cvpr cvpr2013 cvpr2013-186 knowledge-graph by maker-knowledge-mining

186 cvpr-2013-GeoF: Geodesic Forests for Learning Coupled Predictors


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Author: Peter Kontschieder, Pushmeet Kohli, Jamie Shotton, Antonio Criminisi

Abstract: Conventional decision forest based methods for image labelling tasks like object segmentation make predictions for each variable (pixel) independently [3, 5, 8]. This prevents them from enforcing dependencies between variables and translates into locally inconsistent pixel labellings. Random field models, instead, encourage spatial consistency of labels at increased computational expense. This paper presents a new and efficient forest based model that achieves spatially consistent semantic image segmentation by encoding variable dependencies directly in the feature space the forests operate on. Such correlations are captured via new long-range, soft connectivity features, computed via generalized geodesic distance transforms. Our model can be thought of as a generalization of the successful Semantic Texton Forest, Auto-Context, and Entangled Forest models. A second contribution is to show the connection between the typical Conditional Random Field (CRF) energy and the forest training objective. This analysis yields a new objective for training decision forests that encourages more accurate structured prediction. Our GeoF model is validated quantitatively on the task of semantic image segmentation, on four challenging and very diverse image datasets. GeoF outperforms both stateof-the-art forest models and the conventional pairwise CRF.

Reference: text


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Kohli University of Technology, Austria Abstract Conventional decision forest based methods for image labelling tasks like object segmentation make predictions for each variable (pixel) independently [3, 5, 8]. [sent-3, score-0.706]

2 This prevents them from enforcing dependencies between variables and translates into locally inconsistent pixel labellings. [sent-4, score-0.232]

3 This paper presents a new and efficient forest based model that achieves spatially consistent semantic image segmentation by encoding variable dependencies directly in the feature space the forests operate on. [sent-6, score-0.921]

4 Such correlations are captured via new long-range, soft connectivity features, computed via generalized geodesic distance transforms. [sent-7, score-0.598]

5 A second contribution is to show the connection between the typical Conditional Random Field (CRF) energy and the forest training objective. [sent-9, score-0.505]

6 This analysis yields a new objective for training decision forests that encourages more accurate structured prediction. [sent-10, score-0.539]

7 GeoF outperforms both stateof-the-art forest models and the conventional pairwise CRF. [sent-12, score-0.493]

8 In fact, conventional decision forests ignore the structure in output spaces and make predictions for each output variable independently. [sent-22, score-0.586]

9 This assumption prevents them from enforcing dependencies between variables, and for semantic segmentation tasks, translates into pixel labellings that do not follow object boundaries and are inconsistent with context. [sent-23, score-0.405]

10 In the forest approach in [13], spatial smoothness is achieved by combining structured class-labels that are learned by incorporating joint statistics in a small neighborhood. [sent-28, score-0.431]

11 Our framework overcomes the above-mentioned problem by incorporating learned spatial context directly within the forest itself. [sent-31, score-0.426]

12 Long-range corre- lations between pixel labels are captured via new soft connectivity features which can be computed efficiently using generalized geodesic distance transforms. [sent-33, score-0.663]

13 Another contribution is to analyse the relationship between a typical CRFlike energy and the forest training objective. [sent-34, score-0.505]

14 This analysis leads to a new objective for training decision forests that produces more accurate semantic segmentation. [sent-35, score-0.602]

15 Quantitative results demonstrate the superiority of our model both in terms of accuracy and efficiency, with respect to state-ofthe-art forest models and grid-based pairwise CRFs. [sent-37, score-0.435]

16 The recent work on autocontext [24, 26], stacking [18, 28], deep learning [14, 15] and entanglement [17] has shown how a sequence of classifiers using the output of the previous classifier as input to the next can both effectively capture spatial context (e. [sent-40, score-0.221]

17 In [9], the relationship between anytime classification and intermediate predictions within decision trees is shown. [sent-43, score-0.32]

