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201 nips-2012-Localizing 3D cuboids in single-view images

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Author: Jianxiong Xiao, Bryan Russell, Antonio Torralba

Abstract: In this paper we seek to detect rectangular cuboids and localize their corners in uncalibrated single-view images depicting everyday scenes. In contrast to recent approaches that rely on detecting vanishing points of the scene and grouping line segments to form cuboids, we build a discriminative parts-based detector that models the appearance of the cuboid corners and internal edges while enforcing consistency to a 3D cuboid model. Our model copes with different 3D viewpoints and aspect ratios and is able to detect cuboids across many different object categories. We introduce a database of images with cuboid annotations that spans a variety of indoor and outdoor scenes and show qualitative and quantitative results on our collected database. Our model out-performs baseline detectors that use 2D constraints alone on the task of localizing cuboid corners. 1

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Localizing 3D cuboids in single-view images Jianxiong Xiao Bryan C. [sent-1, score-0.485]

2 Russell∗ Massachusetts Institute of Technology ∗ Antonio Torralba University of Washington Abstract In this paper we seek to detect rectangular cuboids and localize their corners in uncalibrated single-view images depicting everyday scenes. [sent-2, score-0.782]

3 In contrast to recent approaches that rely on detecting vanishing points of the scene and grouping line segments to form cuboids, we build a discriminative parts-based detector that models the appearance of the cuboid corners and internal edges while enforcing consistency to a 3D cuboid model. [sent-3, score-1.699]

4 Our model copes with different 3D viewpoints and aspect ratios and is able to detect cuboids across many different object categories. [sent-4, score-0.893]

5 We introduce a database of images with cuboid annotations that spans a variety of indoor and outdoor scenes and show qualitative and quantitative results on our collected database. [sent-5, score-0.85]

6 Our model out-performs baseline detectors that use 2D constraints alone on the task of localizing cuboid corners. [sent-6, score-0.606]

7 The detection and recovery of shape parameters yield at least a partial geometric description of the depicted scene, which allows a system to reason about the affordances of a scene in an object-agnostic fashion [9, 15]. [sent-15, score-0.379]

8 They detect line segments via Canny edges and recover surface orientations [13] to form 3D cuboid hypotheses using bottomup grouping of line and region segments. [sent-20, score-0.75]

9 As shown in Figure 1, we aim to build a 3D cuboid detector to detect individual boxy volumetric structures. [sent-23, score-0.747]

10 We build a discriminative parts-based detector that models the appearance of the corners and internal edges of cuboids while enforcing spatial consistency of the corners and edges to a 3D cuboid model. [sent-24, score-1.71]

11 Given a single-view input image, our goal is to detect the 2D corner locations of the cuboids depicted in the image. [sent-27, score-1.03]

12 With the output part locations we can subsequently recover information about the camera and 3D shape via camera resectioning. [sent-28, score-0.42]

13 Our cuboid detector is trained across different 3D viewpoints and aspect ratios. [sent-29, score-0.903]

14 Moreover, instead of relying on edge detection and grouping to form an initial hypothesis of a cuboid [9, 17, 26, 29], we use a 2D sliding window approach to exhaustively evaluate all possible detection windows. [sent-33, score-0.907]

15 2 Model for 3D cuboid localization We represent the appearance of cuboids by a set of parts located at the corners of the cuboid and a set of internal edges. [sent-40, score-1.918]

16 Let I be the image and pi = (xi , yi ) be the 2D image location of the ith corner on the cuboid. [sent-42, score-0.647]

17 We deﬁne an undirected loopy graph G = (V, E) over the corners of the cuboid, with vertices V and edges E connecting the corners of the cuboid. [sent-43, score-0.421]

18 By reasoning about the 3D shape, our model handles different 3D viewpoints and aspect ratios, as illustrated in Figure 2. [sent-46, score-0.272]

19 Edge(I, pi , pj ): The internal edge information on cuboids is informative and provides a salient feature for the locations of the corners. [sent-50, score-0.82]

