cvpr cvpr2013 cvpr2013-27 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Visesh Chari, Peter Sturm
Abstract: 3D reconstruction of transparent refractive objects like a plastic bottle is challenging: they lack appearance related visual cues and merely reflect and refract light from the surrounding environment. Amongst several approaches to reconstruct such objects, the seminal work of Light-Path triangulation [17] is highly popular because of its general applicability and analysis of minimal scenarios. A lightpath is defined as the piece-wise linear path taken by a ray of light as it passes from source, through the object and into the camera. Transparent refractive objects not only affect the geometric configuration of light-paths but also their radiometric properties. In this paper, we describe a method that combines both geometric and radiometric information to do reconstruction. We show two major consequences of the addition of radiometric cues to the light-path setup. Firstly, we extend the case of scenarios in which reconstruction is plausible while reducing the minimal re- quirements for a unique reconstruction. This happens as a consequence of the fact that radiometric cues add an additional known variable to the already existing system of equations. Secondly, we present a simple algorithm for reconstruction, owing to the nature of the radiometric cue. We present several synthetic experiments to validate our theories, and show high quality reconstructions in challenging scenarios.
Reference: text
sentIndex sentText sentNum sentScore
1 fr Abstract 3D reconstruction of transparent refractive objects like a plastic bottle is challenging: they lack appearance related visual cues and merely reflect and refract light from the surrounding environment. [sent-3, score-1.345]
2 A lightpath is defined as the piece-wise linear path taken by a ray of light as it passes from source, through the object and into the camera. [sent-5, score-0.378]
3 Transparent refractive objects not only affect the geometric configuration of light-paths but also their radiometric properties. [sent-6, score-0.641]
4 Introduction Reconstruction of transparent objects has gathered interest in the last few years [5, 8, 11, 12, 13, 14, 17]. [sent-14, score-0.501]
5 Methods could be broadly classified into approaches that rely on physical (material) properties of transparent objects, and approaches that try to extend traditional shape acquisition approaches to the case of transparent objects. [sent-16, score-0.999]
6 Among the approaches relying on material properties, geometric and radiometric cues are the most prominent inputs to reconstruction algorithms. [sent-17, score-0.422]
7 fr Figure 1: Given a transparent refractive object, a light source and a camera, the pixel q receives light from sources at positions Q1 and Q2. [sent-20, score-1.307]
8 In both works Q1/Q2 is estimated by using a calibrated computer monitor as light source (CRT monitor in our case). [sent-26, score-0.877]
9 In this paper, we focus on specular trans- parent objects, that is objects for which incoming light is partly reflected off the surface and partly entering the object, after undergoing a refraction at the surface. [sent-28, score-0.831]
10 While these works consider specular surfaces (both mirrors and transparent surfaces), they do not utilize the fact that transparent objects leave a shape dependent radiometric signature in images. [sent-32, score-1.366]
11 Since transparent surfaces also reflect light falling on 111444333866 them, photometric stereo and related algorithms have also been proposed to reconstruct the exterior of transparent objects [20, 13]. [sent-33, score-1.346]
12 While reconstruction using such methods gives good results, we argue that modeling transparent surfaces as pure mirrors discards important information about their physical properties (refractive index, internal structure, etc. [sent-35, score-0.659]
13 For every “light-path” that we capture, we record both geometric information (position and direction of light rays captured by and originating from light source, depending on requirement) and radiometric information (radiance of light at the beginning and end of each light-path). [sent-39, score-1.004]
14 A first main result is that this allows to reconstruct a transparent object from a single configuration of the acquisition setup, i. [sent-40, score-0.613]
15 Related Work In the past, several approaches have used either geometric or radiometric cues to reconstruct transparent surfaces. [sent-55, score-0.869]
16 Geometric approaches typically measure the deviation from perspective imaging produced by a refractive transparent object, and recover the shape as a solution that explains the observation [21]. [sent-56, score-0.806]
17 In [17], the authors present a minimal case study of the conditions in which refractive surfaces can be reconstructed. [sent-57, score-0.428]
