nips nips2008 nips2008-116 knowledge-graph by maker-knowledge-mining

116 nips-2008-Learning Hybrid Models for Image Annotation with Partially Labeled Data

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Author: Xuming He, Richard S. Zemel

Abstract: Extensive labeled data for image annotation systems, which learn to assign class labels to image regions, is difﬁcult to obtain. We explore a hybrid model framework for utilizing partially labeled data that integrates a generative topic model for image appearance with discriminative label prediction. We propose three alternative formulations for imposing a spatial smoothness prior on the image labels. Tests of the new models and some baseline approaches on three real image datasets demonstrate the effectiveness of incorporating the latent structure. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract Extensive labeled data for image annotation systems, which learn to assign class labels to image regions, is difﬁcult to obtain. [sent-6, score-0.778]

2 We explore a hybrid model framework for utilizing partially labeled data that integrates a generative topic model for image appearance with discriminative label prediction. [sent-7, score-1.382]

3 We propose three alternative formulations for imposing a spatial smoothness prior on the image labels. [sent-8, score-0.447]

4 Tests of the new models and some baseline approaches on three real image datasets demonstrate the effectiveness of incorporating the latent structure. [sent-9, score-0.47]

5 1 Introduction Image annotation, or image labeling, in which the task is to label each pixel or region of an image with a class label, is becoming an increasingly popular problem in the machine learning and machine vision communities [7, 14]. [sent-10, score-0.864]

6 State-of-the-art methods formulate image annotation as a structured prediction problem, and utilize methods such as Conditional Random Fields [8, 4], which output multiple values for each input item. [sent-11, score-0.42]

7 Learning labeling models with such data would help improve segmentation performance and relax the constraint of discriminative labeling methods. [sent-17, score-0.499]

8 A wide range of learning methods have been developed for using partially-labeled image data. [sent-18, score-0.276]

9 One approach adopts a discriminative formulation, and treats the unlabeled regions as missing data [16], Others take a semi-supervised learning approach by viewing unlabeled image regions as unlabeled data. [sent-19, score-0.561]

10 However, the common assumption about the smoothness of the label distribution with respect to the input data may not be valid in image labeling, due to large intra-class variation of object appearance. [sent-21, score-0.613]

11 Other semi-supervised methods adopt a hybrid approach, combining a generative model of the input data with a discriminative model for image labeling, in which the unlabeled data are used to regularize the learning of a discriminative model [6, 9]. [sent-22, score-0.769]

12 Our approach described in this paper extends the hybrid modeling strategy by incorporating a more ﬂexible generative model for image data. [sent-24, score-0.506]

13 In particular, we introduce a set of latent variables that capture image feature patterns in a hidden feature space, which are used to facilitate the labeling task. [sent-25, score-0.672]

14 First, we extend the Latent Dirichlet Allocation model (LDA) [3] to include not only input features but also label information, capturing co-occurrences within and between image feature patterns and object classes in the data set. [sent-26, score-0.695]

15 Unlike other topic models in image modeling [11, 18], our model integrates a generative model of image appearance and a discriminative model of region 1 labels. [sent-27, score-1.355]

16 Second, the original LDA structure does not impose any spatial smoothness constraint to label prediction, yet incorporating such a spatial prior is important for scene segmentation. [sent-28, score-0.594]

17 Previous approaches have introduced lateral connections between latent topic variables [17, 15]. [sent-29, score-0.438]

18 However, this complicates the model learning, and as a latent representation of image data, the topic variables can be non-smooth over the image plane in general. [sent-30, score-1.021]

19 In this paper, we model the spatial dependency of labels by two different structures: one introduces directed connections between each label variable and its neighboring topic variables, and the other incorporates lateral connections between label variables. [sent-31, score-1.175]

20 We will investigate whether these structures effectively capture the spatial prior, and lead to accurate label predictions. [sent-32, score-0.356]

21 The next section presents the base model, and two different extensions to handle label spatial dependencies. [sent-34, score-0.423]

22 2 Model description The structured prediction problem in image labeling can be formulated as follows. [sent-37, score-0.536]

