cvpr cvpr2013 cvpr2013-349 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Yu Ji, Jinwei Ye, Jingyi Yu
Abstract: Transparent gas flows are difficult to reconstruct: the refractive index field (RIF) within the gas volume is uneven and rapidly evolving, and correspondence matching under distortions is challenging. We present a novel computational imaging solution by exploiting the light field probe (LFProbe). A LF-probe resembles a view-dependent pattern where each pixel on the pattern maps to a unique ray. By . ude l. edu observing the LF-probe through the gas flow, we acquire a dense set of ray-ray correspondences and then reconstruct their light paths. To recover the RIF, we use Fermat’s Principle to correlate each light path with the RIF via a Partial Differential Equation (PDE). We then develop an iterative optimization scheme to solve for all light-path PDEs in conjunction. Specifically, we initialize the light paths by fitting Hermite splines to ray-ray correspondences, discretize their PDEs onto voxels, and solve a large, over-determined PDE system for the RIF. The RIF can then be used to refine the light paths. Finally, we alternate the RIF and light-path estimations to improve the reconstruction. Experiments on synthetic and real data show that our approach can reliably reconstruct small to medium scale gas flows. In particular, when the flow is acquired by a small number of cameras, the use of ray-ray correspondences can greatly improve the reconstruction.
Reference: text
sentIndex sentText sentNum sentScore
1 We present a novel computational imaging solution by exploiting the light field probe (LFProbe). [sent-2, score-0.321]
2 edu observing the LF-probe through the gas flow, we acquire a dense set of ray-ray correspondences and then reconstruct their light paths. [sent-6, score-1.096]
3 To recover the RIF, we use Fermat’s Principle to correlate each light path with the RIF via a Partial Differential Equation (PDE). [sent-7, score-0.343]
4 Specifically, we initialize the light paths by fitting Hermite splines to ray-ray correspondences, discretize their PDEs onto voxels, and solve a large, over-determined PDE system for the RIF. [sent-9, score-0.387]
5 The RIF can then be used to refine the light paths. [sent-10, score-0.207]
6 Experiments on synthetic and real data show that our approach can reliably reconstruct small to medium scale gas flows. [sent-12, score-0.762]
7 Introduction Accurately reconstructing transparent phenomena such as fluid wavefronts and gas flows remains as one of the most challenging problems in computer vision. [sent-15, score-1.016]
8 Second, compared with static transparent objects, transparent gas flows are even more difficult to reconstruct since the refractive index field (RIF) within the gas volume is uneven and rapidly evolving, introducing large image distortions. [sent-19, score-1.962]
9 We acquire ray-ray correspondences to first estimate their light paths and then use them to recover the refractive index field (RIF) of the gas volume. [sent-21, score-1.449]
10 Usually, a known reference pattern is placed near the transparent surface and robust tracking is applied to establish correspondences between a feature point on the pattern and its image in the camera. [sent-24, score-0.38]
11 It then uses Background Oriented Schlieren (BOS) to measure deflections and applies tomographic reconstruction for recovering the gas flow. [sent-30, score-0.742]
12 We, in contrast, present a portable solution for acquiring small to medium scale gas flows. [sent-32, score-0.79]
13 Our solution exploits the light field probe (LF-Probe) [28, 29] which serves as a view-dependent reference pattern. [sent-33, score-0.321]
14 A LF-probe, in essence, is an “inverted” light field camera [22] where each pixel on the pattern maps to a 222555000755 unique ray. [sent-34, score-0.34]
15 , a pattern ray from the LF-probe will be mapped to a pixel ray in the camera, as shown in Fig. [sent-37, score-0.325]
16 Recent studies have shown that ray-ray correspondences greatly benefit specular surface reconstruction. [sent-39, score-0.241]
17 We demonstrate how to use ray-ray correspondences for inferring light paths [16] through the RIF within the gas volume. [sent-43, score-1.071]
18 Under Fermat’s Principle, each light path corresponds to the shortest Optical Path Length (OPL). [sent-44, score-0.333]
19 By using variational method, we show that each light path and the RIF is related via a Partial Differential Equation (PDE). [sent-45, score-0.283]
20 Specifically, we initialize the light paths by fitting Hermite splines [8] to ray-ray correspondences, discretize their PDEs onto voxels, and solve a large, over-determined PDE system for the RIF. [sent-47, score-0.387]
