nips nips2012 nips2012-176 knowledge-graph by maker-knowledge-mining

176 nips-2012-Learning Image Descriptors with the Boosting-Trick

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Author: Tomasz Trzcinski, Mario Christoudias, Vincent Lepetit, Pascal Fua

Abstract: In this paper we apply boosting to learn complex non-linear local visual feature representations, drawing inspiration from its successful application to visual object detection. The main goal of local feature descriptors is to distinctively represent a salient image region while remaining invariant to viewpoint and illumination changes. This representation can be improved using machine learning, however, past approaches have been mostly limited to learning linear feature mappings in either the original input or a kernelized input feature space. While kernelized methods have proven somewhat effective for learning non-linear local feature descriptors, they rely heavily on the choice of an appropriate kernel function whose selection is often difﬁcult and non-intuitive. We propose to use the boosting-trick to obtain a non-linear mapping of the input to a high-dimensional feature space. The non-linear feature mapping obtained with the boosting-trick is highly intuitive. We employ gradient-based weak learners resulting in a learned descriptor that closely resembles the well-known SIFT. As demonstrated in our experiments, the resulting descriptor can be learned directly from intensity patches achieving state-of-the-art performance. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 ch Abstract In this paper we apply boosting to learn complex non-linear local visual feature representations, drawing inspiration from its successful application to visual object detection. [sent-3, score-0.249]

2 The main goal of local feature descriptors is to distinctively represent a salient image region while remaining invariant to viewpoint and illumination changes. [sent-4, score-0.531]

3 This representation can be improved using machine learning, however, past approaches have been mostly limited to learning linear feature mappings in either the original input or a kernelized input feature space. [sent-5, score-0.279]

4 While kernelized methods have proven somewhat effective for learning non-linear local feature descriptors, they rely heavily on the choice of an appropriate kernel function whose selection is often difﬁcult and non-intuitive. [sent-6, score-0.209]

5 We employ gradient-based weak learners resulting in a learned descriptor that closely resembles the well-known SIFT. [sent-9, score-0.864]

6 As demonstrated in our experiments, the resulting descriptor can be learned directly from intensity patches achieving state-of-the-art performance. [sent-10, score-0.584]

7 1 Introduction Representing salient image regions in a way that is invariant to unwanted image transformations is a crucial Computer Vision task. [sent-11, score-0.276]

8 These descriptors have become prevalent, even though they are not truly invariant with respect to various viewpoint and illumination changes which limits their applicability. [sent-13, score-0.308]

9 In an effort to address these limitations, a fair amount of work has focused on learning local feature descriptors [3, 4, 5] that leverage labeled training image patches to learn invariant feature representations based on local image statistics. [sent-14, score-0.773]

10 Learning an invariant feature representation is strongly related to learning an appropriate similarity measure or metric over intensity patches that is invariant to unwanted image transformations, and work on descriptor learning has been predominantly focused in this area [3, 6, 5]. [sent-16, score-0.982]

11 Methods for metric learning that have been applied to image data have largely focused on learning a linear feature mapping in either the original input or a kernelized input feature space [7, 8]. [sent-17, score-0.417]

12 In this way, non-linearities are modeled using a predeﬁned similarity or kernel function that implicitly maps the input features to a high-dimensional feature space where the transformation is assumed to be linear. [sent-19, score-0.291]

13 While these methods have proven somewhat effective for learning non-linear local feature mappings, choosing an appropriate kernel function is often nonintuitive and remains a challenging and largely open problem. [sent-20, score-0.168]

14 Additionally, kernel methods involve 1 an optimization whose problem complexity grows quadratically with the number of training examples making them difﬁcult to apply to large problems that are typical to local descriptor learning. [sent-21, score-0.465]

15 In this paper, we apply boosting to learn complex non-linear local visual feature representations drawing inspiration from its successful application to visual object detection [10]. [sent-22, score-0.249]

16 Image patch appearance is modeled using local non-linear ﬁlters evaluated within the image patch that are effectively selected with boosting. [sent-23, score-0.234]

17 Also, our learning approach scales linearly with the number of training examples making it more easily amenable to large scale problems and results in highly accurate descriptor matching. [sent-26, score-0.398]

18 We build upon [3] that also relies on boosting to compute a descriptor, and show how we can use it as a way to efﬁciently select features, from which we compute a compact representation. [sent-27, score-0.172]

