedded feature selection methods for SVMs (Section 2. [sent-30, score-0.408]

19 After that we describe our new self-similarity descriptor based on curvature to go beyond the straight line approximation of objects to a more accurate description (Section 3). [sent-33, score-0.845]

20 In the experimental section at the end of the paper we evaluate the suggested curvature self-similarity descriptor along with our feature selection method. [sent-35, score-0.954]

21 [12] categorize feature selection methods into ﬁlters, wrappers and embedded methods. [sent-38, score-0.441]

22 Contrary to ﬁlters and wrappers embedded feature selection methods incorporate feature selection as a part of the learning process (for a review see [17]). [sent-39, score-0.716]

23 The focus of this paper is on embedded feature selection methods for SVMs, since most state-of-the-art detection systems use SVM as a classiﬁer. [sent-40, score-0.526]

24 To directly integrate feature selection into the learning process of SVMs sparsity can be enforced on the model parameter w. [sent-41, score-0.275]

25 [30] suggested the doubly regularized SVM (DrSVM) which is not replacing the L2 regularization but adding an additional L1 regularization to automatically select dimensions during the learning process. [sent-45, score-0.175]

26 Contrary to linear SVM enforcing sparsity on the model parameter w does reduce dimensionality for non-linear kernel functions in the higher dimensional kernel space rather than in the number of input features. [sent-46, score-0.229]

27 To reduce the dimensionality for non-linear SVMs in the feature space one can introduce an additional selection vector θ ∈ [0, 1]n , where larger values of θi indicate more useful features. [sent-47, score-0.362]

28 The objective is then to ﬁnd the best kernel of the form Kθ (x, z) = K(θ ∗ x, θ ∗ z), where x, z ∈ Rn are the feature vectors and ∗ is element-wise multiplication. [sent-48, score-0.186]

29 In this paper we integrate the scaling factors into the learning algorithm, but instead of using L2 norm constraint like in [11] on the scaling parameter θ we apply an L1 norm sparsity which is explicitly discarding dimensions of the input feature vector. [sent-51, score-0.212]

30 We are following the concept of embedded feature selection and therefore include the feature selection parameter θ directly in the SVM classiﬁer. [sent-56, score-0.683]

31 We enforce sparsity of the feature selection parameter θ by the last constraint of Eq. [sent-60, score-0.275]

32 The optimization of the selection parameter θ starts at the canonical solution where all dimensions are set to one. [sent-75, score-0.191]

33 An overview of the suggested iterative dimensionality reduction algorithm is given in Algorithm 1. [sent-95, score-0.216]

34 3 Representing Curvature Self-Similarity Although several methods have been suggested for the robust estimation of curvature, it has been mainly represented indirectly in a contour based manner [1, 32] and to locate interest points at boundary points with high curvature value. [sent-96, score-0.642]

35 To design a more exact object representation that represents object curvedness in a natural way we revisit the idea of [21] and design a novel curvature self-similarity descriptor. [sent-97, score-0.908]

36 [29] showed that using color histograms directly is decreasing performance while using color self-similarity (CSS) as a feature is more appropriate. [sent-106, score-0.217]

37 To make use of the aforementioned advantages of global self-similarity we compute all pairwise curvature similarities across the whole image. [sent-109, score-0.542]

38 This results in a very high dimensional object representation. [sent-110, score-0.207]

39 As mentioned before such high dimensional representations have a natural need for dimensionality reduction which we fulﬁll by applying our embedded feature selection algorithm outlined in the previous section. [sent-111, score-0.609]

40 To describe complex objects it is not sufﬁcient to build a self-similarity descriptor solely based on curvature information, since self-similarity of curvature leaves open many ambiguities. [sent-112, score-1.207]

41 To resolve these ambiguities we add 360 degree orientation information to get a more accurate descriptor. [sent-113, score-0.184]

42 We are using 360 degree orientation, since curved lines cannot be fully described by their 180 degree orientation. [sent-114, score-0.179]

43 This is different to straight lines, where 180 degree orientation gives us the full information about the line. [sent-115, score-0.289]

44 The tangent line has an orientation between 0 and 180 degrees. [sent-117, score-0.193]

45 Therefore, using a 180 degree orientation yields to high similarities between a left curved line segment and a right curved line segment. [sent-119, score-0.435]

46 As a ﬁrst step we extract the curvature information and the corresponding 360 degree orientation of all edge pixels in the image. [sent-120, score-0.725]

47 To estimate the curvature we follow our approach presented in [21] and use the distance accumulation method of Han et al. [sent-121, score-0.522]