23 Let an image x be represented as a set of subregions {xi }Nx . [sent-38, score-0.276]

24 The aim is to assign each xi a label li from a i=1 categorical set L. [sent-39, score-0.617]

25 For instance, subregion xi ’s can be image patches or pixels, and L consists of object classes. [sent-40, score-0.387]

26 We ﬁrst introduce our base model for capturing individual patterns in image appearance and label space. [sent-44, score-0.925]

27 Assume each subregion xi is represented by two features (ai , ti ), in which ai describes its appearance (including color, texture, etc. [sent-45, score-0.78]

28 ) in some appearance feature space A and ti is its position on the image plane T . [sent-46, score-0.795]

29 We achieve this by extending the latent Dirichlet allocation model to include both label and appearance. [sent-48, score-0.419]

30 More speciﬁcally, we assume each observation pair (ai , li ) in image x is generated from a mixture of K hidden ‘topic’ components shared across the whole dataset, given the position information ti . [sent-49, score-0.978]

31 Also, zi is used as an indicator variable to specify from which hidden topic component the pair (ai, li ) is generated. [sent-51, score-0.909]

33 We specify the appearance model P (ai |zi ) to be position invariant but the label predictor P (li |ai , ti , zi ) depends on the position information. [sent-54, score-1.077]

34 (a) Label prediction module P (li |ai , ti , zi ). [sent-56, score-0.613]

35 The label predictor P (li |ai , ti , zi ) is modeled by a probabilistic classiﬁer that takes (ai , ti , zi ) as its input and produces a properly normalized distribution for li . [sent-57, score-1.571]

36 We follow the convention of topic models and model the topic conditional distributions of the image appearance using a multinomial distribution with parameters βzi . [sent-62, score-1.046]

37 As the appearance features typically take on real values, we ﬁrst apply k-means clustering to the image features {ai } to build a visual vocabulary V. [sent-63, score-0.551]

38 Thus a feature ai in the appearance space A can be represented as a visual word v, and we have P (ai = v|zi = k) = βk,v . [sent-64, score-0.527]

39 While the topic prediction model in Equation 1 is able to capture regularly co-occurring patterns in the joint space of label and appearance, it ignores spatial priors on the label prediction. [sent-65, score-0.971]

40 However, 2 α α zi β α θ θ θ zi−1 zi zi+1 zi−1 ai−1 ai ai+1 zi zi+1 ai−1 ai ai+1 li−1 li li+1 ai K li ti β K β li li−1 li+1 K N t D t D D Figure 1: Left:A graphical representation of the base topic prediction model (Model I). [sent-66, score-3.412]

41 spatial priors, such as spatial smoothness, are crucial to labeling tasks, as neighboring labels are usually strongly correlated. [sent-71, score-0.525]

42 We introduce a dependency between each label variable and its neighboring topic variables. [sent-74, score-0.556]

43 In this model, each label value is predicted based on the summary information of topics within a neighborhood. [sent-75, score-0.298]

44 More speciﬁcally, we change the label prediction model into the following form: P (li |ai , ti , zN (i) ) = P (li |ai , ti , j∈N (i) wj zj ), (2) where N (i) is a predeﬁned neighborhood for site i, and wj is the weight for the topic variable zj . [sent-76, score-1.428]

45 We add lateral connections between label variables to build a Conditional Random Field of labels. [sent-84, score-0.364]

46 The joint label distribution given input image is deﬁned as 1 P (l|a, t, α) = exp{ f (li , lj ) + γ log Pb (li |a, t, α)}, (3) i,j∈N (i) i Z where Z is the partition function. [sent-85, score-0.65]

47 The pairwise potential f (li , lj ) = a,b uab δli ,a δlj ,b , and the unary potential is deﬁned as log output of the base topic prediction model weighted by γ. [sent-86, score-0.641]

48 Note that Pb (li |a, t, α) = zi P (li |ai , ti , zi )P (zi |a, t). [sent-88, score-0.735]

49 Note that the base model (Model I) obtains spatially smooth labels simply through the topics capturing location-dependent co-occurring appearance/label patterns, which tend to be nearby in image space. [sent-90, score-0.564]

50 Model II explicitly predicts a region’s label from the topics in its local neighborhood, so that neighboring labels share similar contexts deﬁned by latent topics. [sent-91, score-0.516]