19 We also replace the simple weak learners of [3] by non-linear ﬁlters more adapted to the problem. [sent-28, score-0.374]

20 In particular, we employ image gradient-based weak learners similar to [12] that share a close connection with the non-linear ﬁlters used in proven image descriptors such as SIFT and Histogram-of-Oriented Gradients (HOG) [13]. [sent-29, score-0.76]

21 As seen in our experiments, our descriptor can be learned directly from intensity patches and results in state-of-the-art performance rivaling its hand-designed equivalents. [sent-31, score-0.584]

22 To evaluate our approach we consider the image patch dataset of [4] containing several hundreds of thousands of image patches under varying viewpoint and illumination conditions. [sent-32, score-0.395]

23 As baselines we compare against leading contemporary hand-designed and learned local feature descriptors [1, 2, 3, 5]. [sent-33, score-0.424]

24 2 Related work Machine learning has been applied to improve both matching efﬁciency and accuracy of image descriptors [3, 4, 5, 8, 14, 15]. [sent-35, score-0.351]

25 [14] present a spectral hashing approach that learns compact binary codes for efﬁcient image indexing and matching. [sent-39, score-0.21]

26 Many of these approaches presume a given distance or similarity measure over a pre-deﬁned input feature space. [sent-41, score-0.176]

27 In contrast, our approach learns a nonlinear feature mapping that is speciﬁcally optimized to result in highly accurate descriptor matching. [sent-43, score-0.583]

28 Methods to metric learning learn feature spaces tailored to a particular matching task [5, 8]. [sent-44, score-0.196]

29 [8] learn a Mahalanobis distance metric deﬁned using either the original input or a kernelized input feature space applied to image classiﬁcation and matching. [sent-47, score-0.272]

30 While these methods improve matching accuracy through a learned feature space, they require the presence of a pre-selected kernel function to encode non-linearities. [sent-51, score-0.242]

31 Such approaches are well suited for certain image indexing and classiﬁcation tasks where task-speciﬁc kernel functions have been proposed (e. [sent-52, score-0.195]

32 However, they are less applicable to local image feature matching, for which the appropriate choice of kernel function is less understood. [sent-55, score-0.263]

33 While these methods also use boosting to learn a feature mapping, they have emphasized 2 computational efﬁciency only considering linear feature embeddings. [sent-61, score-0.323]

34 [4] also consider different feature pooling and selection strategies of gradient-based features resulting in a descriptor which is both short and discriminant. [sent-64, score-0.564]

35 Moreover, the form of our descriptor is much simpler. [sent-68, score-0.398]

36 Our work on boosted feature learning can be traced back to the work of Doll´ r et al. [sent-71, score-0.456]

37 Our approach is probably most similar to the boosted Similarity Sensitive Coding (SSC) method of Shakhnarovich [3] that learns a boosted similarity function from a family of weak learners, a method that was later extended in [23] to be used with a Hamming distance. [sent-73, score-0.953]

38 We also show that the image gradient-based weak learners of [24] are well adapted to the problem. [sent-77, score-0.469]

39 As seen in our experiments, our approach signiﬁcantly outperforms Boosted SSC when applied to image intensity patches. [sent-78, score-0.156]

40 3 Method Given an image intensity patch x ∈ RD we look for a descriptor of x as a non-linear mapping H(x) into the space spanned by {hi }M , a collection of thresholded non-linear response functions i=1 hi (x) : RD → {−1, 1}. [sent-79, score-0.887]

41 The Boosted SSC method proposed in [3] considers a similarity function deﬁned by a simply weighted sum of thresholded response functions M f (x, y) = αi hi (x)hi (y) . [sent-82, score-0.308]

42 (3) j=1 In practice M is large and in general the number of possible hi ’s can be inﬁnite making the explicit optimization of LSSC difﬁcult, which constitutes a problem for which boosting is particularly well suited [25]. [sent-85, score-0.276]

43 Although boosting is a greedy optimization scheme, it is a provably effective method for constructing a highly accurate predictor from a collection of weak predictors hi . [sent-86, score-0.415]

44 Similar to the kernel trick, the resulting boosting-trick also maps each observation to a highdimensional feature space, however, it computes an explicit mapping for which the αi ’s that deﬁne f (x, y) are assumed to be sparse [11]. [sent-87, score-0.231]

45 [26] have shown that under certain 3 settings boosting can be interpreted as imposing an L1 sparsity constraint over the response function weights αi . [sent-89, score-0.176]