18 They re-cast transparent object reconstruction as the task of reconstructing the path of each individual light-path that is captured by a camera after refraction through a transparent surface. [sent-58, score-1.292]
19 Other examples of shape recovery from distortion analysis include the more recent work by [13], which analyzes the specific case of a single dynamic transparent surface that distorts a known background and is observed by multiple cameras. [sent-60, score-0.591]
20 Apart from geometry, radiometric information also turns out to be very important in the case of transparent objects since they simultaneously reflect and refract light. [sent-62, score-0.767]
21 Since they reflect light like a specular surface, many recent photometric approaches have tried to reconstruct transparent surfaces by studying their specularities. [sent-63, score-0.927]
22 While [20] provides a low cost approach to reconstruction by studying specular highlights, [13] shows how to reconstruct transparent surfaces with inhomogeneous refractive interiors, by measuring highlights multiple times to remove extraneous effects like scattering, interreflections etc. [sent-64, score-1.333]
23 When unpolarized light is reflected or transmitted across a dielectric refractive surface, it gets partially polarized. [sent-66, score-0.898]
24 Since refractive objects present a challenging reconstruction problem, many authors have resorted to using active approaches for reconstructions. [sent-71, score-0.474]
25 Reflection and Refraction Caused by Transparent Surfaces In this section, we describe an image formation model for transparent surfaces, that forms the basis of our reconstruction approach. [sent-74, score-0.577]
26 Let X be a calibrated point light source emitting unpolarized light. [sent-76, score-0.414]
27 By calibrated, we mean here that we know the “amount” of light emitted in every direction (see section 6 for practical approaches/considerations). [sent-77, score-0.314]
28 If the light ray hits a transparent surface, part of its energy gets reflected in a mirror direction and part enters the transparent object, after undergoing a refraction at the surface. [sent-79, score-1.636]
29 Both the reflection and the refraction happen within a plane of refraction π that is spanned by the point of intersection of the light ray and the surface, and the surface normal at that point. [sent-80, score-0.99]
30 The geometric aspects of reflection and refraction 111444333977 Figure 2: (left top) Description ofthe general theory behind our approach. [sent-81, score-0.334]
31 While the acquisition is similar to that of Kutulakos et al [17], we also include radiance in our measurements (depicted by the changing color of rays while they travel from the illuminant to the camera pixel). [sent-82, score-0.529]
32 A camera facing a monitor with transparent objects in between. [sent-90, score-0.869]
33 Let θ1 be the angle between incoming light ray and the surface normal (cf. [sent-92, score-0.666]
34 Figure The reflected light ray forms the opposite angle θ1 with normal whereas the angle θ2, formed by the refracted and the normal, is given by: sinθ2= sinθ1nn12 where n1 and n2 the 2). [sent-93, score-0.845]
35 the ray (1) are the refractive indices of the media on both sides of the surface (n2 for the inside, n1 for the outside, where the light source is located). [sent-94, score-0.866]
36 Let I the be irradiance of the light source in the considered direction. [sent-96, score-0.292]
37 The irradiance of the reflected ray (respectively refracted ray), is given by [1]: Ir = It = 2ssiinn22((θθ11−+ θ θ22))? [sent-97, score-0.465]
38 Note that even for unpolarized light sources, the reflected and refracted light will in general be polarized. [sent-100, score-0.865]
39 if light gets reflected or refracted a second time (see section 5. [sent-103, score-0.531]
40 Surface Depth Reconstruction: Reflection Surface reconstruction is done for individual camera pixels, by estimating the depth of the surface along the lines of sight of pixels. [sent-112, score-0.474]
41 Let d be the depth of the object along this line of sight, P be the intersection point of the object surface and the line of sight, and ˆn the surface normal at that point. [sent-120, score-0.412]
42 3), we know the point Q on the monitor whose reflection is seen in the pixel. [sent-123, score-0.381]
43 We do so by first computing the incident angle θ1 between the surface normal 111444334088 and the incident light ray, after which d is trivial. [sent-125, score-0.571]
44 Since our setup is radiometrically calibrated, we equate the radiance ratio r = IIr to the reflected and refracted an- gles usinrg = eq2usaisnitni2o2(nθ(θ1 21−+ θ θ22) ? [sent-126, score-0.635]