21 The RIF can then be used to refine the light paths. [sent-48, score-0.207]
22 Experiments on synthetic and real data show that our approach can reliably reconstruct small to medium scale gas flows. [sent-50, score-0.762]
23 In particular, when the flow is acquired by a small number of cameras, the use of ray-ray correspondences can greatly improve reconstruction quality. [sent-51, score-0.249]
24 Related Work Reconstructing transparent objects/phenomena such as fluids and gas flows is an important problem to oceanography and fluid mechanics and has recently attracted much attention from computer vision. [sent-53, score-1.013]
25 [24] use pointpixel correspondences to first estimate the specular flow and then apply quadric approximations to recover mirror-type surfaces. [sent-57, score-0.313]
26 A common issue in point-pixel based solutions is ambiguity: a pixel corresponds to a ray from the camera while the specular surface can lie at any position along the ray. [sent-58, score-0.34]
27 Bonfort and Sturm [4] use images captured by multiple calibrated cameras to reconstruct specular surface via space carving. [sent-60, score-0.229]
28 Kutulakos and Steger [16] discover that by analyzing the piecewise linear light paths in homogeneous refractive medium, one can view surface reconstruction as a generalized triangulation problem. [sent-61, score-0.614]
29 In this paper, we demonstrate using non-linear light paths for recovering inhomogeneous refractive media. [sent-63, score-0.511]
30 Morris and Kutulakos [20] track the corners of a checkerboard pattern over time in a stereo camera setting and then impose the refractive disparity constraint to iteratively solve for surface heights and normals. [sent-66, score-0.379]
31 [30] point out that to robustly recover light paths, it is important to establish ray-ray correspondences. [sent-71, score-0.263]
32 For example, they propose using Bokode [19], a special pinhole projector, to acquire ray-ray correspondences for directly recovering fluid surface normals. [sent-72, score-0.348]
33 One of the most challenging transparent objects is 3D gas flows. [sent-77, score-0.735]
34 Schardin [26] uses a knife edge to partially block rays proportional to their refracted directions to visualize dynamic gas flows, refractive solids, and shock waves. [sent-79, score-0.97]
35 Howes [12] modifies the traditional Schlieren to conduct quantitative evaluation of refractive index distribution by encoding the hue. [sent-81, score-0.25]
36 [2] captures distorted wavelet noise patterns through the gas vol- ume from multiple viewpoints. [sent-87, score-0.647]
37 It then measures deflections caused by gas refraction to correlate the incident ray (i. [sent-88, score-0.971]
38 , around 3 meters in their experiments) and is suitable for acquiring large scale gas flow. [sent-95, score-0.714]
39 We develop a low-cost, portable solution for acquiring gas flows of small to medium scales. [sent-96, score-0.918]
40 2, can be viewed as an “inverted” light field camera Lytro (www. [sent-106, score-0.299]
41 In Lytro, a microlenslet array is placed in front of the camera sensor to acquire the 4D light field, where the sensor-lens distance is identical to the microlens’ focal length. [sent-109, score-0.43]
42 Each microlens serves as a virtual pinhole camera and the lenslet array serves as a camera array. [sent-110, score-0.373]
43 To obtain a dense set of correspondences, similar to [28, 29], we use color-coded pattern to encrypt the 4D ray positions and directions emitted by the probe. [sent-113, score-0.212]
44 In particular, we use a combination of horizontal red gradient and vertical blue gradient behind each microlens to discriminate rays of different directions. [sent-114, score-0.204]
45 To find out the position shifted due to refraction, we perform optical flow between the refracted pattern and the original one on the green channel to estimate the deflection vectors. [sent-119, score-0.204]
46 We place 3 LF-probes to surround the target gas flow and 3 synchronized cameras to capture the corresponding LF-probe through the gas volume. [sent-125, score-1.437]
47 Our goal is to first acquire a dense set of correspondences between rays entering the gas volume and the ones exiting the volume and then use these incident-exit ray pairs for estimating the light paths and the RIF. [sent-126, score-1.521]
48 In order to reliably correlate the incidentexit ray pairs, we conduct two calibration procedures, one between each LF-probe and its viewing camera and the secLF-Probe 1 Figure 3. [sent-128, score-0.294]
49 An additional checkerboard pattern is placed next to the probe for measuring the orientation of the probe w. [sent-137, score-0.262]