18 Our geodesic forest model (GeoF) can be seen as a gen- eralization of semantic texton forests [24], auto-context [24, 26], and entanglement forests [17]. [sent-45, score-1.625]

19 In fact, GeoF builds upon these models by using: (i) new, long-range soft connectivity features, and (ii) a new field-inspired objective for forest training. [sent-46, score-0.647]

20 ΩW e⊂ ca Nst th→e seamnadnt aic 2 segmentation otans kis as nthotate do fp associating eaastch th pixel p with its corresponding discrete class label c ∈ C. [sent-50, score-0.194]

21 vWarei use cd etodenote predictions obtained at depth d in the tree. [sent-61, score-0.162]

22 (2) exten- seeks parameters θj which aim to maximize both the class purity and spatial compactnes of pixel clusters in child nodes. [sent-70, score-0.174]

23 Decision forests [3, 5, 8] further assume that the poste? [sent-75, score-0.313]

24 Typically, a decision tree is trained greedily, where for each split node j the parameters θj associated with a low energy (e. [sent-88, score-0.275]

25 Figure 1 illustrates this point and suggests that ideally we would like training to maximize class purity as well as encouraging spatial compactness of the resulting pixel clusters. [sent-91, score-0.221]

26 Coupling forest predictions to reveal hidden correla- tions. [sent-92, score-0.503]

27 In this paper, we overcome this problem and encourage forests 666666 to produce spatially compact/coherent pixel labellings. [sent-94, score-0.378]

28 In what follows, we will show how a learned model of spatial context can be encoded within a decision forest directly. [sent-95, score-0.534]

29 One of the key theoretical insights of our work is the observation that although forests make predictions for each variable independently, these predictions are related due to correlations at the feature level. [sent-97, score-0.527]

30 For instance, in the semantic image segmentation task consider the class predictions of two pixels p and q. [sent-98, score-0.334]

31 Therefore, output-variable dependencies can be encoded in the features that the forest operates on. [sent-102, score-0.46]

32 Long-range, soft connectivity features The need for long-range connectivity features. [sent-106, score-0.354]

33 In [16, 23, 27] the authors have shown how simple pixel comparison features can be effective in classification tasks when used within a decision forest. [sent-107, score-0.173]

34 Since the shortest path connecting them has a high geodesic length (it cuts through high image gradients, see definition in (4)), this provides a hint that the two points may not be part of the same object/class. [sent-115, score-0.456]

35 (a) Given a pixel pair (a reference and a probe pixel) popular features only look at the intensities at the two pixel positions, and ignore what happens in between. [sent-117, score-0.277]

36 (b) In contrast, the length of the shortest path connecting the pixel pair carries richer information. [sent-118, score-0.175]

37 The geodesic length of the shortest path connecting two points provides hints about the points belonging (or not) to the same object class (e. [sent-119, score-0.535]

38 They are based on the use of generalized geodesic distances, as introduced in [7] and summarized next. [sent-123, score-0.383]

39 Given a grey-valued image J, and a real-valued object “soft mask” (that encodes pixel likelihood) M(p) : Ω ∈ → [0, 1] the generalized geodesic ldihisotaondc)e M MQ( ips )d e:fi Ωne ∈d as fo→llow [0s,:1 Nd Q(p;M,∇J) = p m? [sent-125, score-0.448]

40 )) (4) with the geodesic distance between two points p and q: δ(p,q) =Γ∈inPfp,q? [sent-128, score-0.346]

41 Soft connectivity between a pixel and a class region. [sent-134, score-0.283]

42 They efficiently capture long-range connectivity (of a pixel to a class region). [sent-158, score-0.283]

43 We can use those probabilities to construct the soft masks M needed for the generalized geodesic distance transform, and the corresponding filtered probabilities will be g(c = torso) and g(c = left leg). [sent-160, score-0.561]

44 Contrast sensitivity is modulated by the geodesic strength parameter γ ≥ 0 in (5). [sent-162, score-0.346]

45 Entangled geodesic forests Here we are interested in extremely efficient semantic segmentation. [sent-166, score-0.757]