45 Note that although we are considering the case of reflec- tion here, the refracted angle θ2 nevertheless appears in the equation, due to the object’s refractive property. [sent-128, score-0.52]
46 Second, θ1 is typically (much) larger than 30◦, due to the practical setup which requires that the camera have both a reflected and a direct view of the monitor. [sent-149, score-0.37]
47 Consider the graph of r as a function of θ1 for the refractive index of water (n2 = 1. [sent-150, score-0.464]
48 From images acquired with a completely static setup, we are able to compute the depth of the transparent object, for each pixel in which a reflection is visible. [sent-157, score-0.692]
49 To do so, we need to know the refractive index of the object’s material. [sent-158, score-0.389]
50 Note that in the same scenario, we have much better normal information because of radiometric information. [sent-166, score-0.306]
51 While LP-2 is robust because correspondences are far away, its highly impractical since use of LCD’s for correspondence is problematic (because of light fall-off, scattering etc. [sent-167, score-0.329]
52 The main difference is however that in order to observe the refraction, the camera must be inside the same medium as the object or, be located in a medium with the same refractive index as that of the object. [sent-171, score-0.476]
53 For example, a camera looking at a monitor immersed in water (or, more realistically, put next to an aquarium’s bottom plate), might allow to reconstruct the water’s surface. [sent-172, score-0.557]
54 In practice however, we require dense matches between the camera image and the CRT monitor, which is why we acquire multiple images of a sequence of Gray-coded patterns displayed on the monitor [2]. [sent-176, score-0.368]
55 for each individual camera pixel we determine the point on the monitor whose reflection or refraction in the object, is seen by that pixel. [sent-179, score-0.626]
56 Unknown Refractive Index The above approach requires knowledge of the object’s refractive index. [sent-186, score-0.336]
57 We thus have a total of three unknowns, the refractive index (or, the ratio n12 of refractive indices of object and air) and the two angles θ1, and three constraints: the two constraints of form (4) and one that links rhe two angles θ1 (ref Figure 2 [1]). [sent-191, score-0.756]
58 However, even when light is only reflected off a transparent object surface, equations (4) can be used to solve for relative refractive index n12 = nn21, even from a single pixel. [sent-193, score-1.254]
59 Thus, we have extended the scenarios where reconstruction is possible to the case of reflection off the object surface, when refractive index is unknown. [sent-194, score-0.596]
60 if the camera acquires an image of the monitor through a transparent object, with refractions happening both at its front and back sides. [sent-200, score-0.898]
61 Let us reconsider equations (2) and (3): they indicate how much energy of the incoming light is reflected respectively refracted. [sent-204, score-0.439]
62 In addition however, for dielectric materials, the reflected and refracted light is polarized, even if the incoming light is not. [sent-205, score-0.845]
63 It can be shown that polarization adds a factor to the radiance ratio that is dependent on the angle between the two planes of reflection/refraction encountered along a single light-path. [sent-206, score-0.416]
64 Consider two cameras looking at a transparent object, which refracts light from a known illuminant twice. [sent-208, score-0.81]
65 In this case, radiance ratio observations are made by each camera for each light-path. [sent-211, score-0.363]
66 It is possible to show that for every light-path, there exists a 1D curve of incident angle pairs such that one angle occurs at each “bounce” of a light-path and the radiance ratio is satisfied [1]. [sent-212, score-0.418]
67 In addition to the geometric constraints expressed in [17] we have one extra constraint per light ray, so it is now possible to solve for the 3D structure of the transparent object given known refractive index. [sent-214, score-1.084]
68 An ∗ symbol represents the fact that even in the case of only reflection, the relative refractive index can be computed. [sent-217, score-0.389]
69 c oen satr uicotison of transparent objects that can be solved with the help of radiance measurements, are summarized in Table 1. [sent-221, score-0.746]
70 It is interesting to note that transparent objects have lesser minimal requirements for reconstruction than mirror like objects. [sent-222, score-0.644]
71 Practical considerations The above theory shows that the radiance of a final light ray in a light-path contains information that could be used to reconstruct the entire light-path. [sent-225, score-0.74]
72 In this section we describe important elements of our experiments to collect radiance measurements for reconstruction. [sent-226, score-0.288]