51 The third model uses a conventional form of spatial dependency by directly incorporating local smoothing in the label ﬁeld. [sent-93, score-0.526]

52 3 Inference and Label Prediction Given a new image x = {a, t} and our topic models, we predict its labeling based on the Maximum Posterior Marginals (MPM) criterion: ∗ li = arg max P (li |a, t). [sent-95, score-1.04]

53 (4) li We consider the label inference procedure for three models separately as follows. [sent-96, score-0.649]

54 Models I&II;: The marginal label distribution P (li |a, t) can be computed as: P (li |a, t) = zN (i) P (li |ai , ti , 3 j∈N (i) wj zj )P (zN (i) |a, t) (5) The summation here is difﬁcult when N (i) is large. [sent-97, score-0.669]

55 Denote vi = j∈N (i) wj zj and vi,q = j∈N (i) wj q(zj ), where q(zj ) = {P (zj |a, t)} is the vector form of posterior distribution. [sent-99, score-0.424]

56 The marginal label distribution can be written as P (li |a, t) = P (li |ai , ti , vi ) P (zN (i) |a,t) . [sent-101, score-0.533]

58 P (zN (i) |a, t) (notice that vi P (zN (i) |a,t) = vi,q ), we have the following approximation: P (li |a, t) ≈ zN (i) P (li |ai , ti , j∈N (i) wj q(zj )). [sent-106, score-0.402]

59 Model III: We ﬁrst compute the unary potential of the CRF model from the base topic prediction model, i. [sent-107, score-0.439]

60 , Pb (li |a, t) = zi P (li |ai , ti , zi )P (zi |a, t). [sent-109, score-0.735]

61 Then the label marginals in Equation 4 are computed by applying loopy belief propagation to the conditional random ﬁeld. [sent-110, score-0.309]

62 In both situations, we need the conditional distribution of the hidden topic variables z given observed data components to compute the label prediction. [sent-111, score-0.584]

63 From Equation 1, we can derive the posterior of each topic variable zi given other variables, which is required by Gibbs sampling: P (zi = k|z−i , ai ) ∝ P (ai |zi )(αk + m∈S\i δzm ,k ) (7) where z−i denotes all the topic variables in z except zi , and S is the set of all sites. [sent-113, score-1.3]

64 4 Learning with partially labeled data Here we consider estimating the parameters of both extended models from a partially labeled image set D = {xn , ln }. [sent-115, score-0.643]

65 For an image xn , its label ln = (ln , ln ) in which ln denotes the observed labels, o h o and ln are missing. [sent-116, score-0.799]

66 The lower bound of the likelihood can be written as n n log P (li |an , tn , zN (i) ) + i i Q= n n log P (an |zi ) + log P (z) i i∈o P (zn |ln ,an ) o (9) i In the E step, the posterior distributions of the topic variables are estimated by a Gibbs sampling procedure similar to Equation 7. [sent-122, score-0.458]

67 It uses the following conditional probability: P (zi = k|z−i , ai , l, t) ∝ P (lj |aj , tj , zN (j) )P (ai |zi )(αk + j∈N (i)∩o δzm ,k ) (10) m∈S\i Note that any label variable is marginalized out if it is missing. [sent-123, score-0.567]

68 Denote the posterior distribution of z as q(·), the updating equation for parameters of the appearance module P (a|z) can be derived from the stationary point of Q: ∗ βk,v ∝ n,i n q(zi = k)δ(an , v). [sent-125, score-0.316]

69 i (11) The classiﬁer in the label prediction module is learned by maximizing the following log likelihood, n log P (li |an , tn , i i Lc = n,i∈o wj zj ) q(zN (i) ) n log P (li |an , tn , i i ≈ n,i∈o j∈N (i) 4 wj q(zj )). [sent-126, score-0.938]

70 The parameters of the base topic prediction model are learned using the same procedure as in Models I&II. [sent-132, score-0.396]

71 ; More speciﬁcally, we set N (i) = i and estimate the parameters of the appearance module and label classiﬁer based on Maximum Likelihood. [sent-133, score-0.525]

