nips nips2005 nips2005-55 knowledge-graph by maker-knowledge-mining

55 nips-2005-Describing Visual Scenes using Transformed Dirichlet Processes

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Author: Antonio Torralba, Alan S. Willsky, Erik B. Sudderth, William T. Freeman

Abstract: Motivated by the problem of learning to detect and recognize objects with minimal supervision, we develop a hierarchical probabilistic model for the spatial structure of visual scenes. In contrast with most existing models, our approach explicitly captures uncertainty in the number of object instances depicted in a given image. Our scene model is based on the transformed Dirichlet process (TDP), a novel extension of the hierarchical DP in which a set of stochastically transformed mixture components are shared between multiple groups of data. For visual scenes, mixture components describe the spatial structure of visual features in an object–centered coordinate frame, while transformations model the object positions in a particular image. Learning and inference in the TDP, which has many potential applications beyond computer vision, is based on an empirically effective Gibbs sampler. Applied to a dataset of partially labeled street scenes, we show that the TDP’s inclusion of spatial structure improves detection performance, ﬂexibly exploiting partially labeled training images. 1

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract Motivated by the problem of learning to detect and recognize objects with minimal supervision, we develop a hierarchical probabilistic model for the spatial structure of visual scenes. [sent-9, score-0.335]

2 In contrast with most existing models, our approach explicitly captures uncertainty in the number of object instances depicted in a given image. [sent-10, score-0.159]

3 Our scene model is based on the transformed Dirichlet process (TDP), a novel extension of the hierarchical DP in which a set of stochastically transformed mixture components are shared between multiple groups of data. [sent-11, score-0.705]

4 For visual scenes, mixture components describe the spatial structure of visual features in an object–centered coordinate frame, while transformations model the object positions in a particular image. [sent-12, score-0.575]

5 1 Introduction In this paper, we develop methods for analyzing the features composing a visual scene, thereby localizing and categorizing the objects in an image. [sent-15, score-0.216]

6 We would like to design learning algorithms that exploit relationships among multiple, partially labeled object categories during training. [sent-16, score-0.253]

7 Working towards this goal, we propose a hierarchical probabilistic model for the expected spatial locations of objects, and the appearance of visual features corresponding to each object. [sent-17, score-0.298]

8 In contrast, generative approaches can discover large, visually salient categories (such as foliage and buildings [2]) without supervision. [sent-21, score-0.17]

9 Partial segmentations can then be used to learn semantically interesting categories (such as cars and pedestrians) which are less visually distinctive, or present in fewer training images. [sent-22, score-0.164]

10 Moreover, generative models provide a natural framework for learning contextual relationships between objects, and transferring knowledge between related, but distinct, visual scenes. [sent-23, score-0.136]

11 Constellation LDA Transformed DP Figure 1: A scene with faces as described by three generative models. [sent-24, score-0.127]

12 Note: The LDA and TDP images are sampled from models learned from training images, while the Constellation image is a hand-constructed illustration. [sent-28, score-0.132]

13 The principal challenge in developing hierarchical models for scenes is specifying tractable, scalable methods for handling uncertainty in the number of objects. [sent-29, score-0.204]

14 We address this problem using Dirichlet processes [3], a tool from nonparametric Bayesian analysis for learning mixture models whose number of components is not ﬁxed, but instead estimated from data. [sent-31, score-0.132]

15 In particular, we extend the recently proposed hierarchical Dirichlet process (HDP) [4, 5] framework to allow more ﬂexible sharing of mixture components between images. [sent-32, score-0.228]

16 The resulting transformed Dirichlet process (TDP) is naturally suited to our scene understanding application, as well as many other domains where “style and content” are combined to produce the observed data [6]. [sent-33, score-0.235]

17 2 by reviewing several related generative models for objects and scenes. [sent-35, score-0.15]

18 5 by demonstrating object recognition and segmentation in street scenes. [sent-40, score-0.238]

19 2 Generative Models for Objects and Scenes Constellation models [7] describe single objects via the appearance of a ﬁxed, and typically small, set of spatially constrained parts (see Fig. [sent-41, score-0.159]

20 Although they can successfully recognize objects in cluttered backgrounds, they do not directly provide a mechanism for detecting multiple object instances. [sent-43, score-0.293]

