nips nips2007 nips2007-172 knowledge-graph by maker-knowledge-mining

172 nips-2007-Scene Segmentation with CRFs Learned from Partially Labeled Images

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Author: Bill Triggs, Jakob J. Verbeek

Abstract: Conditional Random Fields (CRFs) are an effective tool for a variety of different data segmentation and labeling tasks including visual scene interpretation, which seeks to partition images into their constituent semantic-level regions and assign appropriate class labels to each region. For accurate labeling it is important to capture the global context of the image as well as local information. We introduce a CRF based scene labeling model that incorporates both local features and features aggregated over the whole image or large sections of it. Secondly, traditional CRF learning requires fully labeled datasets which can be costly and troublesome to produce. We introduce a method for learning CRFs from datasets with many unlabeled nodes by marginalizing out the unknown labels so that the log-likelihood of the known ones can be maximized by gradient ascent. Loopy Belief Propagation is used to approximate the marginals needed for the gradient and log-likelihood calculations and the Bethe free-energy approximation to the log-likelihood is monitored to control the step size. Our experimental results show that effective models can be learned from fragmentary labelings and that incorporating top-down aggregate features signiﬁcantly improves the segmentations. The resulting segmentations are compared to the state-of-the-art on three different image datasets. 1

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 For accurate labeling it is important to capture the global context of the image as well as local information. [sent-2, score-0.278]

2 We introduce a CRF based scene labeling model that incorporates both local features and features aggregated over the whole image or large sections of it. [sent-3, score-0.357]

3 Secondly, traditional CRF learning requires fully labeled datasets which can be costly and troublesome to produce. [sent-4, score-0.113]

4 We introduce a method for learning CRFs from datasets with many unlabeled nodes by marginalizing out the unknown labels so that the log-likelihood of the known ones can be maximized by gradient ascent. [sent-5, score-0.238]

5 Our experimental results show that effective models can be learned from fragmentary labelings and that incorporating top-down aggregate features signiﬁcantly improves the segmentations. [sent-7, score-0.264]

6 The resulting segmentations are compared to the state-of-the-art on three different image datasets. [sent-8, score-0.131]

7 1 Introduction In visual scene interpretation the goal is to assign image pixels to one of several semantic classes or scene elements, thus jointly performing segmentation and recognition. [sent-9, score-0.489]

8 This is useful in a variety of applications ranging from keyword-based image retrieval (using the segmentation to automatically index images) to autonomous vehicle navigation [1]. [sent-10, score-0.176]

9 Their applications range from low-level noise reduction [2] to high-level object or category recognition (this paper) and semi-automatic object segmentation [3]. [sent-12, score-0.2]

10 CRF models can be applied either at the pixel-level [5, 6, 7] or at the coarser level of super-pixels or patches [8, 9, 10]. [sent-14, score-0.176]

11 In this paper we label images at the level of small patches, using CRF models that incorporate both purely local (single patch) feature functions and more global ‘context capturing’ feature functions that depend on aggregates of observations over the whole image or large regions. [sent-15, score-0.389]

12 In practice it is difﬁcult and time-consuming to label every pixel in an image and most of the available image interpretation datasets contain unlabeled pixels. [sent-17, score-0.461]

13 Working at the patch level exacerbates this problem because many patches contain several different pixel-level labels. [sent-18, score-0.438]

14 Our CRF training algorithm handles this by allowing partial and mixed labelings and optimizing the probability for the model segmentation to be consistent with the given labeling constraints. [sent-19, score-0.338]

15 2 A Conditional Random Field using Local and Global Image Features We represent images as rectangular grids of patches at a single scale, associating a hidden class label with each patch. [sent-21, score-0.34]

16 Our CRF models incorporate 4-neighbor couplings between patch labels. [sent-22, score-0.348]

17 The local image content of each patch is encoded using texture, color and position descriptors as in [10]. [sent-23, score-0.392]

18 For texture we compute the 128-dimensional SIFT descriptor [11] of the patch and vector quantize it by nearest-neighbour assignement against a ks = 1000 word texton dictionary learned by k-means clustering of all patches in the training dataset. [sent-24, score-0.53]

19 Position is encoded by overlaying the image with an m × m grid of cells (m = 8) and using the index of the cell in which the patch falls as its position feature. [sent-26, score-0.387]

20 Each patch is thus coded by three binary vectors with respectively ks , kh and kp = m2 bits, each with a single bit set corresponding to the observed visual word. [sent-27, score-0.389]