46 Thus, we build upon decision forests [3, 5, 8], because of their speed and flexibility. [sent-167, score-0.421]

47 4 in the spirit of entangled forests [17] we train all trees: (i) in parallel, (ii) in breadthfirst order, and (iii) in sections. [sent-172, score-0.672]

48 In fact, the class posteriors p(c|v) of the previous section may be tuhseed c as input freioatrusre ps( |tov )th oef tnheext p r[1ev7]io. [sent-177, score-0.168]

49 Given a class posterior psi (c|v) computed at the ith section (with i> 0), its geodesically )sm coomotphueted dve artsti ohne i is defined as gsi(c|v(p)) = W1psi(c|v(p)) e−Q(p;psi(c|σv2(Ω)),∇J)2 (6) Figure 4. [sent-184, score-0.181]

50 The trees are entangled because intermediate predictions of their top section are used (together with raw intensity features) as features for training of the lower sections. [sent-187, score-0.625]

51 Feature responses for a reference pixel r are defined as a function of tree depth d, and as sum, differences or absolute differences between two pixel probe values in different feature channels3, i. [sent-198, score-0.365]

52 the intermediate class posteriors computed in the( cs|e(cpti)o),n i s. [sent-204, score-0.201]

53 The entangled feature channels (k = 1, 2) are available only for section s1 and greater, and are computed very efficiently as table look-ups. [sent-210, score-0.359]

54 Field-inspired forest training objective This section describes our second contribution: the use of a new objective for the forest training procedure. [sent-213, score-0.958]

55 Most algorithms for training classification forests are greedy and find the optimal parameters for a split node j as θj = argminθ E(Sj , θ) (Fig. [sent-216, score-0.393]

56 ∈Cn(c,Sij) logn(|cS,jiS|ji) (7) with n(c, S) denoting the number of training pixels of class c i tnh hth ne( training nsuotbinsget tSh (please erre foefr t rtoa Fig. [sent-225, score-0.173]

57 f training each tree split node by using an MRF energy E = ERF, which is typically defined as ERF(Sj,θ) =i∈? [sent-229, score-0.214]

58 Thus, conventional entropy-based tree training corresponds exactly to minimizing an MRF-like energy which uses the log-loss as unary and no pairwise term4. [sent-238, score-0.323]

59 This is particularly important in the context of semantic segmentation, where often the pixels in the background class are much more numerous than those in other classes. [sent-248, score-0.207]

60 Results and Comparisons We validate our semantic segmentation approach on four, very diverse labelled image datasets. [sent-267, score-0.218]

61 We have the following 9 classes: background (BG), heart (HR), liver (LI), spleen (SP), left/right lung (LL/RL), left/right kidney (LK/RK) and aorta (AO). [sent-276, score-0.486]

62 In the latter, as energy model, we used a log-loss as unary term and a contrast-sensitive Potts model as pairwise term. [sent-289, score-0.146]

63 Additionally, we also implemented an auto-context [26] version of classification forests where: A first forest is trained using raw intensity features; Then, a second forest is trained using both raw intensities and the probabilities from the first forest as features. [sent-290, score-1.671]

64 Both entangled geodesic features and un-entangled class posteriors are 666999 Figure5. [sent-291, score-0.873]

65 Entangling the p feature channels only helps spatial Enabling the long-range geodesic feature channels g helps The spurious hand region is gone. [sent-302, score-0.346]

66 (f, i, l) Results from forest with geodesic entanglement and field-inspired energy term. [sent-303, score-0.926]

67 The combination of entangled geodesic features and log-loss training produces coherent segmentations without the need for field-based post-processing. [sent-314, score-0.752]

68 For all forest based algorithms we fix T = 10 and D = 20, except for the CamVid dataset where we use a maximum depth D = 17 since the number of training samples is considerably smaller. [sent-316, score-0.498]

69 However, decision forests are well-suited for GPU implementations [22]. [sent-318, score-0.421]

70 The baseline forest (0 1) yields a mean Jaccard score of only 38. [sent-320, score-0.396]

71 2%, still lower than what our implemented auto-context forest (0 3) and our proposed geodesic forests achieve (0 7-16). [sent-324, score-1.055]