21 In addition, it seems difﬁcult to generalize the ﬁxed set of constellation parts to problems where the number of objects is uncertain. [sent-44, score-0.163]

22 More recently, distributions over hierarchical tree–structured partitions of image pixels have been used to segment simple scenes [9, 10]. [sent-46, score-0.256]

23 In addition, an image parsing [11] framework has been proposed which explains an image using a set of regions generated by generic or object–speciﬁc processes. [sent-47, score-0.136]

24 Inspired by techniques from the text analysis literature, several recent papers analyze scenes using a spatially unstructured bag of features extracted from local image patches (see Fig. [sent-51, score-0.232]

25 In particular, latent Dirichlet allocation (LDA) [13] describes the features xji in image j using a K component mixture model with parameters θk . [sent-53, score-0.36]

26 Each image reuses these same mixture parameters in different proportions πj (see the graphical model of Fig. [sent-54, score-0.199]

27 By appropriately deﬁning these shared mixtures, LDA may be used to discover object cat- egories from images of single objects [2], categorize natural scenes [14], and (with a slight extension) parse presegmented captioned images [15]. [sent-56, score-0.524]

28 While these LDA models are sometimes effective, their neglect of spatial structure ignores valuable information which is critical in challenging object detection tasks. [sent-57, score-0.231]

29 We recently proposed a hierarchical extension of LDA which learns shared parts describing the internal structure of objects, and contextual relationships among known groups of objects [16]. [sent-58, score-0.423]

30 The transformed Dirichlet process (TDP) addresses a key limitation of this model by allowing uncertainty in the number and identity of the objects depicted in each image. [sent-59, score-0.258]

31 1, the TDP effectively provides a textural model in which locally unstructured clumps of features are given global spatial structure by the inferred set of objects underlying each scene. [sent-62, score-0.278]

32 We then introduce the transformed Dirichlet process (TDP) (Sec. [sent-68, score-0.148]

33 Computationally, this process is conveniently described by a set z of independently sampled variables zi ∼ Mult(β) indicating the component of the mixture G(θ) (see eq. [sent-83, score-0.176]

34 This process is sometimes described by analogy to a Chinese restaurant in which the (inﬁnite collection of) tables correspond to the mixture components θk , and customers to observations xi [4]. [sent-90, score-0.385]

35 Customers are social, tending to sit at tables with many other customers (observations), and each table shares a single dish (parameter). [sent-91, score-0.336]

36 For example, in this paper’s applications each group is an image, and the data are visual features composing a scene. [sent-94, score-0.164]

37 , xjnj ) denote the nj exchangeable data points in group j. [sent-98, score-0.155]

38 LDA directly assigns observations xji to clusters via indicators zji . [sent-103, score-0.34]

39 HDP and TDP models use “table” indicators tji as an intermediary between observations and assignments kjt to an inﬁnite global mixture with weights β. [sent-104, score-0.743]

40 Specializing the TDP to visual scenes (right), we model the position yji and appearance wji of features using distributions ηo indexed by unobserved object categories oji . [sent-106, score-0.778]

41 To construct an HDP, a global probability measure G0 ∼ DP(γ, H) is ﬁrst chosen to deﬁne a set of shared mixture components. [sent-108, score-0.181]

42 The generative process underlying HDPs may be understood in terms of an extension of the DP analogy known as the Chinese restaurant franchise [4]. [sent-112, score-0.204]

43 Each group deﬁnes a separate restaurant in which customers (observations) xji sit at tables tji . [sent-113, score-0.689]

44 Each table shares a single dish (parameter) θ, which is ordered from a menu G0 shared among restaurants (groups). [sent-114, score-0.202]

45 Letting kjt indicate the parameter θkjt assigned to table t in group j, we may integrate over G0 and Gj (as in eq. [sent-115, score-0.442]

46 As before, customers prefer tables t at which many customers njt are already seated (eq. [sent-126, score-0.27]

47 Each new table is assigned a dish kj t according to eq. [sent-128, score-0.203]

48 Given the assignments tj and kj for group j, observations are sampled as xji ∼ F (θzji ), where zji = kjtji indexes the shared parameters assigned to the table associated with xji . [sent-133, score-0.802]

