cvpr cvpr2013 cvpr2013-279 knowledge-graph by maker-knowledge-mining

279 cvpr-2013-Manhattan Scene Understanding via XSlit Imaging


Source: pdf

Author: Jinwei Ye, Yu Ji, Jingyi Yu

Abstract: A Manhattan World (MW) [3] is composed of planar surfaces and parallel lines aligned with three mutually orthogonal principal axes. Traditional MW understanding algorithms rely on geometry priors such as the vanishing points and reference (ground) planes for grouping coplanar structures. In this paper, we present a novel single-image MW reconstruction algorithm from the perspective of nonpinhole cameras. We show that by acquiring the MW using an XSlit camera, we can instantly resolve coplanarity ambiguities. Specifically, we prove that parallel 3D lines map to 2D curves in an XSlit image and they converge at an XSlit Vanishing Point (XVP). In addition, if the lines are coplanar, their curved images will intersect at a second common pixel that we call Coplanar Common Point (CCP). CCP is a unique image feature in XSlit cameras that does not exist in pinholes. We present a comprehensive theory to analyze XVPs and CCPs in a MW scene and study how to recover 3D geometry in a complex MW scene from XVPs and CCPs. Finally, we build a prototype XSlit camera by using two layers of cylindrical lenses. Experimental results × on both synthetic and real data show that our new XSlitcamera-based solution provides an effective and reliable solution for MW understanding.

Reference: text


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu ,yu} s Abstract A Manhattan World (MW) [3] is composed of planar surfaces and parallel lines aligned with three mutually orthogonal principal axes. [sent-3, score-0.237]

2 Traditional MW understanding algorithms rely on geometry priors such as the vanishing points and reference (ground) planes for grouping coplanar structures. [sent-4, score-0.335]

3 Specifically, we prove that parallel 3D lines map to 2D curves in an XSlit image and they converge at an XSlit Vanishing Point (XVP). [sent-7, score-0.224]

4 In addition, if the lines are coplanar, their curved images will intersect at a second common pixel that we call Coplanar Common Point (CCP). [sent-8, score-0.212]

5 Finally, we build a prototype XSlit camera by using two layers of cylindrical lenses. [sent-11, score-0.175]

6 Introduction A pinhole camera collects rays passing through a common Center-of-Projection (CoP) and has been the dominating imaging model for computer vision tasks. [sent-14, score-0.246]

7 First, pinhole geometry is simple; it is uniquely defined by only 3 parameters (the position of CoP in 3D) and its imaging process can be uniformly described by the classic 3 4 pinhole camera umnaitfroixrm [1ly2 d]. [sent-16, score-0.287]

8 , they observe lines as lines and parallel lines converging at a vanishing point. [sent-19, score-0.533]

9 In this paper, we demonstrate using a special multi-perspective camera, the XSlit camera [30], for reconstructing the Manhattan World scenes. [sent-25, score-0.104]

10 A Manhattan World (MW) [3] is composed of planar surfaces and parallel lines aligned with three mutually orthogonal principal axes. [sent-27, score-0.237]

11 Tremendous efforts have been focused on reconstructing MW from images [1, 5, 10, 11] and using the MW assumption for camera calibration [3, 15, 24]. [sent-29, score-0.104]

12 [10, 11] assign a plane to each pixel and then apply graph-cut on discretized plane parameters. [sent-32, score-0.11]

13 Most previous approaches exploit monocular cues such as the vanishing points and the reference planes (e. [sent-34, score-0.19]

14 Kosecka and Zhang [15] detect line structures in the image for recovering the vanishing points and camera parameters [29]. [sent-42, score-0.262]

15 [4] use the vanishing points and ground plane as priors for recovering affine scene structures. [sent-44, score-0.216]

16 We observe that the core challenge in pinhole-based solutions is coplanar ambiguities: although one can easily detect the vanishing point of a group of parallel 3D lines, there is an ambiguity on which lines belong to the same plane. [sent-52, score-0.435]

17 Conceptually, 3D parallel lines will be mapped to 2D curves in a multi-perspective camera and these curves will intersect at multiple points instead of a single vanishing point. [sent-54, score-0.506]

18 [2] examine the curves in a non-centric catadioptric camera for line localization. [sent-56, score-0.145]

19 In this paper, we show how to group parallel 3D lines on the same plane by analyzing their images in a special multi-perspective cameras, the XSlit camera [30]. [sent-59, score-0.347]