21 Generatively, the three modalities are modelled as being independent given the patch label. [sent-29, score-0.262]

22 The naive Bayes model of the image omits the 4-neighbor couplings and thus assumes that each patch label depends only on its three observation functions. [sent-30, score-0.478]

23 On the MSRC 9class image dataset this model returns an average classiﬁcation rate of 67. [sent-32, score-0.124]

24 1% (see Section 4), so isolated appearance alone does not sufﬁce for reliable patch labeling. [sent-33, score-0.284]

25 In recent years models based on histograms of visual words have proven very successful for image categorization (deciding whether or not the image as a whole belongs to a given category of scenes) [13]. [sent-34, score-0.236]

26 Motivated by this, many of our models take the global image context into account by including observation functions based on image-wide histograms of the visual words of their patches. [sent-35, score-0.185]

27 The hope is that this will help to overcome the ambiguities that arise when patches are classiﬁed in isolation. [sent-36, score-0.176]

28 To this end, we deﬁne a conditional model for patch labels that incorporates both local patch level features and global aggregate features. [sent-37, score-0.833]

29 , C} denote the label of patch i, yi denote the W -dimensional concatenated binary indicator vector of its three visual words (W = ks + hh + kp ), and h denote the normalized histogram of all visual words in the image, i. [sent-41, score-0.498]

30 The conditional probablity of the label xi is then modeled as p(xi = l|yi , h) ∝ exp − W w=1 (αwl yiw + βwl hw ) , (1) where αwl , βwl are W × C matrices of coefﬁcients to be learned. [sent-44, score-0.168]

31 We can think of this as a multiplicative combination of a local classiﬁer based on the patch-level observation yi and a global context or bias based on the image-wide histogram h. [sent-45, score-0.11]

32 To account for correlations among spatially neighboring patch labels, we add couplings between the labels of neighboring patches to the single patch model (1). [sent-46, score-0.801]

33 Let X denote the collection of all patch labels in the image and Y denote the collected patch features. [sent-47, score-0.658]

34 Then our CRF model for the coupled patch labels is: p(X|Y ) ∝ exp − E(X|Y ) , (2) W φij (xi , xj ), (αwxi yiw + βwxi hw ) + E(X|Y ) = i w=1 (3) i∼j where i ∼ j denotes the set of all adjacent (4-neighbor) pairs of patches i, j. [sent-48, score-0.533]

35 We have explored two forms of pairwise potential: φij (xi , xj ) = γxi ,xj [xi = xj ], and φij (xi , xj ) = (σ + τ dij ) [xi = xj ], where [·] is one if its argument is true and zero otherwise, and dij is some similarity measure over the appearance of the patches i and j. [sent-50, score-0.295]

36 The second potential is designed to favor label transitions at image locations with high contrast. [sent-52, score-0.153]

37 As in [3] we use dij = exp(− zi − zj 2 /(2λ)), with zi ∈ IR3 denoting the average RGB value in the patch and λ = zi − zj 2 , the average L2 norm between neighboring RGB values in the image. [sent-53, score-0.294]

38 2 Figure 1: Graphical representation of the model with a single image- wide aggregate feature function denoted by h. [sent-56, score-0.144]

39 Arrows denote single node potentials due to feature functions, and undirected edges represent pairwise potentials. [sent-58, score-0.105]

40 The dashed lines indicate the aggregation of the single- patch observations yi into h. [sent-59, score-0.29]

41 In practice this is restrictive and it is useful to develop methods that can learn from partially labeled examples – images that include either completely unlabeled patches or ones with a retricted but nontrivial set of possible labels. [sent-67, score-0.51]

42 Formally, we will assume that an incomplete labeling X is known to belong to an associated set of admissible labelings A and we maximise the log- likelihood for the model to predict any labeling in A: L = log p(X ∈ A | Y ) = log p(X|Y ) X∈A exp − E(X|Y ) = log X∈A − log exp − E(X|Y ) . [sent-68, score-0.329]

43 Here LBP is run twice (with the singleton marginals initialized from the single node potentials), once to estimate the marginals of p(X|Y ) and once for p(X | Y, X ∈ A). [sent-77, score-0.115]

44 A simple and often- used alternative is to discard unlabeled patches by excising nodes 3 Class and frequency Model Building 16. [sent-82, score-0.325]

45 5% Per Pixel IND loc only IND loc+glo CRFσ loc only CRFσ loc+glo CRFσ loc+glo del unlabeled CRFγ loc only CRFγ loc+glo CRFτ loc only CRFτ loc+glo Schroff et al. [sent-91, score-1.664]

46 For each class its frequency in the ground truth labeling is also given. [sent-203, score-0.103]

47 that correspond to unlabeled or partially labeled patches from the graph. [sent-204, score-0.422]