48 The perpendicular distance Dik 4 Figure 2: Our visualization shows the original images along with their curvature self-similarity matrices displaying the similarity between all pairs of curvature histogram cells. [sent-128, score-1.018]

49 While curvature self-similarity descriptor is similar for the same object category it looks quite different to other object categories is computed from Li to the point pk , using the euclidean distance. [sent-129, score-1.023]

50 To get the 360 degree orientation information we compute the gradient of the probabilistic boundary edge image [20] and extend the resulting 180 degree gradient orientation to a 360 degree orientation using the sign of the curvature. [sent-132, score-0.69]

51 Contrary to the original curvature feature proposed in [21] where histograms of curvature are computed using differently sized image regions we build our basic curvature feature using equally sized cells to make it more suitable for computing self-similarities. [sent-133, score-1.915]

52 We divide the image into nonoverlapping 8 × 8 pixel cells and build histograms over the curvature values in each cell. [sent-134, score-0.661]

53 Next we do the same for the 360 degree orientation and concatenate the two histograms. [sent-135, score-0.184]

54 This results in histograms of 28 bins, 10 bins representing the curvature and 18 bins representing the 360 degree orientation. [sent-136, score-0.689]

55 We follow the scheme that was applied to compute self similarities between color histograms [29] and use histogram intersection as a comparison measure to compute the similarities between different curvature histograms in the same bounding box. [sent-138, score-0.808]

56 Let D be the number of cells in an image, then computing all pairwise similarities results in a D2 large curvature self-similarity matrix. [sent-141, score-0.542]

57 To discard such superﬂuous dimensions we apply our embedded feature selection method to the proposed curvature self-similarity representation. [sent-147, score-0.951]

58 4 Experiments We evaluate our curvature self-similarity descriptor in combination with the suggested embedded dimensionality reduction algorithm for the object detection task on the PASCAL dataset [7]. [sent-148, score-1.234]

59 Our experiments show, that curvature self-similarity is providing complementary information to straight lines, while our feature selection algorithm is further improving performance by fulﬁlling its natural need for dimensionality reduction. [sent-151, score-0.962]

60 The common basic concept shared by many current detection systems are high-dimensional, holistic representations learned with a discriminative classiﬁer, mostly an SVM [28]. [sent-152, score-0.217]

61 These systems rely on high-dimensional holistic image statistics primarily utilizing straight line approximations. [sent-154, score-0.253]

62 In this paper we explore a orthogonal direction to these extensions and focus on how one can improve on the basic system by extending the straight line representation of HOG to a more discriminative description using curvature self-similarity. [sent-155, score-0.696]

63 At the same time our aim is to reduce the dimensionality 5 Table 1: Average precision of our iterative feature reduction algorithm for linear and non-linear kernel function using our ﬁnal feature vector consisting of HOG+Curv+CurvSS. [sent-156, score-0.548]

64 For linear kernel function we compare our feature selection (linSVM+FS) to L2 normalized linear SVM (linSVM) and to the doubly regularized SVM (DrSVM) [30]. [sent-157, score-0.4]

65 For non-linear kernel function we compare the fast intersection kernel SVM (FIKSVM) [19] with our feature selection (FIKSVM+FS) linSVM DrSVM linSVM + FS FIKSVM FIKSVM + FS aero 66. [sent-158, score-0.469]

66 In the ﬁrst part of our experiments we adjust the selection parameter λ of our iterative dimensionality reduction technique via cross-validation. [sent-264, score-0.303]

67 Furthermore, we compare the performance of our feature selection algorithm to L2 regularized SVM [3, 19] and DrSVM [30]. [sent-265, score-0.307]

68 In the second part we evaluate the suggested curvature self-similarity feature after applying our feature selection method to it. [sent-266, score-0.958]

69 1 Evaluation of Feature Selection All experiments in this section are performed using our ﬁnal feature vector consisting of HOG, curvature (Curv) and curvature self-similarity (CurvSS). [sent-268, score-1.148]

70 We apply our iterative dimensionality reduction algorithm in combination with linear L2 regularized SVM classiﬁer (linSVM) [3] and nonlinear fast intersection kernel SVM (FIKSVM) by Maji et al. [sent-269, score-0.295]

71 All training and validation data from the PASCAL VOC 2007 dataset are used to train an SVM using our ﬁnal object representation on all positive samples and randomly chosen negative samples. [sent-275, score-0.257]

72 Out of the collected set of samples every tenth sample is assigned to the hold out test set which is used to compare the performance of our feature selection method. [sent-278, score-0.275]