20 We show that same as in the pinhole camera, images of parallel lines in an XSlit image, although curved, will still converge at a vanishing point, i. [sent-60, score-0.385]

21 What is different though is that images of coplanar 3D lines will generally intersect at a second common point that we call Coplanar Common Point or CCP. [sent-63, score-0.294]

22 We show that the geometry of 3D lines can be directly recovered from their XVPs and CCPs. [sent-66, score-0.176]

23 Finally, we construct a prototype XSlit camera by using two layers of cylindrical lenses. [sent-68, score-0.175]

24 Experimental methods on both synthetic and real data show that our XSlit camera based solution provides an effective and reliable solution for MW scene understanding. [sent-69, score-0.128]

25 Our contributions include: • A new theory to characterize the XVP and CCP of coplanar parallel 3D lines in an XSlit image. [sent-70, score-0.316]

26 • A prototype XSlit camera for validating our theory. [sent-72, score-0.132]

27 collected in the camera and the mapping from the ray to a pixel. [sent-77, score-0.16]

28 In 2PP, each ray is parameterized as [u, v, s, t], where [u, v] and [s, t] are the intersections with the two parallel planes Πuv and Πst lying at z = 0 and z = 1respectively. [sent-79, score-0.306]

29 XSlit Camera Geometry An XSlit camera collects rays that simultaneously pass through two oblique (neither parallel nor coplanar) slits in 3D space [30]. [sent-86, score-0.38]

30 Given two slits l1 and l2, we construct the 2PP as follows: we choose Πuv and Πst that are parallel to both slits but do not contain them, as shown in Fig. [sent-87, score-0.335]

31 Next, we orthogonally project both slits on Πuv and use their intersection point as the origin of the coordinate system. [sent-89, score-0.137]

32 We first explore ray geometry constraints for all rays in an XSlit camera. [sent-93, score-0.162]

33 τσ == ( CAuu + + D Bvv) / EE 888222 where (2) A = d2xdy1Z2 − dx1d2yZ1, B = d1xdx2(Z1 − Z2), D = d2xdy1Z1 − dx1d2yZ2, C = d1ydy2(Z2 − Z1), E = (d1xdy2 − dx2d1y)Z1Z2 = Recall that the two slits are oblique, therefore E 0. [sent-96, score-0.12]

34 a ray r[u, v, σ, τ] passes through l, there must exist some λ and λl so that [u, v, 0] + λ[σ, τ, 1] = [xl , yl , zl] + λl [dlx , dly, 0] It is easy to see that λ = linear constraint: zl (3) . [sent-113, score-0.121]

35 ec Πtion of land therefore all 3D lines parallel to Πuv will be mapped to 2D parallel lines. [sent-124, score-0.301]

36 Similar to case 1, there must exist some and λl so that λ [u, v, 0] + λ[σ, τ, 1] = [ul , vl , 0] + λl [σl , τl , 1] λ λ andλl, we obtain a σ − σl (6) We have = λl and eliminating bilinear constraint: u − ul v vl − = (5) τ − τl We call Eqn. [sent-126, score-0.14]

37 , the image of las 1Although slits are essentially lines, we distinguish them two for clarity: slits refer to the XSlit camera geometry and lines refer to 3D scene. [sent-133, score-0.472]

38 The last crucial ray geometry constraint is for rays lying on a common plane. [sent-146, score-0.219]

39 This lies at the core of this paper as our goal is to disambiguate parallel 3D lines lying on different planes. [sent-147, score-0.248]

40 Given a plane Π Πuv : nxx + nyy + nzz + d = 0, with = [nx , ny, nz] being the normal and d the offset, we can intersect Π with Πuv at line: nxu + nyv + d = 0 (9) All rays [u, v, σ, τ] that lie on Π must originate from this line, i. [sent-148, score-0.189]

41 XSlit Vanishing Points (XVP) Next, we use the ray geometry constraints for studying the vanishing points of parallel 3D lines in an XSlit image. [sent-156, score-0.435]

42 Given a set of parallel lines L ∦ Πuv, their images on 1Π. [sent-158, score-0.206]

43 The results are independent aosf tthhee origin of the line and therefore the images of parallel 3D lines, although being hyperbolas, have a vanishing point. [sent-164, score-0.241]

44 Coplanar Common Points (CCP) What differs XSlit from pinhole cameras and hence makes it appealing is that parallel 3D lines lying on a plane will converge at a second common point in an XSlit image. [sent-168, score-0.392]

