iccv iccv2013 iccv2013-79 knowledge-graph by maker-knowledge-mining

79 iccv-2013-Coherent Object Detection with 3D Geometric Context from a Single Image

Source: pdf

Author: Jiyan Pan, Takeo Kanade

Abstract: Objects in a real world image cannot have arbitrary appearance, sizes and locations due to geometric constraints in 3D space. Such a 3D geometric context plays an important role in resolving visual ambiguities and achieving coherent object detection. In this paper, we develop a RANSAC-CRF framework to detect objects that are geometrically coherent in the 3D world. Different from existing methods, we propose a novel generalized RANSAC algorithm to generate global 3D geometry hypothesesfrom local entities such that outlier suppression and noise reduction is achieved simultaneously. In addition, we evaluate those hypotheses using a CRF which considers both the compatibility of individual objects under global 3D geometric context and the compatibility between adjacent objects under local 3D geometric context. Experiment results show that our approach compares favorably with the state of the art.

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Such a 3D geometric context plays an important role in resolving visual ambiguities and achieving coherent object detection. [sent-7, score-0.321]

2 Different from existing methods, we propose a novel generalized RANSAC algorithm to generate global 3D geometry hypothesesfrom local entities such that outlier suppression and noise reduction is achieved simultaneously. [sent-9, score-0.328]

3 In addition, we evaluate those hypotheses using a CRF which considers both the compatibility of individual objects under global 3D geometric context and the compatibility between adjacent objects under local 3D geometric context. [sent-10, score-1.179]

4 etry is recovered together with object detection, the joint optimal solution would enforce 3D geometric coherence among detected objects and therefore improve object detection performance. [sent-26, score-0.351]

5 represents the scene geometry with a ground plane parameterized by its pitch angle (i. [sent-33, score-0.783]

6 horizon position) and height with respect to the camera [14]. [sent-35, score-0.367]

7 The ground plane is more flexible in [3] and [18] where it is allowed to have a non-zero roll angle (i. [sent-36, score-0.58]

8 In all those works, ground plane parameters are quantized into a small number of bins for tractability. [sent-39, score-0.332]

9 Different from the existing works, we also model gravity direction in addition to the ground plane (please see Figure 3), so that scenes like sloped streets can be represented as well. [sent-40, score-0.704]

10 derives an approximate relationship between ground plane parameters and the position and height of object bounding box in the image [14]. [sent-44, score-0.626]

11 As only bounding box information is used, the simplified geometric relationship is effective only when ground plane roll is zero and ground plane pitch is small. [sent-45, score-1.316]

12 The methods proposed in [3] and [18] use object 2D appearance to estimate its pitch angle with respect to the camera, and compute the ground plane from at least 3 objects. [sent-46, score-0.688]

13 build a Bayes net in which every object candidate is attached to the common global 3D geometry (i. [sent-50, score-0.49]

14 Inference over the Bayes net gives the optimal ground plane parameters and the validity of each candidate. [sent-53, score-0.434]

15 To make the inference tractable, the ground plane is assumed to have zero roll angle, and the quantization of the ground plane parameters is relatively coarse. [sent-54, score-0.847]

16 For each enumerated ground plane hypothesis, the validity of object candidates are checked against it, and the ground plane with the highest compatibility is chosen. [sent-57, score-1.219]

17 An improved method is presented in [18], where all object candidates cast votes for the ground plane parameters in a Hough voting space, and the peak in the voting space is regarded as the optimal ground plane. [sent-59, score-0.631]

18 Another novelty of our approach is that surface regions are also involved in generating and evaluating global 3D geometry hypotheses. [sent-62, score-0.441]

19 After an overview of our algorithm in Section 2, we describe in Section 3 how we generate the hypotheses of global 3D geometry in a way that suppresses outliers and reduces noise simultaneously. [sent-66, score-0.461]

20 Evaluation of those hypotheses that incorporates both global and local 3D geometric constraints is detailed in Section 4. [sent-67, score-0.442]

21 camera is represented by the orange horizon line, and the ground plane is represented by the blue mesh. [sent-71, score-0.616]

