nips nips2004 nips2004-47 knowledge-graph by maker-knowledge-mining

47 nips-2004-Contextual Models for Object Detection Using Boosted Random Fields

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Author: Antonio Torralba, Kevin P. Murphy, William T. Freeman

Abstract: We seek to both detect and segment objects in images. To exploit both local image data as well as contextual information, we introduce Boosted Random Fields (BRFs), which uses Boosting to learn the graph structure and local evidence of a conditional random ﬁeld (CRF). The graph structure is learned by assembling graph fragments in an additive model. The connections between individual pixels are not very informative, but by using dense graphs, we can pool information from large regions of the image; dense models also support efﬁcient inference. We show how contextual information from other objects can improve detection performance, both in terms of accuracy and speed, by using a computational cascade. We apply our system to detect stuff and things in ofﬁce and street scenes. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Contextual models for object detection using boosted random ﬁelds Antonio Torralba MIT, CSAIL Cambridge, MA 02139 torralba@mit. [sent-1, score-0.22]

2 edu Abstract We seek to both detect and segment objects in images. [sent-7, score-0.144]

3 To exploit both local image data as well as contextual information, we introduce Boosted Random Fields (BRFs), which uses Boosting to learn the graph structure and local evidence of a conditional random ﬁeld (CRF). [sent-8, score-0.431]

4 The graph structure is learned by assembling graph fragments in an additive model. [sent-9, score-0.231]

5 The connections between individual pixels are not very informative, but by using dense graphs, we can pool information from large regions of the image; dense models also support efﬁcient inference. [sent-10, score-0.104]

6 We show how contextual information from other objects can improve detection performance, both in terms of accuracy and speed, by using a computational cascade. [sent-11, score-0.287]

7 We apply our system to detect stuff and things in ofﬁce and street scenes. [sent-12, score-0.252]

8 1 Introduction Our long-term goal is to build a vision system that can examine an image and describe what objects are in it, and where. [sent-13, score-0.192]

9 5(a), objects of interest, such as the keyboard or mouse, are so small that they are impossible to detect just by using local features. [sent-15, score-0.377]

10 Murphy et al [9] used global scene context to help object recognition, but did not model relationships between objects. [sent-18, score-0.093]

11 Fink and Perona [4] exploited local dependencies in a boosting framework, but did not allow for multiple rounds of communication between correlated objects. [sent-19, score-0.361]

12 He et al [6] do not model connections between objects directly, but rather they induce such correlations indirectly, via a bank of hidden variables, using a “restricted Boltzmann machine” architecture. [sent-20, score-0.144]

13 In this paper, we exploit contextual correlations between the object classes by introducing Boosted Random Fields (BRFs). [sent-21, score-0.217]

14 Boosted random ﬁelds build on both boosting [5, 10] and conditional random ﬁelds (CRFs) [8, 7, 6]. [sent-22, score-0.299]

15 Boosting is a simple way of sequentially constructing “strong” classiﬁers from “weak” components, and has been used for singleclass object detection with great success [12]. [sent-23, score-0.169]

16 Dietterich et al [3] combine boosting and 1D CRFs, but they only consider the problem of learning the local evidence potentials; we consider the much harder problem of learning the structure of a 2D CRF. [sent-24, score-0.374]

17 We propose a method for learning densely connected random ﬁelds with long range connections. [sent-27, score-0.101]

18 The topology of these connections is chosen by a weak learner which has access to a library of graph fragments, derived from patches of labeled training images, which reﬂect typical spatial arrangments of objects (similar to the segmentation fragments in [2]). [sent-28, score-0.599]

19 At each round of the learning algorithm, we add more connections from other locations in the image and from other classes (detectors). [sent-29, score-0.22]

20 The connections are assumed to be spatially invariant, which means this update can be performed using convolution followed by a sigmoid nonlinearity. [sent-30, score-0.101]

21 In addition to recognizing things, such as cars and people, we are also interested in recognizing spatially extended “stuff” [1], such as roads and buildings. [sent-32, score-0.129]

22 The traditional sliding window approach to object detection does not work well for detecting “stuff”. [sent-33, score-0.2]

23 Instead, we combine object detection and image segmentation (c. [sent-34, score-0.306]

24 We do not rely on a bottom-up image segmentation algorithm, which can be fragile without top-down guidance. [sent-37, score-0.137]

25 2 Learning potentials and graph structure A conditional random ﬁeld (CRF) is a distribution of the form 1 φi (Si ) ψi,j (Si , Sj ) P (S|x) = Z i j∈Ni where x is the input (e. [sent-38, score-0.182]