45 Given a set of lines L that lie on plane Π uTnhpeaorraelmlel 2to. [sent-170, score-0.189]

46 t Ghei tewno asl sites,t t ohfei lrin images hina tth leie e X oSnlit p camera generally intersect at a second common point, the Coplanar Common Point or CCP. [sent-171, score-0.159]

47 Notice that the CCP corresponds to some ray r that 1) is collected by the XSlit, 2) lies on Π, and 3) will intersect all lines in L, as shown in Fig. [sent-173, score-0.243]

48 For the pinhole camera to have a ray to lie completely on a 3D plane, the plane has to pass the pinhole. [sent-191, score-0.312]

49 Recovering Planes We first show how to recover a plane Π that contains parallel 3D lines L using their CCP and XVP. [sent-197, score-0.276]

50 Given a set of coplanar parallel lines L, if they hTahveeo a CmC 3P. [sent-199, score-0.316]

51 Notice that the CCP corresponds to a ray that intersect all lines at a finite distance whereas the XVP corresponds to a ray that intersects the lines at the infinite distance. [sent-202, score-0.428]

52 στv == ( CAuuvv++ D Bvv v) / EE (17) Now consider the CCP [uc, vc] that also corresponds to a ray lying on Π. [sent-209, score-0.116]

53 Manhattan World An important requirement for applying the plane recovery algorithm is to know which point is CCP and which one is XVP, as they both appear as the common intersection points ofthe curves. [sent-221, score-0.117]

54 In particular, if only one set ofcoplanar parallel lines is available, we cannot distinguish CCP from XVP. [sent-222, score-0.206]

55 In reality, a typical Manhattan scene contains multiple sets of coplanar parallel lines for resolving this ambiguity. [sent-224, score-0.342]

56 Manhattan World (MW) Assumption [3]: We assume that objects in the scene are composed of planes and lines aligned with three mutually orthogonal principal axes, i. [sent-226, score-0.238]

57 , it is parallel to ΠL2L3, lies on the line XVP2-XVP3. [sent-233, score-0.136]

58 Therefore, the CCPs for all planes parallel to ΠL2L3 will lie on the line XVP2-XVP3. [sent-254, score-0.229]

59 Similar conclusions hold for planes parallel to the other two principal (a)(b) Figure 3. [sent-255, score-0.181]

60 The blue dots are the outliers and the yellow ones are either XVPs or CCPs; (b) We fit three lines using only the yellow dots. [sent-258, score-0.125]

61 Therefore, Theorem 4 provides an effective and robust means for disambiguating CCPs and XVPs: in a MW scene, all CCPs and XVPs should lie on a triangle where XVPs correspond to the triangle vertices and CCPs lie on triangle edges (or the extension of edges). [sent-261, score-0.156]

62 MW Scene Reconstruction In order to use Theorem 4 for reconstructing a MW scene, we strategically tilt our XSlit camera to make the slits unparallel to the principal axes L1, L2, and L3 of the buildings so that we can use XVPs and CCPs of different building faces. [sent-264, score-0.304]

63 We first fit conics to images of the lines and compute pairwise intersections. [sent-266, score-0.208]

64 2 that the images of lines are hyperbolas with the form: + + C˜v2 + + + = 0 where A˜, B˜, A˜u2 C˜ B˜uv D˜u E˜v F˜ and are uniquely determined by the XSlit camera intrinsics that can be precomputed and are identical for all hyperbolas. [sent-269, score-0.239]

65 We apply a similar curve fitting scheme as [7] by forming an over-determined linear system of conic coefficients using the sampled points on the curves. [sent-270, score-0.126]

66 Notice that in addition to XVPs and CCPs, every two conics that correspond to two unparallel 3D lines may also intersect. [sent-274, score-0.225]

67 Therefore, we fit three lines using the rest intersections and use the resulting triangle vertices and edges to separate the XVPs from the CCPs. [sent-277, score-0.196]

68 3 illustrates this process for a simple scene composed of 18 lines on 6 planes. [sent-279, score-0.137]

69 Each plane has 3 parallel lines lying on it and the directions of all lines are aligned with the three principal axes. [sent-280, score-0.43]

70 We further map each curve segment back to a 3D line segment by intersecting the XSlit rays originated from the conic with the reconstructed plane. [sent-293, score-0.185]

71 , a POX-Slit [30]) and the two slits and the image plane are evenly spaced. [sent-308, score-0.175]