22 We start by generating object/surface candidates (including cars, pedestrians, vertical and horizontal surface regions) using state-of-the-art object detectors (e. [sent-75, score-0.621]

23 Each object/surface candidate gives an estimate of the global 3D geometry (i. [sent-80, score-0.426]

24 gravity direction and ground plane parameters) based on their 2D appearance. [sent-82, score-0.704]

25 Those noisy estimates are then pooled together using an generalized RANSAC algorithm to generate a set of global 3D geometry hypotheses. [sent-83, score-0.328]

26 Given each hypothesis, we compute the compatibility of each object/surface candidate and infer their validity according to global and local 3D geometric context. [sent-84, score-0.767]

27 Finally the hypothesis with the highest quality is selected as the optimal estimate of the global 3D geometry, and the inference result of object candidate validity associated with the best hypothesis gives the final object detection result. [sent-86, score-0.784]

28 The first group contains global variables depicting the global 3D geometry: (inverse) gravity direction ng, ground plane orientation np, and ground plane height hp. [sent-92, score-1.442]

29 The orange and purple lines in the image plane are ground horizon and gravity horizon, respectively. [sent-94, score-0.915]

30 Now we list all the geometric relationships that exist among those variables: dt = H sin θ/ sin α; (1) db = H(sin θ/ tan α + cos θ) ; (2) nv = m{dtr{xt , f} − dbr{xb, f}}; (3) nv = g{−r{xb, f}, θ, γ}; (4) α = arccos{< r{xt , f}, r{xb, f} >}; (5) hnpv= −? [sent-96, score-0.634]

31 In addition, we could also estimate the distributions of object pitch and roll angles given object appearance I and category c: θ ∼ p1(I, c) ; (8) γ ∼ p2 (I, c) . [sent-104, score-0.624]

32 Among all the geometric variables, only xt (10) and xb are directly observable. [sent-106, score-0.353]

33 Therefore, instead of attempting to directly solve them, we use those equations to propose hypotheses of the global 3D geometry (ng, np, hp), and to evaluate those hypotheses. [sent-109, score-0.429]

34 The pitch and roll angles, together with landmark locations, produce a non-parametric distribution of object vertical orientation nv, according to the algorithm summarized in Figure 4. [sent-118, score-0.858]

35 Following constraint 7, the vertical orientation distributions obtained from cars are regarded as the estimations of the ground plane orientation np, and those from pedestrians are for the gravity direction ng. [sent-119, score-1.241]

36 In addition to estimating ng and np, given the vertical orientation, each object candidate also provides cues for the ground plane height hp according to its size and location. [sent-120, score-1.0]

37 The algorithm for using an object candidate to generate a non-parametric distribution of hp is summarized in Figure 5. [sent-121, score-0.368]

38 For each surface candidate: Given a vertical surface region like a building facade, we extract long edges within it and compute vertical and horizontal vanishing points (VP) using Gaussian sphere [1]. [sent-122, score-0.778]

39 The vertical direction of the surface nv can be estimated directly from the vertical 22557788 non-parametric distribution of the ground plane height. [sent-124, score-1.142]

40 Therefore, for the vertical VP, it directly yields a set of nv samples from its constituent circle-intersection points. [sent-127, score-0.406]

41 For each pair of horizontal VPs, we compute the cross product of their respective constituent circle-intersection points and generate a set of nv samples. [sent-128, score-0.354]

42 The nv samples from the vertical VP and all pairs of horizontal VPs are pooled together to generate a non-parametric distribution of nv over the dense grid Gn using Kernel Density Estimation (KDE). [sent-129, score-0.737]

43 Estimating the vertical direction of a horizontal surface region (e. [sent-130, score-0.489]

44 In outdoor street scenes, vertical surfaces usually correspond to building facades which typically agree with the gravity direction, while horizontal surfaces usually fall on roads which relate to the ground plane orientation. [sent-133, score-1.04]

45 Therefore, we have nv = ng for vertical surfaces and nv = np for horizontal surfaces. [sent-134, score-0.872]

46 An example of each object/surface candidate giving an estimate of the global 3D geometry is shown in Figure 6a and b. [sent-135, score-0.426]