73 The remaining samples are randomly split into training and validation set of equal size which are used to perform the feature selection. [sent-279, score-0.186]

74 For each set we train an L2 norm SVM on all samples from the training and validation set using only the remaining dimensions of the feature vector. [sent-281, score-0.234]

75 Since DrSVM is solving a similar optimization problem as our suggested feature selection algorithm for a linear kernel this comparison is of particular interest. [sent-285, score-0.385]

76 It is evident that objects like the sheep are not deﬁned by their boundary shape and are thus beyond the scope of approaches base on contour shape it is performing feature selection in the higher dimensional kernel space rather than in the original feature space. [sent-289, score-0.799]

77 Instead we compare our feature selection method to that of FIKSVM for the nonlinear case. [sent-290, score-0.275]

78 Our feature selection method reduces the dimensionality of the feature by up to 55% for the linear case and by up to 40% in the non-linear case, while the performance in average precision is constant or increases beyond the performance of linSVM and FIKSVM. [sent-291, score-0.567]

79 On average our feature selection increases performance about 1. [sent-292, score-0.275]

80 Our results conﬁrm that our feature selection method reduces the amount of noisy dimensions of highdimensional representations and therefore increases the average precision compared to an linear and non-linear SVM classiﬁer without applying any feature selection. [sent-299, score-0.535]

81 For the linear kernel we showed furthermore that the proposed feature selection algorithm achieves gain over the DrSVM. [sent-300, score-0.329]

82 2 Object Detection using Curvature Self-Similarity In this section we provide a structured evaluation of the parts of our ﬁnal object detection system. [sent-302, score-0.291]

83 [8, 9] as baseline system, since it is the basis for many powerful object detection systems. [sent-304, score-0.291]

84 All detection results are measured in terms of average precision performing object detection on the PASCAL VOC 2007 dataset. [sent-305, score-0.453]

85 To the best of our knowledge neither curvature nor self-similarity was used to perform object detection on a dataset of similar complexity as the PASCAL dataset so far. [sent-306, score-0.786]

86 [5] evaluated their global self-similarity descriptor (GSS) on the simpler classiﬁcation challenge on the PASCAL VOC 2007 dataset, while the object detection evaluation was performed on the ETHZ shape dataset. [sent-308, score-0.461]

87 However, we showed in [21], that including curvature already solves the detection task almost perfectly on the ETHZ dataset. [sent-309, score-0.613]

88 Since the proposed approach models the shape of curved object contours and reduces the dimensionality of the representation, we expect it to be of particular value for objects that are characterized by their shape and where their contours can be extracted using state-of-the-art methods. [sent-312, score-0.548]

89 Therefore state-of-the-art edge extraction fails to provide any basis for contour based approaches on these images and one can therefore only expect a signiﬁcant gain on categories where proper edge information can be computed for a majority of the images. [sent-315, score-0.189]

90 Due to the large amount of data in the PASCAL database the usage of intersection kernel for object detection becomes comparable intractable. [sent-318, score-0.394]

91 Results of our ﬁnal system consisting of HOG, curvature (Curv), curvature self-similarity (CurvSS) and our embedded feature selection method (FS) are reported in terms of average precision in Table 2. [sent-319, score-1.468]

92 7 and without feature selection to show the individual gain of the curvature self-similarity descriptor and our embedded feature selection algorithm. [sent-450, score-1.306]

93 The results show that the suggested self-similarity representation in combination with feature selection improves performance on most of the categories. [sent-451, score-0.361]

94 One can observe that curvature information in combination with our feature selection algorithm is already improving performance over the HOG baseline and that adding curvature self-similarity additionally increases performance by 1. [sent-454, score-1.265]

95 The gain obtained by applying our feature selection (FS) depends obviously on the dimensionality of the feature vector; the higher the dimensionality the more can be gained by removing noisy dimensions. [sent-456, score-0.581]

96 For HOG+Curv applying our feature selection is improving performance by 0. [sent-457, score-0.275]

97 The results underline that curvature information provides complementary information to straight lines and that feature selection is needed when dealing with high dimensional features like self-similarity. [sent-459, score-0.909]

98 An embedded feature selection method for SVMs has therefore been proposed in this paper, which has been demonstrated to successfully deal with high-dimensional descriptions and it increases the performance of linear and intersection kernel SVM. [sent-461, score-0.511]

99 Moreover, the proposed curvature self-similarity representation has been shown to add complementary information to widely used orientation histograms. [sent-462, score-0.652]

100 Discriminative structure learning of hierarchical representations for object detection. [sent-627, score-0.209]

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