26 Our goal is to learn the local evidence potentials, φi , the compatibility potentials ψ, and the set of neighbors Ni . [sent-42, score-0.296]

27 We propose the following simple approximation: use belief propagation (BP) to estimate the marginals, P (Si |x), and then use boosting to maximize the likelihood of each node’s training data with respect to φi and ψ. [sent-43, score-0.331]

28 If we assume that the local potentials t t have the form φt (si ) = [eFi /2 ; e−Fi /2 ], where Fit is some function of the input data, then: i bt (+1) = σ(Fit + Gt ), Gt = log Mit (+1) − log Mit (−1) (3) i i i −u where σ(u) = 1/(1 + e ) is the sigmoid function. [sent-51, score-0.538]

29 Input: a set of labeled pairs {xi,m ; Si,m }, bound T t Output: Local evidence functions fit (x) and message update functions gi (bNi ). [sent-55, score-0.45]

30 (a) Fit local potential fi (xi,m ) by weighted LS to t t t Yi,m = Si,m (1 + e−Si,m (Fi +Gi,m ) ) t t . [sent-61, score-0.113]

31 (b) Fit compatibilities gi (bt−1 ) to Yi,m by weighted LS. [sent-62, score-0.193]

32 Ni ,m t−1 t (c) Compute local potential Fi,m = Fi,m + fit (xi,m ) t g n (bt−1 ) Ni ,m n=1 i t the beliefs bt = σ(Fi,m + Gt ) i,m i,m t+1 weights wi,m = bt (−1) bt (+1) i,m i,m (d) Compute compatibilities Gt = i,m (e) Update (f) Update Figure 1: BRF training algorithm. [sent-63, score-1.681]

33 We assume that the graph is very densely connected so that the information that one single node sends to another is so small that we can make the approximation µt+1 (+1)/µt+1 (−1) ≃ 1. [sent-64, score-0.243]

34 (This is a reasonable approximation in the case of images, k→i k→i where each node represents a single pixel; only when the inﬂuence of many pixels is taken into account will the messages become informative. [sent-65, score-0.165]

35 Therefore, We can write the beliefs at iteration t as a function of the local evidences and the beliefs at time t − 1: bt (+1) = σ(Fit (xi,m ) + Gt (bt−1 )). [sent-67, score-0.85]

36 The key idea i i m behind BRFs is to use boosting to learn the G functions, which approximately implement message passing in densely connected graphs. [sent-68, score-0.435]

37 1 Learning local evidence potentials Deﬁning Fit (xi,m ) = Fit−1 (xi,m ) + fit (xi,m ) as an additive model, where xi,m are the features of training sample m at node i, we can learn this function in a stagewise fashion by optimizing the second order Taylor expansion of Eq. [sent-71, score-0.539]

38 4 wrt fit , as in logitBoost [5]: arg min log Jit ≃ arg min t t fi fi t t t wi,m (Yi,m − fit (xi,m ))2 (7) m t t where Yi,m = Si,m (1+e−Si,m (Fi +Gi,m ) ). [sent-72, score-0.494]

39 In the case that the weak learner is a “regression stump”, fi (x) = ah(x)+b, we can ﬁnd the optimal a, b by solving a weighted least squares t problem, with weights wi,m = bt (−1) bt (+1); we can ﬁnd the best basis function h(x) by i i searching over all elements of a dictionary. [sent-73, score-1.002]

40 2 Learning compatibility potentials and graph structure In this section, we discuss how to learn the compatibility functions ψij , and hence the structure of the graph. [sent-75, score-0.35]

41 Instead of learning the compatibility functions ψij , we propose to t 1. [sent-76, score-0.097]

42 Input: a set of inputs {xi,m } and functions fit , gi Output: Set of beliefs bi,m and MAP estimates Si,m . [sent-77, score-0.46]

43 From t = 1 to T , repeat t−1 t (a) Update local evidences Fi,m = Fi,m + fit (xi,m ) (b) Update compatibilities Gt = i,m (c) Compute current beliefs bt i,m = t g n (bt−1 ) Ni ,m n=1 i t σ(Fi,m + Gt ) i,m 4. [sent-80, score-0.906]

44 We propose to use an additive model for Gt+1 as we i i t n did for learning F : Gt+1 = n=1 gi (bt ), where bt is a vector with the beliefs of all m m i,m n nodes in the graph at iteration t for the training sample m. [sent-84, score-0.859]