47 Generating hypotheses of global 3D geometry with generalized RANSAC One of the keys for RANSAC to succeed is that at least one hypothesis should be close to the ground truth. [sent-140, score-0.72]

48 Generate hypotheses of global 3D geometry from object/surface candidates. [sent-149, score-0.429]

49 Here, red and green shades indicate vertical and horizontal surface candidates, respectively. [sent-151, score-0.416]

50 Here, magenta lines represent gravity horizons, and yellow grids indicate ground planes, where the grid size is 1m. [sent-153, score-0.469]

51 After each object/surface candidate has estimated a distribution of the global 3D geometry, we generate a set of mixed distributions by mixing individual distributions together with randomly generated weights. [sent-159, score-0.515]

52 To verify this claim, we perform experiments on the 100 images that are provided with the ground truth horizon in Hoiem’s dataset [14], and the results are plotted in Figure 7. [sent-163, score-0.367]

53 The error of hy- pothesis generation is defined as the difference between the ground truth and the best hypothesis among all the hypotheses generated. [sent-165, score-0.424]

54 Evaluating global 3D geometry hypotheses Given a global 3D geometry hypothesis ( n˜g, we evaluate its quality by measuring how well it is supported by object/surface candidates after excluding the influence of np, h˜p), outliers. [sent-176, score-0.909]

55 For this purpose, we evaluate the global and local geometric compatibilities of each object/surface candidate, and employ a CRF to infer the validity of each candidate. [sent-177, score-0.342]

56 Global geometric compatibility Global geometric compatibility refers to the compatibility of an individual object/surface candidate w. [sent-181, score-1.269]

57 the global 3D geometry such as ground plane and gravity. [sent-184, score-0.588]

58 Individual object candidate: We use two sources of geometric constraints to compute the global compatibility of an individual object candidate. [sent-186, score-0.7]

59 In both the two sources, landmark locations xt and xb take the mean value produced by the landmark regressor. [sent-187, score-0.427]

60 The first source compares the pitch and roll angles predicted by the pose regressor (using constraints 8 and 9) with those directly computed from the current hypothesis of the global 3D geometry (using constraint 4 where nv = for pedestrians and nv = for cars). [sent-188, score-1.352]

61 The resulting compatibility score is ng sg1= exp{−(θ˜−2 σ θθ20)2} · exp{−( γ˜2 −σγ γ20)2} − 0. [sent-189, score-0.351]

62 5, np (11) where θ0, γ0 and σθ2, σγ2 are the mean and variance of the pitch and roll regressor outputs, respectively. [sent-190, score-0.548]

63 Given the ground plane hypothesis and we compute the bottom landmark depth db using constraint 6. [sent-197, score-0.575]

64 Denote the angle between and the direction of Xt − Xb as δ, then the resulting compatibility score is np ng nv ˜hp, np nv sg2= exp{−2δσ22} · exp{−(? [sent-201, score-1.097]

65 The final compatibility score sg for an individual object candidate is the average of sg1 and sg2. [sent-205, score-0.614]

66 Individual surface candidate: The compatibility of a surface candidate also comes from two sources. [sent-206, score-0.721]

67 Firstly, we check how well the vertical orientation distribution produced by the surface candidate agree with the current hypothesis (for vertical surface) or (for horizontal surface). [sent-207, score-1.032]

68 Secondly, we check the plausibility of the location of the surface candidate with respect to the ground horizon in the image. [sent-211, score-0.685]

69 For the horizontal surface candidate, denote the proportion of the surface region above the ground horizon as rh, then the compatibility score sg2 is −rh with range between -1 and 0. [sent-212, score-1.044]

70 For the vertical surface c−arndidate, this type of compatibility does not apply, as it usually straddles across the horizon. [sent-213, score-0.579]

71 The final compatibility score sg is the average of sg1 and sg2 for the horizontal surface candidate, and is sg1 for the vertical surface candidate. [sent-214, score-0.896]

72 Local geometric compatibility Local geometric compatibility refers to the compatibility between nearby object candidates. [sent-217, score-1.115]