46 As will be seen below, unlike the kernel trick, this allows for the deﬁnition of high-dimensional embeddings well suited to the descriptor matching task whose features have an intuitive explanation. [sent-90, score-0.605]

47 Boosted SSC employs linear response weak predictors based on a linear projection of the input. [sent-91, score-0.223]

48 In contrast, we consider non-linear response functions more suitable for the descriptor matching task as discussed in Section 3. [sent-92, score-0.513]

49 In what follows, we will present our approach for learning compact boosted feature descriptors called Low-Dimensional Boosted Gradient Maps (L-BGM). [sent-95, score-0.703]

50 First, we present a modiﬁed similarity function well suited for learning low-dimensional, discriminative embeddings with boosting. [sent-96, score-0.189]

51 Next, we show how we can factorize the learned embedding to form a compact feature descriptor. [sent-97, score-0.252]

52 Finally, the gradient-based weak learners utilized by our approach are detailed. [sent-98, score-0.374]

53 (5) i,j k=1 Although it can be shown that LLBGM can be jointly optimized for A and the hi ’s using boosting, this involves a fairly complex procedure. [sent-104, score-0.194]

54 Note that because the weak learners are binary, we can precompute the exponential terms involved in the derivatives for all the data samples, as they are constant with respect to AP . [sent-116, score-0.374]

55 2 Embedding factorization The similarity function of Equation (4) deﬁnes an implicit feature mapping over example pairs. [sent-119, score-0.252]

56 We now show how the AP matrix in fLBGM can be factorized to result in compact feature descriptors computed independently over each input. [sent-120, score-0.348]

57 In addition, assuming a Gaussian weighting of the α’s results in a descriptor that closely resembles SIFT [1] and is one of the many solutions afforded by our learning framework. [sent-122, score-0.557]

58 (7) j=1 i=1 k=1  P bk,i hi (x)  wk fLBGM (x, y) =  P d This factorization deﬁnes a signed inner product between the embedded feature vectors and provides increased efﬁciency with respect to the original similarity measure 1 . [sent-125, score-0.362]

59 As seen in our experiments, in the case of redundant hi this results in a considerable feature compression, also offering a more compact description than the original input patch. [sent-131, score-0.306]

60 3 Weak learners The boosting-trick allows for a variety of non-linear embeddings parameterized by the chosen weak learner family. [sent-133, score-0.454]

61 In what follows, we extend these features to the descriptor matching task illustrating their close connection with the well-known SIFT descriptor. [sent-136, score-0.487]

62 The gradient energy is computed based on the dot product between e and the gradient orientation at pixel m [12]. [sent-138, score-0.165]

63 The learned weighting closely resembles the Gaussian weighting employed by SIFT (white circles indicate σ/2 and σ used by SIFT). [sent-155, score-0.254]

64 The non-linear gradient response functions φR,e along with their thresholding T deﬁne the parameterization of the weak learner family optimized with our approach. [sent-158, score-0.336]

65 This corresponds to a selection of weak learners whose R and e values are parameterized such that they lie along a regular grid, equally sampling each edge orientation within each grid cell. [sent-160, score-0.427]

66 In addition, if we assume a Gaussian weighting centered about the patch, the resulting descriptor closely resembles SIFT2 [1]. [sent-161, score-0.53]

67 In [4], they note the importance of allowing for alternative pooling and feature selection strategies, both of which are effectively optimized within our framework. [sent-163, score-0.177]

68 We then show the results obtained using Boosted SSC combined with gradient-based weak learners described in Sec. [sent-166, score-0.374]

69 Finally, we present a comparison of our ﬁnal descriptor with the state of the art. [sent-170, score-0.398]

70 These patches are sampled around interest points detected using Difference of Gaussians and the correspondences between patches are found using a multi-view stereo algorithm. [sent-174, score-0.168]

71 3(a), a 128-dimensional Boosted SSC descriptor can be easily outperformed by a 32-dimensional BGM descriptor. [sent-182, score-0.398]

72 When comparing descriptors with the same dimensionality, the improvement measured in terms of 95% error rate reaches over 50%. [sent-183, score-0.233]

73 This indicates that boosting with a similar number of non-linear classiﬁers adds to the performance, and proves how well tuned the SIFT descriptor is. [sent-229, score-0.519]

74 To plot the visualizations we sum the α’s across orientations within the rectangular regions of the corresponding weak learners. [sent-231, score-0.168]