45 The weak learners gi (bt ) can m n be regression stumps with the form gi (bt ) = aδ(w · bt > θ) + b, where a, b, θ are the m m parameters of the regression stump, and wi is a set of weights selected from a dictionary. [sent-85, score-0.77]

46 The weak learners gi (bt ) will also be linear m t functions. [sent-87, score-0.271]

47 Hence the belief update simpliﬁes to bt+1 (+1) = σ(αi · bt + βi + Fi,m ), which m i,m is similar to the mean-ﬁeld update equations. [sent-88, score-0.505]

48 The neighborhood Ni over which we sum incoming messages is determined by the graph structure, which is encoded in the non-zero n values of αi . [sent-89, score-0.166]

49 Each weak learner gi will compute a weighted combination of the beliefs of the some subset of the nodes; this subset may change from iteration to iteration, and can be t quite large. [sent-90, score-0.484]

50 At iteration t, we choose the weak learner gi so as to minimize t t t−1 log 1 + e−Si,m (Fi,m +gi (bm log Jit (bt−1 ) = − )+ t−1 n=1 n gi (bt−1 )) m m which reduces to a weighted least squares problem similar to Eq. [sent-91, score-0.458]

51 3 BRFs for multiclass object detection and segmentation With the BRF training algorithm in hand, we describe our approach for multiclass object detection and region-labeling using densely connected BRFs. [sent-96, score-0.599]

52 1 Weak learners for detecting stuff and things The square sliding window approach does not provide a natural way of working with irregular objects. [sent-98, score-0.256]

53 Using region labeling as an image representation allows dealing with irregular and extended objects (buildings, bookshelf, road, . [sent-99, score-0.252]

54 Extended stuff [1] may be a very important source of contextual information for other objects. [sent-103, score-0.223]

55 (a) Examples from the dictionary of about 2000 patches and masks, Ux,y , Vx,y . [sent-104, score-0.129]

56 Figure 3: Examples of patches from the dictionary and an example of the segmentation obtained using boosting trained with patches from (a). [sent-110, score-0.524]

57 The weak learners we use for the local evidence potentials are based on the segmentation fragments proposed in [2]. [sent-111, score-0.509]

58 Speciﬁcally, we create a dictionary of about 2000 image patches U , chosen at random (but overlapping each object), plus a corresponding set of binary (inclass/ out-of-class) image masks, V : see Fig. [sent-112, score-0.271]

59 At each round t, for each class c, and for each dictionary entry, we construct the following weak learner, whose output is a binary matrix of the same size as the image I: v(I) = ((I ⊗ U ) > θ) ∗ V > 0 (9) where ⊗ represents normalized cross-correlation and ∗ represents convolution. [sent-114, score-0.367]

60 The intuition behind this is that I ⊗ U will produce peaks at image locations that contain this patch/template, and then convolving with V will superimpose the segmentation mask on top of the peaks. [sent-115, score-0.206]

61 To be able to detect objects at multiple scales, we ﬁrst downsample the image to scale σ, compute v(I ↓ σ), and then upsample the result. [sent-117, score-0.215]

62 The ﬁnal weak learner does this for multiple scales, ORs all the results together, and then takes a linear transformation. [sent-118, score-0.162]

63 3(c) shows an example of segmentation obtained by using boosting without context. [sent-120, score-0.339]

64 The weak learners we use for the compatibility functions have a similar form: C gc (b) = α bc′ ∗ Wc′ +β (11) c′ =1 where bc′ is the image formed by the beliefs at all pixels for class c′ . [sent-121, score-0.541]

65 The binary kernels (graph fragments) W deﬁne, for each node x, y of object class c, all the nodes from which it will receive messages. [sent-124, score-0.172]

66 These kernels are chosen by sampling patches of various sizes from the labeling of images from the training set. [sent-125, score-0.178]

67 This allows generating complicated patterns of connectivity that reﬂect the statistics of object co-occurrences in the training set. [sent-126, score-0.123]

68 The overall incoming message is given by adding the kernels obtained at each boosting round. [sent-127, score-0.375]

69 (This is the key difference from mutual boosting [4], where the incoming message is just the output of a single weak learner; thus, in mutual boosting, previously learned inter-class connections are only used once. [sent-128, score-0.563]

70 ) Although it would seem to take O(t) time to compute Gt , we can precompute a single equivalent kernel W ′ , so at runtime the overall complexity is still linear in the number of boosting rounds, O(T ). [sent-129, score-0.301]