73 Therefore, we define the pairwise compatibility score related to depth ordering as s(idjep) s(idjep) = −(|Rij|/|Rj|)λ, (13) where |Rij | is the overlapping area of candidates iand j, |Rj e| ies |thRe area othfe eca onvedirldaaptpe j,ga andre λa oisf a parameter sie atn as j5,. [sent-220, score-0.393]

74 on the ground plane significantly overlap, they are unlikely to co-exist due to space occupancy conflict, as is illustrated by the upper pair of orange cubes in Figure 8. [sent-222, score-0.415]

76 The footprint of an object candidate is obtained by mapping several ground-touching landmarks in the image to the ground plane. [sent-224, score-0.427]

77 Inferring candidate validity with CRF We construct a CRF over the object/surface candidates to infer their validity. [sent-228, score-0.376]

78 Each candidate forms a node, and two object candidates have an edge between them iftheir bounding boxes and/or footprints overlap. [sent-229, score-0.423]

79 ), ), and ωi (oi) are the unary potentials for the vertical surface candidate, horizontal surface candidate, and object candidate i, respectively. [sent-239, score-0.798]

80 5) and ω(o = 0) = 0, where sg is the compatibility score d0. [sent-241, score-0.332]

81 After the inference is complete, the quality of the current global 3D geometry hypothesis is the maximum value V∗ of the objective function. [sent-247, score-0.376]

82 When proposing hypotheses from distributions, 50 random mixtures are usually enough, and the total number of hypotheses to evaluate is in the hundreds. [sent-263, score-0.379]

83 This is probably because Hoiem’s algorithm takes the bounding box height as the object height in the image. [sent-275, score-0.425]

84 The dataset provides the ground truth of horizon in the form of the row index where the horizon is located. [sent-279, score-0.603]

85 It does not distinguish between gravity and ground horizons, since the two are almost the same for most of the images in the dataset. [sent-280, score-0.43]

86 After converting the row index of a horizon to the corresponding orientation vector, we compute the error of an estimated gravity direction (or ground plane orientation) by measuring the angle between it and the ground truth orientation vector. [sent-281, score-1.298]

87 Here, ”Det” shows the result of the DPM baseline detector; ”Det+GlbGeo” shows the result of including global geometric context alone; ”Det+LocGeo” shows the result of including local geometric context alone; ”Det+FullGeo” shows the result of our full system using both types of context. [sent-289, score-0.513]

88 The estimated ground plane height by our method is centered around 1. [sent-292, score-0.463]

89 It is worth noting that, unlike Hoiem’s algorithm, we do not assume the ground plane is perpendicular to the gravity direction and has zero roll and small pitch. [sent-294, score-0.887]

90 Even with a greater flexibility, our approach still outperforms Hoiem’s algorithm both in object detection and global geometry estimation, on the test dataset that largely satisfies those assumptions. [sent-295, score-0.367]

91 Global and local 3D geometric context: Different from existing works, we use both global and local 3D geometric context when inferring the validity of object candidates. [sent-303, score-0.614]

92 Both the global and local 3D geometric context enhance detection performance, and the highest gain is achieved when they are applied simultaneously. [sent-305, score-0.352]

93 Benefit is mutual: Not only does 3D geometric context enhance object detection performance, but coherent object detection in turn improves the estimation of gravity and ground horizons. [sent-306, score-0.909]

94 To verify this argument, we estimate the gravity direction and ground plane orientation from vertical Figure 10. [sent-307, score-0.961]

95 The first row shows the distributions of gravity direction error, ground orientation error, and ground height from our algorithm. [sent-309, score-0.892]

96 We are not able to compute the error of the ground plane height estimation due to the lack of ground truth. [sent-312, score-0.594]

97 Yellow grid: ground plane where the grid spacing is 1m. [sent-352, score-0.332]

98 We can see that some false detections from DPM are rejected due to inconsistency with global geometry (e. [sent-355, score-0.43]

99 the huge ”pedestrian” in (a)); some false detections from DPM are rejected due to inconsistency with local geometry (e. [sent-357, score-0.333]

100 The case when gravity direction and ground orientation do not agree is shown in (f), where the ground horizon is illustrated by the thick yellow line. [sent-363, score-0.983]

similar papers computed by tfidf model

tfidf for this paper:

wordName wordTfidf (topN-words)

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