75 Note that although there are some differences, interestingly this weighting closely resembles the Gaussian weighting employed by SIFT. [sent-232, score-0.213]

76 3 Low-Dimensional Boosted Gradient Maps To further improve performance, we optimize over the correlation matrix of the weak learners’ responses, as explained in Sec. [sent-234, score-0.168]

77 In these experiments, we learn our L-BGM descriptor using the responses of 512 gradient-based weak learners selected with boosting. [sent-241, score-0.772]

78 We ﬁrst optimize over the weak learners’ correlation matrix which is constrained to be diagonal. [sent-242, score-0.168]

79 This corresponds to a global optimization of the weights of the weak learners. [sent-243, score-0.168]

80 The resulting 32-dimensional L-BGM-Diag descriptor performs only slightly better than the corresponding 32-dimensional BGM. [sent-244, score-0.398]

81 , the descriptor of the same length as SIFT, we observe 15% improvement in terms of 95% error rate. [sent-248, score-0.398]

82 However, when we increase the descriptor length from 256 to 512 we can see a slight performance drop since we begin to include the “noisy” dimensions of our embedding which correspond to the eigenvalues of low magnitude, a trend typical to many dimensionality reduction techniques. [sent-249, score-0.487]

83 Hence, as our ﬁnal descriptor, we select the 64-dimensional L-BGM descriptor, as it provides a decent trade-off between performance and descriptor length. [sent-250, score-0.398]

84 Figure 3(b) also shows the results obtained by applying PCA on the responses of 512 gradient-based weak learners (BGM-PCA). [sent-251, score-0.374]

85 The descriptor generated this way performs similarly to SIFT, however our method still provides better results even for the same dimensionality, which shows the advantage in optimizing the exponential loss of Eq. [sent-252, score-0.398]

86 We have also tested recent binary descriptors such as BRIEF [27], ORB [28] or BRISK [29], however, they performed much worse than the baselines presented in the paper. [sent-256, score-0.228]

87 The maximal performance boost is obtained by using our 64-dimensional L-BGM descriptor that results in an up to 18% improvement in terms of 95% error rate with respect to the state-of-the-art SIFT descriptor. [sent-305, score-0.468]

88 Finally, our BGM and L-BGM descriptors far outperform SIFT which relies on hand-crafted ﬁlters applied to gradient maps. [sent-309, score-0.266]

89 However, since the code for their compact descriptors is not publicly available, we can only compare the performance in terms of the 95% error rates. [sent-314, score-0.274]

90 Only the composite descriptors of [4] provide some advantage over our compact L-BGM, as their average 95% error rate is 2% lower than this of L-BGM. [sent-315, score-0.284]

91 Nevertheless, we outperform their non-parametric descriptors by 12% and perform slightly better than the parametric ones, while using descriptors of an order of magnitude shorter. [sent-316, score-0.42]

92 This comparison indicates that even though our approach does not require any complex pipeline optimization and parameter tuning, we perform similarly to the ﬁnely optimized descriptors presented in [4]. [sent-317, score-0.236]

93 5 Conclusions In this paper we presented a new method for learning image descriptors by using Low-Dimensional Boosted Gradient Maps (L-BGM). [sent-318, score-0.291]

94 L-BGM offers an attractive alternative to traditional descriptor learning techniques that model non-linearities based on the kernel-trick, relying on a pre-speciﬁed kernel function whose selection can be difﬁcult and unintuitive. [sent-319, score-0.438]

95 In contrast, we have shown that for the descriptor matching problem the boosting-trick leads to non-linear feature mappings whose features have an intuitive explanation. [sent-320, score-0.624]

96 We demonstrated the use of gradient-based weak learner functions for learning descriptors within our framework, illustrating their close connection with the well-known SIFT descriptor. [sent-321, score-0.395]

97 A discriminative embedding technique was also presented, yielding fairly compact and discriminative feature descriptions compared to the baseline methods. [sent-322, score-0.311]

98 We evaluated our approach on benchmark datasets where L-BGM was shown to outperform leading contemporary hand-designed and learned feature descriptors. [sent-323, score-0.197]

99 Unlike previous approaches, our L-BGM descriptor can be learned directly from raw intensity patches achieving state-of-the-art performance. [sent-324, score-0.584]

100 Interesting avenues of future work include the exploration of other weak learner families for descriptor learning, e. [sent-325, score-0.597]

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