48 This leaves a random ﬁeld with one or more completely labeled connected components whose log-likelihood p(X |Y ) we maximize directly using gradient based methods. [sent-205, score-0.135]

49 Equivalently, we can use the complete model but set all of the pair-wise potentials connected to unlabeled nodes to zero: this decouples the labels of the unlabeled nodes from the rest of the ﬁeld. [sent-206, score-0.387]

50 As a result p(X|Y ) and p(X | Y, X ∈ A) are equivalent for the unlabeled nodes and their contribution to the log-likelihood in Eq. [sent-207, score-0.149]

51 Looking at the training labelings in Figure 3 and Figure 4, we see that pixels near class boundaries often remain unlabeled. [sent-211, score-0.269]

52 Since we leave patches unlabeled if they contain unlabeled pixels, label transitions are underrepresented in the training data, which causes the strength of the pairwise couplings to be greatly overestimated. [sent-212, score-0.609]

53 In contrast, the full CRF model provides realistic estimates because it is forced to include a (fully coupled) label transition somewhere in the unlabeled region. [sent-213, score-0.181]

54 This consists of 240 images of 213 × 320 pixels and their partial pixel-level labelings. [sent-216, score-0.223]

55 The labelings assign pixels to one of nine classes: building, grass, tree, cow, sky, plane, face, car, and bike. [sent-217, score-0.261]

56 Some sample images and labelings are shown in Figure 4. [sent-219, score-0.166]

57 In our experiments we divide the dataset into 120 images for training and 120 for testing, reporting average results over 20 random train-test partitions. [sent-220, score-0.125]

58 We used 20 × 20 pixel patches with centers at 10 pixel intervals. [sent-221, score-0.3]

59 (For the patch size see the red disc in Figure 4). [sent-222, score-0.341]

60 To obtain a labeling of the patches, pixels are assigned to the nearest patch center. [sent-223, score-0.501]

61 Patches are allowed to have any label seen among their pixels, with unlabeled pixels being allowed to have any label. [sent-224, score-0.317]

62 Learning and inference takes place at the patch level. [sent-225, score-0.262]

63 To map the patch-level segmentation back to the pixel level we assign each pixel the marginal of the patch with the nearest center. [sent-226, score-0.49]

64 (In Figure 4 the segmentations were post-processed by a applying a Gaussian ﬁlter over the pixel marginals with the scale set to half the patch spacing). [sent-227, score-0.406]

65 Models that incorporate 4-neighbor spatial couplings are denoted ‘CRF’ while ones that incorporate only (local or global) patch-level potentials are denoted ‘IND’. [sent-230, score-0.251]

66 Models that include global aggregate features are denoted ‘loc+glo’, while ones that include only on local patch-level features are denoted ‘loc only’. [sent-231, score-0.336]

67 Aggregate features (AF) were computed in each cell of a c × c image partition. [sent-236, score-0.169]

68 Accuracy 80 only c 1 to c 75 c to 10 local only 70 0 2 4 6 8 10 C Beneﬁts of aggregate features. [sent-238, score-0.153]

69 The ﬁrst main conclusion is that including global aggregate features helps, for example improving the average classiﬁcation rate on the MSRC dataset from 67. [sent-239, score-0.236]

70 We experimented with dividing the image into c × c grids for a range of values of c. [sent-245, score-0.138]

71 In each cell of the grid we compute a separate histogram over the visual words, and for each patch in the cell we include an energy term based on this histogram in the same way as for the image-wide histogram in Eq. [sent-246, score-0.457]

72 Figure 2 shows how the performance of the individual patch classiﬁer depends on the use of aggregate features. [sent-248, score-0.381]

73 From the dotted curve in the ﬁgure we see that although using larger cells to aggregate features is generally more informative, even ﬁne 10 × 10 subdivisions (containing only 6–12 patches per cell) provide a signiﬁcant performance increase. [sent-249, score-0.339]

74 The second main conclusion from Table 1 is that including spatial couplings (pairwise CRF potentials) helps, respectively increasing the accuracy by 10. [sent-253, score-0.104]

75 The improvement is particularly noticeable for rare classes when global aggregate features are not included: in this case the single node potentials are less informative and frequent classes tend to be unduly favored due to their large a priori probability. [sent-256, score-0.354]

76 The performance increment from global features is smallest for ‘CRFγ’, the model that also includes local contextual information. [sent-258, score-0.156]

77 The overall inﬂuence of the local label transition preferences expressed in ‘CRFγ’ appears to be similar to that of the global contextual information provided by image-wide aggregate features. [sent-259, score-0.288]