72 Both the use of entangled geodesic features and the field-inspired energy help achieve the highest accuracy in this dataset. [sent-325, score-0.767]

73 Entangled geodesic forests using either of the two energy models (14 ,16) work better than the conventional forest (0 1). [sent-329, score-1.175]

74 Accuracy as a function of tree depth D, for different forest variants, evaluated on the LFW face dataset. [sent-332, score-0.523]

75 Our auto-context geodesic forest (0 8) does well, but the second forest does not seem to yield much additional improvement. [sent-334, score-1.138]

76 In terms of runtime, the standard forest + CRF (0 2) takes ∼ 0. [sent-335, score-0.396]

77 3% (0 2) we find again that providing entangled geodesic features improves on all our compared methods. [sent-345, score-0.705]

78 The autocontext forest performs well here too, even without these additional features. [sent-346, score-0.465]

79 However, the best results are achieved 777000 with one or two sections ofentanglement in geodesic forests (12 16). [sent-347, score-0.659]

80 2s per frame (w1h2i,le geodesic efo CrResFts a p(1p r2o) ancehed (0 ∼2 0 ta. [sent-349, score-0.346]

81 e best results are achieved by our auto-context geodesic forests (0 7, 0 8) which yield strong improvements over the baseline (+ 6. [sent-354, score-0.659]

82 0 3, 0 7 , 0 8) results in higher runtimes as two forests need to be evaluated (resulting in ∼ 1. [sent-359, score-0.313]

83 r3am9se/f rwamhilee) entangled geodesic fhor (e0st2s) are emsu c∼h 1fa. [sent-363, score-0.705]

84 3% which we are able to considerably outperform with all our geodesic forest variants. [sent-371, score-0.742]

85 The best performing geodesic forest (16) improves over the recent work in [13] (+2. [sent-372, score-0.742]

86 tried training forests by adding pairwise terms or other global smoothness terms in the energy (10), but without consistently improving the accuracy further. [sent-383, score-0.461]

87 7a we see that at depth 10 (after one level of entanglement) when the reference pixel is in the liver, the two probes tend to be selected (during training) to also be in the liver. [sent-391, score-0.23]

88 7b the probes tend to be selected frequently also in the heart and right lung regions. [sent-395, score-0.174]

89 Conclusion This paper has presented a new forest-based model for structured-output learning, applied to the task of semantic Class of reference pixels = liver (LI) Depht 10 Depht 13 Depht 17 (a)ABRLSHGOKLPR IBGHRLISP RLK AO0 0. [sent-402, score-0.247]

90 8765432 Class of reference pixels = left kidney (LK) Figure 7. [sent-413, score-0.185]

91 In this dataset (CT) classes are: background (BG), heart (HR), liver (LI), spleen (SP), l. [sent-418, score-0.229]

92 in b’ when trying to identify the left kidney it helps to use probes either in the spleen region (just above the left kidney) or in the left kidney itself (encouraging local smoothness). [sent-426, score-0.423]

93 Our model encourages spatial smoothness and long-range, semantic context within the forest itself, via the use of new, soft connectivity features which build upon entangled, generalized geodesic distances. [sent-428, score-1.122]

94 In addition, the paper shows how training forests by minimizing a new random field-inspired energy yields higher accuracy than entropy based approaches. [sent-429, score-0.422]

95 27 6 for our geodesic forest algorithm as compared to existing techniques (e. [sent-490, score-0.742]

96 random classification forest, and forest + CRF), for four different labelled image databases. [sent-492, score-0.466]

97 As time goes by anytime semantic segmentation with iterative context forests. [sent-498, score-0.211]

98 Structured class-labels in random forests for semantic image labelling. [sent-528, score-0.411]

99 Entangled decision forests and their application for semantic segmentation of CT images. [sent-561, score-0.569]

100 Hough forest random field for object recognition and segmentation. [sent-586, score-0.396]


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