49 2, the group distributions Gj are derived from the global distribution G0 by resampling the mixture weights from a Dirichlet process (see eq. [sent-136, score-0.204]

50 Consider, for example, a Gaussian distribution describing the location at which object features are detected in an image. [sent-139, score-0.24]

51 While the covariance of that distribution may stay relatively constant across object instances, the mean will change dramatically from image to image (group to group), depending on the objects’ position relative to the camera. [sent-140, score-0.263]

52 Motivated by these difﬁculties, we propose the Transformed Dirichlet Process (TDP), an extension of the HDP in which global mixture components undergo a set of random transformations before being reused in each group. [sent-141, score-0.333]

53 (1) to create a global measure describing both parameters and transformations: ∞ βk δ(θ, θk )q(ρ | φk ) G0 (θ, ρ) = θk ∼ H φk ∼ R (6) k=1 As before, β is sampled from a stick–breaking process with parameter γ. [sent-144, score-0.139]

54 Marginalizing over transformations ρ, Gj (θ) reuses parameters from G0 (θ) exactly as in eq. [sent-146, score-0.129]

55 Conditioning on θk , it can be shown that Gj (ρ | θk ) ∼ DP(αβk , Q(φk )), so that the proportions ω jk of features associated with each transformation of θk follow a stick–breaking process with parameter αβk . [sent-149, score-0.17]

56 ¯ ¯ Each observation xji is now generated by sampling (θji , ρji ) ∼ Gj , and then choosing ¯ ¯ ¯ xji ∼ F (θji , ρji ) from a distribution which transforms θji by ρji . [sent-150, score-0.366]

57 Although the global ¯ family of transformation distributions Q(φ) is typically non–atomic, the discreteness of Gj ensures that transformations are shared between observations within group j. [sent-151, score-0.29]

58 Computationally, the TDP is more conveniently described via an extension of the Chinese restaurant franchise analogy (see Fig. [sent-152, score-0.138]

59 As before, customers (observations) xji sit at tables tji according to the clustering bias of eq. [sent-154, score-0.589]

60 (4), and new tables choose dishes according to their popularity across the franchise (eq. [sent-155, score-0.143]

61 Now, however, the dish (parameter) θkjt at table t is seasoned (transformed) according to ρjt ∼ q(ρjt | φkjt ). [sent-157, score-0.141]

62 The simplest implementation samples table assignments t, cluster assignments k, transformations ρ, and parameters θ, φ. [sent-161, score-0.327]

63 Let t−ji denote all table assignments excluding tji , and deﬁne k−jt , ρ−jt similarly. [sent-162, score-0.31]

64 2), we have p tji = t | t−ji , k, ρ, θ, x ∝ p t | t−ji f xji | θkjt , ρjt (8) The ﬁrst term is given by eq. [sent-164, score-0.394]

65 For a ﬁxed set of transformations ρ, the second term is a simple likelihood evaluation for existing tables, while new tables may be evaluated by marginalizing over possible cluster assignments (eq. [sent-166, score-0.3]

66 Right: Global TDP distribution G0 (θ, ρ) over both clusters θ (solid) and translations ρ of those clusters (dashed). [sent-173, score-0.136]

67 Conditioned on kjt , we again use conjugacy to sample ρjt . [sent-175, score-0.316]

68 For the moment, we assume that the observed data xji = (oji , yji ), where yji is the position of a feature corresponding to object category oji , and the number of object categories O is known (see Fig. [sent-182, score-0.962]

69 We then choose cluster parameters θk = (¯k , µk , Λk ) to describe the mean µk and o covariance Λk of a Gaussian distribution over feature positions, as well as the single object category ok assigned to all observations sampled from that cluster. [sent-184, score-0.39]

70 Although this cluster ¯ parameterization does not capture contextual relationships between object categories, the results of Sec. [sent-185, score-0.259]

71 5 demonstrate that it nevertheless provides an effective model of the spatial variability of individual categories across many different scenes. [sent-186, score-0.141]

72 Density models for spatial transformations have been previously used to recognize isolated objects [17], and estimate layered decompositions of video sequences [18]. [sent-189, score-0.28]