20 For adjacent corners on the cuboid, we identify the edge between the two corners and calculate the image evidence to support the existence of such an edge. [sent-52, score-0.538]

21 Given the corner locations pi and pj , we use Chamfer matching to align the straight line between the two corners to edges extracted from the image. [sent-53, score-0.908]

22 We ﬁnd image edges using Canny edge detection [3] and efﬁciently compute the distance of each pixel along the line segment to the nearest edge via the truncated distance transform. [sent-54, score-0.471]

23 We use Bresenham’s line algorithm [2] to efﬁciently ﬁnd the 2D image locations on the line between the two points. [sent-55, score-0.272]

24 In (a) and (b) the displayed corner locations are the average 2D locations across all viewpoints and aspect ratios in our database. [sent-63, score-0.95]

25 Shape3D (p): The 3D shape of a cuboid constrains the layout of the parts and edges in the image. [sent-66, score-0.75]

26 We propose to deﬁne a shape term that measures how well the conﬁguration of corner locations respect the 3D shape. [sent-67, score-0.59]

27 In other words, given the 2D locations p of the corners, we deﬁne a term that tells us how likely this conﬁguration of corner locations p can be interpreted as the reprojection of a valid cuboid in 3D. [sent-68, score-1.22]

28 For each corner, we use the other six 2D corner locations to estimate the product PL using camera resectioning [10]. [sent-72, score-0.652]

29 The estimated matrix is used to predict the corner location. [sent-73, score-0.372]

30 We use the negative L2 distance to the predicted corner location as a feature for the corner in our model. [sent-74, score-0.787]

31 1 Inference Our goal is to ﬁnd the 2D corner locations p over the HOG grid of I that maximizes the score given in Equation (1). [sent-78, score-0.505]

32 Therefore, we propose a spanning tree approximation to the graph to obtain multiple initial solutions for possible corner locations. [sent-80, score-0.401]

33 Then we adjust the corner locations using randomized simple hill climbing. [sent-81, score-0.534]

34 We use the following scoring function for the initialization: ST (I, p) = i∈V H wi · HOG(I, pi ) + ij∈T D wij · Displacement2D (pi , pj ) (2) Note that the model used for obtaining initial solutions is similar to [7, 27], which is only able to handle a ﬁxed viewpoint and 2D aspect ratio. [sent-85, score-0.32]

35 With the tree approximation, we pick the top 1000 possible conﬁgurations of corner locations from each image and optimize our scoring function by adjusting the corner locations using randomized simple hill climbing. [sent-87, score-1.188]

36 Given the initial corner locations for a single conﬁguration, we iteratively choose a random corner i with the goal of ﬁnding a new pixel location pi that increases the scoring ˆ function given in Equation (1) while holding the other corner locations ﬁxed. [sent-88, score-1.558]

37 We also consider the pixel location that the 3D rigid model predicts when estimated from the other corner locations. [sent-90, score-0.457]

38 The algorithm terminates when no corner can reach a location that improves the score, which indicates that we have reached a local maxima. [sent-93, score-0.415]

39 Also, since only one corner can change locations at each iteration, we can reuse the computed scoring function from previous iterations during hill climbing. [sent-97, score-0.581]

40 Finally, we perform non-maximal suppression among the parts and then perform non-maximal suppression over the entire object to get the ﬁnal detection result. [sent-98, score-0.285]

41 We tried mining negatives from the wrong corner locations in the positive examples but found that it did not improve the performance. [sent-106, score-0.505]

42 Since the latent positive mining helped, we also tried an offset compensation as post-processing to obtain the offset of corner locations introduced during latent positive mining. [sent-108, score-0.505]

43 3 Discussion Sliding window object detectors typically use a root ﬁlter that covers the entire object [4] or a combination of root ﬁlter and part ﬁlters [7]. [sent-112, score-0.309]

44 The use of a root ﬁlter is sufﬁcient to capture the appearance for many object categories since they have canonical 3D viewpoints and aspect ratios. [sent-113, score-0.493]

45 However, cuboids in general span a large number of object categories and do not have a consistent 3D viewpoint or aspect ratio. [sent-114, score-0.672]