72 Given the base topic prediction model, we compute the marginal label probability Pb (li |a, t) and plug in the unary potential function in the CRF model (see Equation 3). [sent-135, score-0.678]

73 (13) n n where Zi = li exp{ j∈N (i) a,b uab δli ,a δlj ,b + γ log Pb (li |a, t)} is the normalizing constant. [sent-137, score-0.483]

74 This subset includes 240 images and 9 different label classes. [sent-142, score-0.288]

75 The second set is the full MSRC image dataset, including 591 images and 21 object classes. [sent-143, score-0.369]

76 We use the normalized cut segmentation algorithm [13] to build a super-pixel representation of the images, in which the segmentation algorithm is tuned to generate approximately 1000 segments for each image on average. [sent-146, score-0.38]

77 We extract a set of basic image features, including color, edge and texture information, from each pixel site. [sent-147, score-0.383]

78 We also augment each feature by a SIFT descriptor extracted from a 30 × 30 image patch centered at the super-pixel. [sent-154, score-0.317]

79 The image position of a super-pixel is the average position of its pixels. [sent-155, score-0.376]

80 To compute the vocabulary of visual words in the topic model, we apply k-means to group the super-pixel descriptors into clusters. [sent-156, score-0.315]

81 In the basic CRF, the conditional distribution of the labels of an image is deﬁned as: P (l|a, t) ∝ exp{ σu,v δli ,u δlj ,v + γ i,j u,v h(li |ai , ti )} (14) i where h(·) is the log output from the super-pixel classiﬁer. [sent-163, score-0.647]

82 We train the CRF model by maximizing its conditional pseudo-likelihood, and label the image based on the marginal distribution of each label variable, computed by the loopy belief propagation algorithm. [sent-164, score-0.878]

83 The classiﬁers for label prediction have 15 hidden units. [sent-233, score-0.351]

84 The appearance model for topics and the classiﬁer are initialized randomly. [sent-234, score-0.32]

85 Also, Model II and III improve the accuracy further by incorporating the label spatial priors. [sent-241, score-0.453]

86 We notice that the lateral connections between label variables are more effective than integrating information from neighboring latent topic variables. [sent-242, score-0.727]

87 In order to test the robustness of the latent feature representation, we evaluate our models using data with different amount of labeling information. [sent-245, score-0.295]

88 We use an image dilation operator on the image regions labeled as ‘void’, and control the proportion of labeled data by varying the diameters of the dilation operator (see [16] for similar processing). [sent-246, score-0.962]

89 The model setting is the same as in MSRC-9 except that we use a MLP with 20 hidden units for label prediction. [sent-277, score-0.348]

90 For the full MSRC set, the two extended versions of our model achieve the similar performance as in [14], and we can see that the latent topic representation 6 S_Class Model−I Model−II Model−III 0. [sent-281, score-0.395]

91 Right bottom: Examples of original labeling and labeling after dilation (the ratio is 36. [sent-297, score-0.394]

92 Also, our models have the same accuracy as reported in [5] on the Corel-B dataset, while we have a simpler label random ﬁeld and use a smaller training set. [sent-300, score-0.301]

93 It is interesting to note that the topics and spatial smoothness play less roles in the labeling performance on CorelB. [sent-301, score-0.398]

94 We can see that our models handle the extended regions better than those ﬁne object structures, due to the tendency of (over)smoothing caused by super-pixelization and the two spatial dependency structures. [sent-303, score-0.284]

95 6 Discussion In this paper, we presented a hybrid framework for image labeling, which combines a generative topic model with discriminative label prediction models. [sent-304, score-1.046]

96 The generative model extends latent Dirichlet allocation to capture joint patterns in the label and appearance space of images. [sent-305, score-0.726]

97 This latent representation of an image then provides an additional input to the label predictor. [sent-306, score-0.638]

98 We also incorporated the spatial dependency into the model structure in two different ways, both imposing a prior of spatial smoothness for labeling on the image plane. [sent-307, score-0.835]

99 The results of applying our methods to three different image datasets suggest that this integrated approach may extend to a variety of image databases with only partial labeling available. [sent-308, score-0.72]

100 Using a stronger appearance model may help us understand the role of different visual cues, as well as construct a more powerful generative model. [sent-318, score-0.347]

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