73 In contrast, the proposed TDP models the variability of object positions across scenes, and couples this with a nonparametric prior allowing uncertainty in the number of objects. [sent-190, score-0.159]

74 To ensure that the TDP scene model is identiﬁable, we deﬁne p (ρjt | kj , φ) to be a zero– mean Gaussian with covariance φkjt . [sent-191, score-0.143]

75 The parameter prior R is uniform across object categories, while R and H both use inverse–Wishart position distributions, weakly biased towards moderate covariances. [sent-192, score-0.159]

76 3 shows a 2D synthetic example based on a single object category (O = 1). [sent-194, score-0.226]

77 In contrast, the learned HDP uses a large set of global clusters to discretize the transformations underlying the data, and thus generalizes poorly to new translations. [sent-196, score-0.21]

78 1 to images, we must learn the relationship between object categories and visual features. [sent-200, score-0.311]

79 We assume that the appearance wji of each detected feature is independently sampled conditioned on the underlying object category oji (see Fig. [sent-204, score-0.484]

80 Placing a symmetric Dirichlet prior, with parameter λ, on each category’s multinomial appearance distribution ηo , p wji = b | oji = o, w−ji , t, k, θ ∝ cbo + λ (10) where cbo is the number of times feature b is currently assigned to object o. [sent-206, score-0.476]

81 Because a single object category is associated with each cluster, the Gibbs sampler of Sec. [sent-207, score-0.279]

82 5 Analyzing Street Scenes To demonstrate the potential of our TDP scene model, we consider a set of street scene images (250 training, 75 test) from the MIT-CSAIL database. [sent-211, score-0.265]

83 All categories were labeled in 112 images, while in the remainder only cars were segmented. [sent-213, score-0.132]

84 Training from semi–supervised data is accomplished by restricting object category assignments for segmented features. [sent-214, score-0.293]

85 4 shows the four global object clusters learned following 100 Gibbs sampling iterations. [sent-216, score-0.27]

86 There is one elongated car cluster, one large building cluster, and two road clusters with differing shapes. [sent-217, score-0.267]

87 Interestingly, the model has automatically determined that building features occur in large homogeneous patches, while road features are sparse and better described by many smaller transformed clusters. [sent-218, score-0.321]

88 4 shows segmentations produced by averaging these samples, as well as transformed clusters from the ﬁnal iteration. [sent-221, score-0.222]

89 Qualitatively, results are typically good, although foliage is often mislabeled as road due to the textural similarities with features detected in shadows across roads. [sent-222, score-0.156]

90 For comparison, we also trained an LDA model based solely on feature appearance, allowing three topics per object category and again using object labels to restrict the Gibbs sampler’s assignments [16]. [sent-223, score-0.452]

91 4, our TDP model of spatial scene structure signiﬁcantly improves segmentation performance. [sent-225, score-0.165]

92 In addition, through the set of transformed car clusters generated by the Gibbs sampler, the TDP explicitly estimates the number of object instances underlying each image. [sent-226, score-0.409]

93 These detections, which are not possible using LDA, are based on a single global parsing of the scene which automatically estimates object locations without a “sliding window” [1]. [sent-227, score-0.321]

94 6 Discussion We have developed the transformed Dirichlet process, a hierarchical model which shares a set of stochastically transformed clusters among groups of data. [sent-228, score-0.498]

95 Applied to visual scenes, TDPs provide a model of spatial structure which allows the number of objects generating an image to be automatically inferred, and lead to improved detection performance. [sent-229, score-0.292]

96 8 1 Figure 4: TDP analysis of street scenes containing cars (red), buildings (green), and roads (blue). [sent-262, score-0.23]

97 Top right: Global model G0 describing object shape (solid) and expected transformations (dashed). [sent-263, score-0.291]

98 Left: Four test images (ﬁrst row), estimated segmentations of features into object categories (second row), transformed global clusters associated with each image interpretation (third row), and features assigned to different instances of the transformed car cluster (fourth row). [sent-265, score-0.989]

99 A Bayesian approach to unsupervised one-shot learning of object categories. [sent-313, score-0.159]

100 A Bayesian hierarchical model for learning natural scene categories. [sent-370, score-0.183]

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