72 We rotate the camera 45◦ around the y axis and 15◦ around both x and z axes so that axis-aligned lines will have XVPs and CCPs in the XSlit image. [sent-309, score-0.215]

73 We also re-render the recovered faces using a perspective camera as shown in Fig. [sent-326, score-0.151]

74 In this example, we use the image synthesis technique for producing an XSlit panorama [25, 30]: we translate a perspective camera horizontally from left to right with constant speed and then stitch linearly varying columns of pixels. [sent-337, score-0.121]

75 Each view is rendered at resolution of 300 600 and the perspective camera views the scene forfo m30 top t 6o0 d0o awnnd a tnhde t pieltersdp by 1v5e◦ c aarmoeunrad vthieew z tahxeis. [sent-338, score-0.147]

76 (a) We use two layers of cylindrical lenses, each with a slit aperture; (b) We mount the XSlit lens on an interchangeable lens camera. [sent-351, score-0.189]

77 We re-render the reconstructed geometry using a perspective camera and compare it with the ground truth (Fig. [sent-354, score-0.156]

78 Real Scene Experiments Finally, we have constructed a prototype XSlit camera by modifying a commercial interchangeable lens camera (Sony NEX-5N). [sent-359, score-0.284]

79 We replace its lens with a pair of cylindrical lenses, each using two slit apertures as shown in Fig. [sent-360, score-0.144]

80 We choose to modify an interchangeable lens camera rather than an SLR is that it has a shorter flange focal distance (FFD), i. [sent-362, score-0.152]

81 This indicates that we need to put the camera closer to the objects as well as use lenses with a large field-of-view and a smaller focal length. [sent-370, score-0.118]

82 The mirror-free interchangeable camera has a much shorter FFD than SLRs and therefore highly suitable. [sent-371, score-0.123]

83 To calibrate the XSlit camera, we use a pattern of five lines and use an auxiliary perspective camera to determine line positions and orientations. [sent-374, score-0.273]

84 7, we construct a scene composed of the parallel lines lying on two different planes. [sent-377, score-0.274]

85 When viewed by a perspective camera, the lines appear nearly identical: although they intersect at a common vanishing point, it is difficult to tell if they belong to different planes, as shown in Fig. [sent-379, score-0.339]

86 In contrast, these lines are apparently different in our XSlit camera image, as shown in Fig. [sent-381, score-0.197]

87 Next, we apply the conic fitting and CCP detection methods on these curves and we are able to identify one XVP and two CCPs. [sent-383, score-0.107]

88 7(d) maps the recovered planes (highlighted in red and green) back onto plane 2plane 1(a)CaXmSelitr a(b) Figure7. [sent-385, score-0.155]

89 (a) Scene acquisition; (b) A perspective image; (c) An XSlit image; (d) We detect the two planes (highlighted in red and green) using the XSlit image. [sent-387, score-0.105]

90 e7ct”iv ×e and orient the XSlilt camera to guarantee it observes enough curviness of vertical parallel lines. [sent-398, score-0.202]

91 Without any processing, the XSlit image shows that the four groups of parallel lines exhibit different curviness. [sent-399, score-0.206]

92 Our solution directly resolves parallel line ambiguity by utilizing a unique class of image features in XSlit images, 888777 i. [sent-405, score-0.166]

93 , the XSlit Vanishing Point (XVP) and Coplanar Common Point (CCP), for grouping coplanar parallel lines. [sent-407, score-0.205]

94 Our main contribution is a new theory that shows each group of coplanar parallel lines will intersect at an XVP and a CCP in their XSlit image and its geometry can be directly recovered from the XVP and CCP. [sent-408, score-0.439]

95 Our solution relies on accurately detecting curves and fitting conics to locate XVPs and CCPs. [sent-410, score-0.138]

96 If a captured curve is too short or too straight, our conic fitting scheme can introduce large errors and therefore generate incorrect XVPs and CCPs. [sent-411, score-0.111]

97 For example, due to the small distance between the slits, only 3D lines lying close to the camera will appear sufficiently curved. [sent-415, score-0.254]

98 Finally, our prototype XSlit camera may also benefit several other vision tasks. [sent-421, score-0.132]

99 For example, we can combine an area light source with two cylindrical lenses for creating a prototype XSlit light source. [sent-428, score-0.159]

100 On the localization of straight lines in 3D space from single 2D images. [sent-444, score-0.111]


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