46 The diversity of 3D viewpoints and aspect ratios causes dramatic changes in the root ﬁlter response. [sent-115, score-0.36]

47 Moreover, we argue that a purely view-based approach that trains separate models for the different viewpoints and aspect ratios may not capture well this diversity. [sent-117, score-0.312]

48 As our model handles different viewpoints and aspect ratios, we are able to make use of the entire database during training. [sent-121, score-0.341]

49 Due to the diversity of cuboid appearance, our model is designed to capture the most salient features, namely the corners and edges. [sent-122, score-0.729]

50 A projection of the cuboid model is overlaid on the image and the user must select and drag anchor points to their corresponding location in the image. [sent-127, score-0.691]

51 (b) Scatter plot of 3D azimuth and elevation angles for annotated cuboids with zenith angle close zero. [sent-128, score-0.694]

52 (c) Crops of cuboids at different azimuth angles for a ﬁxed elevation, with the shown examples marked as red points in the scatter plot of (b). [sent-130, score-0.612]

53 Furthermore, we do not make use of other appearance cues, such as the appearance within the cuboid faces, since they have a larger variation across the object categories (e. [sent-132, score-0.834]

54 Compared with recent approaches that detect cuboids by reasoning about the shape of the entire scene [9, 11, 12, 17, 19, 29], one of the key differences is that we detect cuboids directly without consideration of the global scene geometry. [sent-136, score-1.231]

55 These prior approaches rely heavily on the assumption that the camera is located inside a cuboid-like room and held at human height, with the parameters of the room cuboid inferred through vanishing points based on a Manhattan world assumption. [sent-137, score-0.72]

56 As our detector is agnostic to the scene geometry, we are able to detect cuboids even when these assumptions are violated. [sent-141, score-0.693]

57 We observe that not all cuboid-like objects are perfect cuboids in practice. [sent-143, score-0.492]

58 With our approach, if a rigid cuboid is needed, we can recover the 3D shape parameters via camera resectioning, as shown in Figure 9. [sent-154, score-0.773]

59 3 Database of 3D cuboids To develop and evaluate any models for 3D cuboid detection in real-world environments, it is necessary to have a large database of images depicting everyday scenes with 3D cuboids labeled. [sent-155, score-1.766]

60 We have built a labeling tool that allows a user to select and drag key points on a projected 3D cuboid model to its corresponding location in the image. [sent-157, score-0.618]

61 Given the corner correspondences, the parameters for the 3D cuboids and camera are estimated. [sent-161, score-0.903]

62 The cuboid and camera parameters are estimated up to a similarity transformation via camera resectioning using Levenberg-Marquardt optimization [10]. [sent-162, score-0.793]

63 5 Figure 5: Single top 3D cuboid detection in each image. [sent-163, score-0.663]

64 The false positives tend to occur when a part ﬁres on a “cuboid-like” corner region (e. [sent-166, score-0.372]

65 Figure 6: All 3D cuboid detections above a ﬁxed threshold in each image. [sent-171, score-0.545]

66 Notice that our model is able to detect the presence of multiple cuboids in an image (e. [sent-172, score-0.562]

67 For our database, we have 785 images with 1269 cuboids annotated. [sent-182, score-0.485]

68 We have also collected a negative set containing 2746 images that do contain any cuboid like objects. [sent-183, score-0.6]

69 In Figure 4(b) we show a scatter plot of the azimuth and elevation angles for all of the labeled cuboids with zenith angle close to zero. [sent-186, score-0.735]

70 Notice that the cuboids cover a large range of azimuth angles for elevation angles between 0 (frontal view) and 45 degrees. [sent-187, score-0.702]

71 Figure 8(c) shows the distribution of objects from the SUN database [25] that overlap with our cuboids (there are 326 objects total from 114 unique classes). [sent-189, score-0.623]

72 Compared with [12], our database covers a larger set of object and scene categories, with images focusing on both objects and scenes (all images in [12] are indoor scene images). [sent-190, score-0.623]