71 C Gt x,y,c = t n αn Wc′ b c′ ∗ c′ =1 n=1 def C βn = + n ′ b c′ ∗ W c′ + β ′ c′ =1 car car building car road car F Road b=σ(F+G) Car x car building building building road building Building car road building road a) Incoming messages to a car node. [sent-130, score-1.92]

72 t=1 t=2 t=4 G road road y t=20 c) A car out of context (outside 3rd ﬂoor windows) is less of a car. [sent-132, score-0.413]

73 t=40 Final labeling b(car) S(all) d) Evolution of the beliefs for the car nodes (b) and labeling (S) for road, building, car. [sent-133, score-0.462]

74 The BRF is trained to detect cars, buildings and the road. [sent-135, score-0.119]

75 4(a-b), we show the structures of the graph and the weights W ′ deﬁned by GT for a BRF trained to detect cars, buildings and roads in street scenes. [sent-137, score-0.263]

76 2 Learning and inference For training we used a labeled dataset of ofﬁce and street scenes with about 100 images in each set. [sent-139, score-0.146]

77 During the training, in the ﬁrst 5 rounds we only update the local potentials, to allow local evidence to accrue. [sent-140, score-0.233]

78 After the 5th iteration we start updating also the compatibility functions. [sent-141, score-0.144]

79 At each round, we update only the local potential and compatibility function associated with a single object class that reduces the most the multiclass cost. [sent-142, score-0.346]

80 This allows objects that need many features to have more complicated local potentials. [sent-143, score-0.138]

81 The easy-to-detect objects can then pass information to the harder ones. [sent-145, score-0.087]

82 A similar behavior is obtained for the car detector (Fig. [sent-149, score-0.137]

83 The detection of building and road provides strong constraints for the locations of the car. [sent-151, score-0.271]

84 3 Cascade of classiﬁers with BRFs The BRF can be turned into a cascade [12] by thresholding the beliefs. [sent-153, score-0.094]

85 At each round we update a t binary rejection mask for each object class, Rx,y,c , by thresholding the beliefs at round t: t t−1 t t Rx,y,c = Rx,y,c δ(bx,y,c > θc ). [sent-155, score-0.615]

86 A pixel in the rejection mask is set to zero when we can t decide that the object is not present (when bt x,y,c is below the threshold θc ≃ 0), and it is set t to 1 when more processing is required. [sent-156, score-0.613]

87 Similarity we can deﬁne a detection mask that will indicate pixels in which we decide the object is present. [sent-158, score-0.285]

88 The mask is then used for computing the features v(I) and messages G by applying the convolutions only on the pixels not yet classiﬁed. [sent-159, score-0.214]

89 In this desk scene, it is easy to identify objects like the screen, keyboard and mouse, even though the local information is sometimes insufﬁcient. [sent-163, score-0.32]

90 Middle: the evolution of the beliefs (b and F and G) during detection for a test image. [sent-164, score-0.27]

91 The graph bellow shows the average evolution of the area under the ROC for the three objects on 120 test images. [sent-166, score-0.174]

92 6 we compare the reduction of the search space when implementing a cascade using independent boosting (which reduces to Viola and Jones [12]), and when using BRF’s. [sent-169, score-0.394]

93 We see that for objects for which context is the main source of information, like the mouse, the reduction in search space is much more dramatic using BRFs than using boosting alone. [sent-170, score-0.389]

94 4 Conclusion The proposed BRF algorithm combines boosting and CRF’s, providing an algorithm that is easy for both training and inference. [sent-171, score-0.303]

95 We have demonstrated object detection in cluttered scenes by exploiting contextual relationships between objects. [sent-172, score-0.328]

96 The BRF algorithm is computationally efﬁcient and provides a natural extension of the cascade of classiﬁers by integrating evidence from other objects in order to quickly reject certain image regions. [sent-173, score-0.271]

97 The BRF’s densely connected graphs, which efﬁciently collect information over large image regions, provide an alternative framework to nearest-neighbor grids for vision problems. [sent-174, score-0.206]

98 5 False alarm rate 1 Figure 6: Contextual information reduces the search space in the framework of a cascade and improves performances. [sent-183, score-0.171]

99 Discriminative random ﬁelds: A discriminative framework for contextual interaction in classiﬁcation. [sent-229, score-0.124]

100 Using the forest to see the trees: a graphical model relating features, objects and scenes. [sent-244, score-0.087]

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