73 1) We use an illuminant with known geometry to emit unpolarized light in a desired set of directions. [sent-228, score-0.433]
74 2) Light from the illuminant interacts with the transparent object, and reflects / refracts off its surface towards the camera after one bounce. [sent-229, score-0.783]
75 3) The camera then captures both the direction and radiance of some of reflected / refracted light rays, which is used for reconstruction. [sent-230, score-0.863]
76 Since we need to capture the position and radiance of an individual light ray, we adopt the pin-hole model for the camera (smallest aperture and large focal length). [sent-232, score-0.567]
77 We arrived on an acceptable range of focal lengths that have desired depth of field and capture both the monitor and object in focus, by trial and error. [sent-234, score-0.376]
78 Finally, for each captured ray, we compute the corresponding pixel on the monitor from which the ray originated using standard methods [3]. [sent-235, score-0.424]
79 Unpolarized illuminant In our experiments, we use a flat CRT monitor (LCD montiors emit polarized light), whose pose is computed with respect to an internally calibrated camera [18]. [sent-236, score-0.576]
80 We capture the light emitted by each pixel of the monitor in 111444444200 Figure 4: (Left top) Normal map of “Fanta bottle” sequence. [sent-238, score-0.554]
81 Phenomenon like scratches on the bottle, inhomegenous refractive index, violation of single bounce through occlusion are some bad effects, but still reliable reconstructions are achieved. [sent-243, score-0.475]
82 Interreflections A common problem with measuring illumination reflected / refracted off specular transparent objects is interreflections. [sent-255, score-0.879]
83 They not only corrupt the radiance measurement, but also pose a problem to correspondence estimation. [sent-256, score-0.297]
84 Instead of using a projector to light the scene, we use the CRT monitor instead. [sent-258, score-0.516]
85 Correspondence Acquiring correspondence between pixels on the monitor and pixels on the camera that correspond to the same light-path becomes slightly cumbersome when transparent objects are involved [2]. [sent-269, score-0.921]
86 Experiments and Results In the previous sections, we showed that radiance ratios could be used to reconstruct transparent surfaces, which can help in reducing the number of measurements required for reconstruction. [sent-274, score-0.842]
87 t camera noise and refractive index mismatch are present in the supplementary materials. [sent-288, score-0.476]
88 Experiment 2: “Water Sequence” Figure 5 (Left column) shows some images acquired in order to reconstruct the surface of water in a plastic bowl. [sent-289, score-0.333]
89 Because of the planar nature of the scene, we compute correspondence by simply computing a homography between the reflected image and the direct image of a photograph displayed on the monitor. [sent-293, score-0.295]
90 Note how global compoments of the image are present even in places where there is no direct light (Figure 5, red square). [sent-302, score-0.287]
91 On the other hand, robust measurement of the position and direction of light incident on the glasses from the monitor requires a large set of images to be captured while moving the monitor over, say, an optical bench. [sent-305, score-0.843]
92 Again, like in the case of the “Water Sequence” we hypothesize various depth values along each back-projected pixel, and test its validity using computed radiance ratios. [sent-307, score-0.34]
93 Note that optimizing depth and normal simultaneously would serve to remove the artefacts seen in the figure, especially enforcing the depth-normal consistency (differentiation of depth gives normal). [sent-313, score-0.291]
94 Discussion and Conclusion Reconstruction of transparent objects remains a challenging problem because of the lack of cues that are normally available for other objects. [sent-315, score-0.542]
95 Other applications of our approach are in verifying validity of light transport matrices, radiometric calibration etc. [sent-318, score-0.492]
96 111444444422 Figure 5: (Left column) Two of 25 images used to compute the direct and global images [15] to remove the effect of interreflections and caustics on radiance measurement. [sent-320, score-0.48]
97 Shape and refractive index recovery from single-view polarisation images. [sent-386, score-0.389]
98 Shape estimation of transparent objects by using inverse polarization ray tracing. [sent-401, score-0.736]
99 Reconstructing the surface of inhomogeneous transparent scenes by scatter-trace photography. [sent-412, score-0.619]
100 Adequate reconstruction of transparent objects on a shoestring budget. [sent-458, score-0.608]
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