73 Moreover, we annotate objects closely resembling a 3D cuboid (in [12] there are many non-cuboids that are annotated with a bounding cuboid) and overall our cuboids are more accurately labeled. [sent-191, score-1.069]

74 4 Evaluation In this section we show qualitative results of our model on the 3D cuboids database and report quantitative results on two tasks: (i) 3D cuboid detection and (ii) corner localization accuracy. [sent-192, score-1.634]

75 Notice that our model is able to better localize cuboid corners over the baseline 2D tree-based model, which corresponds to 2D parts-based models used in object detection and articulated pose estimation [7, 27]. [sent-199, score-1.01]

76 The last column shows a failure case where a part ﬁres on a “cuboid-like” corner region in the image. [sent-200, score-0.372]

77 to mirror left-right and orient the 3D cuboid to minimize the variation in rotational angle. [sent-201, score-0.57]

78 During testing, we run the detector on left-right mirrors of the image and select the output at each location with the highest detector response. [sent-202, score-0.356]

79 For the parts we extract HOG features [4] in a window centered at each corner with scale of 10% of the object bounding box size. [sent-203, score-0.57]

80 Figure 5 shows the single top cuboid detection in each image and Figure 6 shows all of the most conﬁdent detections in the image. [sent-204, score-0.736]

81 We note that our model fails when a corner ﬁres on a “cuboid-like” corner region (e. [sent-209, score-0.744]

82 The ﬁrst baseline is a root HOG template [4] trained over the appearance within a bounding box covering the entire object. [sent-213, score-0.271]

83 A single model using the root HOG template is trained for all viewpoints and aspect ratios. [sent-214, score-0.318]

84 During detection, output corner locations corresponding to the average training corner locations relative to the bounding boxes are returned. [sent-215, score-1.042]

85 The second baseline is the 2D tree-based approximation of Equation (2), which corresponds to existing 2D parts models used in object detection and articulated pose estimation [7, 27]. [sent-216, score-0.31]

86 We evaluate geometric primitive detection accuracy using the bounding box overlap criteria in the Pascal VOC [6]. [sent-219, score-0.284]

87 We have observed that all of the cornerbased models achieve almost identical detection accuracy across all recall levels, and out-perform the root HOG template detector [4]. [sent-221, score-0.344]

88 This in effect does not allow us to detect additional cuboids but allows for better part localization. [sent-223, score-0.489]

89 In addition to detection accuracy, we also measure corner localization accuracy for correctly detected examples for a given model. [sent-224, score-0.602]

90 A corner is deemed correct if its predicted image location is within t pixels of the ground truth corner location. [sent-225, score-0.913]

91 The reported trends in the corner localization performance hold for nearby values of t. [sent-227, score-0.448]

92 In Figure 8 we plot corner localization accuracy as a function of recall and compare our model against the two baselines. [sent-228, score-0.474]

93 Also, the additional edge and 3D shape terms provide a gain in performance over using the appearance and 2D spatial terms alone. [sent-231, score-0.296]

94 Notice that all of the corner-based models achieve almost identical detection accuracy across all recall levels and out-perform the root HOG template detector [4]. [sent-274, score-0.344]

95 For the task of corner localization, our full model out-performs the two baseline detectors or when either the Edge or Shape3D terms are omitted from our model. [sent-275, score-0.433]

96 Figure 9: Detected cuboids and subsequent synthesized new views via camera resectioning. [sent-279, score-0.531]

97 5 Conclusion We have introduced a novel model that detects 3D cuboids and localizes their corners in single-view images. [sent-280, score-0.641]

98 Our 3D cuboid detector makes use of both corner and edge information. [sent-281, score-1.134]

99 Moreover, we have constructed a dataset with ground truth cuboid annotations. [sent-282, score-0.598]

100 Our detector handles different 3D viewpoints and aspect ratios and, in contrast to recent approaches for 3D cuboid detection, does not make any assumptions about the scene geometry and allows for deformation of the 3D cuboid shape. [sent-283, score-1.692]

similar papers computed by tfidf model

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