78 Our third main conclusion from Table 1 is that our marginalization based training method for handling missing labels is superior to the common heuristic of deleting any unlabeled patches. [sent-261, score-0.194]

79 Learning a ‘CRFσ loc+glo’ model by removing all unlabeled patches (‘del unlabeled’ in the table) leads to an estimate σ ≈ 11. [sent-262, score-0.3]

80 In particular, with ‘delete unlabeled’ training the accuracy of the model drops signiﬁcantly for the classes plane and bike, both of which have a relatively small area relative to their boundaries and thus many partially labeled patches. [sent-265, score-0.215]

81 It is interesting to note that even though σ has been severely over-estimated in the ‘delete unlabeled’ model, the CRF still improves over the individual patch classiﬁcation obtained with ‘IND loc+glo’ for most classes, albeit not for bike and only marginally for plane. [sent-266, score-0.309]

82 We now consider how the performance drops as the fraction of labeled pixels decreases. [sent-268, score-0.223]

83 5 85 Accuracy disc 0 75 disc 10 disc 20 80 70 65 60 CRFσ loc+glo IND loc+glo 20 30 40 50 60 70 Percentage of pixels labeled Figure 3: Recognition performance when learning from increasingly eroded label images (left). [sent-273, score-0.61]

84 The ﬁgure also shows the recognition performance of ‘CRFσ loc+glo’ and ‘IND loc+glo’ as a function of the fraction of labeled pixels. [sent-276, score-0.133]

85 Note that ‘CRFσ loc+glo’ learned from label images eroded with a disc of radius 30 (only 28% of pixels labeled) still outperforms ‘IND loc+glo’ learned from the original labeling (71% of pixels labeled). [sent-278, score-0.604]

86 Also, the CRF actually performs better with 5 pixels of erosion than with the original labeling, presumably because ambiguities related to training patches with mixed pixel labels are reduced. [sent-279, score-0.476]

87 Our CRF model clearly outperforms the approach of [15], which uses aggregate features of an optimized scale but lacks spatial coupling in a random ﬁeld, giving a performance very similar to that of our ‘IND loc+glo’ model. [sent-282, score-0.204]

88 The Sowerby dataset consists of 104 images of 96 × 64 pixels of urban and rural scenes labeled with 7 different classes: sky, vegetation, road marking, road surface, building, street objects and cars. [sent-285, score-0.38]

89 The subset of the Corel dataset contains 100 images of 180 × 120 pixels of natural scenes, also labeled with 7 classes: rhino/hippo, polar bear, water, snow, vegetation, ground, and sky. [sent-286, score-0.316]

90 Here we used 10 × 10 pixel patches, with a spacing of respectively 2 and 5 pixels for the Sowerby and Corel datasets. [sent-287, score-0.221]

91 Table 2 compares the recognition accuracies averaged over pixels for our CRF and independent patch models to the results reported on these datasets for TextonBoost [7] and the multi-scale CRF model of [5]. [sent-289, score-0.47]

92 In this table ‘IND’ stands for results obtained when only the single node potentials are used in the respective models, disregarding the spatial random ﬁeld couplings. [sent-290, score-0.113]

93 The total training time and test time per image are listed for the full CRF models. [sent-291, score-0.128]

94 5 Conclusion We presented several image-patch-level CRF models for semantic image labeling that incorporate both local patch-level observations and more global contextual features based on aggregates of observations at several scales. [sent-293, score-0.447]

95 We showed that partially labeled training images could be handled by maximizing the total likelihood of the image segmentations that comply with the partial labeling, using Loopy BP and Bethe free-energy approximations for the calculations. [sent-294, score-0.394]

96 This allowed us to learn effective CRF models from images where only a small fraction of the pixels were labeled and class transitions were not observed. [sent-295, score-0.288]

97 wide aggregate features is very helpful, while including additional aggregates at ﬁner scales gives relatively little further improvement. [sent-310, score-0.232]

98 Comparative experiments showed that our patch-level CRFs have comparable performance to state-of-the-art pixel-level models while being much more efﬁcient because the number of patches is much smaller than the number of pixels. [sent-311, score-0.176]

99 A semi-supervised learning approach to o u object recognition with spatial integration of local features and segmentation cues. [sent-366, score-0.282]

100 7 MSRC CRFσ loc+glo Labeling Sowerby CRFσ loc+glo Labeling Corel CRFσ loc+glo Labeling Figure 4: Samples from the MSRC, Sowerby, and Corel datasets with segmentation and labeling. [sent-400, score-0.106]

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