50 Once we determine the direction β of a ray collected by the camera and the angle α between the probe’s normal and the camera’s principal axis, we can then compute the ray’s direction as γ = α + β, as shown in Fig. [sent-141, score-0.253]
51 We obtain the ground truth by acquiring the LF-probe without any gas flows. [sent-148, score-0.714]
52 When capturing the gas flows, we then use the optical flow for tracking the pattern. [sent-149, score-0.754]
53 To resolve this issue, we place three addi- tional cameras between the viewing cameras and conduct pair-wise camera calibrations. [sent-154, score-0.221]
54 Once we finish the calibration process, each camera is able to acquire a dense set of ray-ray correspondences w. [sent-155, score-0.26]
55 in) to represent rays emitting from the LF-Probes (the incident rays) and for the rays entering the camera (the exit rays) as shown in Fig. [sent-160, score-0.295]
56 Volumetric Gas Reconstruction Given a dense set of ray-ray correspondences across the gas volume, our goal is to recover the RIF that best matches these correspondences. [sent-167, score-0.782]
57 We instead derive how RIF is correlated with the light path using Fermat’s principle: the light always travels along the path with the shortest Optical Path length (OPL) [5]. [sent-169, score-0.616]
58 the refractive index n at every point p(x, y, z) (or voxel in the discrete case) on the path c: S =? [sent-173, score-0.343]
59 cn(p)ds (1) We can further parameterize p(x, y, z) as function of the time t that light reaches (x, y, z) as p(x(t) , y(t) , z(t)), then we have: S =? [sent-174, score-0.207]
60 xt2+ yt2+ zt2 (2) = ∂∂tx, = ∂∂ty, = ∂∂tz and n(p) is the refractive where xt yt zt index at p. [sent-176, score-0.221]
61 Our goal is to solve for both the light path c and the RIF n. [sent-178, score-0.283]
62 Base on the Fermat’s Principle, each light path c corresponds to the shortest OPL. [sent-179, score-0.333]
63 RIF Estimation If we have the light paths, we can then estimate the RIF. [sent-183, score-0.207]
64 e light ray reaches the gas volume at t = t0 and leaves at t = t1. [sent-198, score-1.065]
65 To recover the RIF, we discretize 3-D space into voxels and estimate the refraction index at each voxel. [sent-218, score-0.237]
66 Specifically, we can predefine the gas volume and discretize Eqn. [sent-219, score-0.783]
67 For voxels at the bounding faces of the gas volume, we assume their refractive indices are equal to nair = 1. [sent-228, score-0.937]
68 Using all light paths, we form a PDE system of the RIF. [sent-232, score-0.207]
69 The RIF estimation method presented above requires knowing the light paths. [sent-234, score-0.207]
70 Therefore, we initialize light paths by fitting a Hermite spline [8] to each rayray correspondence (Pin, Pout, . [sent-236, score-0.352]
71 Light-Path Refinement × × Once we obtain the initial estimation of the RIF, we refine the light paths within the gas volume using Fermat’s Principle. [sent-245, score-1.036]
72 However, such graph approximation does not consider how much the distance light travels inside each voxel. [sent-251, score-0.207]
73 To speed up 2sh×or3te2st v path computation, we aggressively prune the nodes based on the observation that light paths only slightly deviate from a linear path. [sent-257, score-0.42]
74 Specifically, we impose a “bounding volume” along the previously estimated light path as shown in Fig. [sent-258, score-0.283]
75 Furthermore, inside each voxel, we prune a large amount of corners/Steiner points from the search by assuming that the light direction will not change drastically after the refinement. [sent-260, score-0.256]
76 Synthetic Scene Simulations We first test our solution on a static gas volume whose RIF follows Gaussian distribution: n(x, y, z) = nair − (nair where (x0, y0, z (n0) is −the 1 )ceenter of flow. [sent-272, score-0.759]
77 × T6o0 capture tnhsee LF-probe image, we dheasvcer ibmedplemented a voxel-based Ray-tracer that can trace along non-linear light paths within the volume. [sent-278, score-0.32]
78 In this synthetic scene, we use three LF-probes surrounding the gas volume to mimic the real setup. [sent-282, score-0.745]
79 − 1)e−((x−x0)2+(y−y0)2+(z−z0)2)/2, Since our synthesized images are noise-free, we directly map the red/blue channels to incident ray directions and apply optical flow on the green channel to determine incident ray origins. [sent-286, score-0.548]
80 The measured optical flows and angular variations are shown in Fig. [sent-287, score-0.227]
81 4 to iteratively estimate the light paths and the RIF. [sent-290, score-0.32]
82 Since this volume data has more complex geometric structures, we discretize the volume into 32 32 32 voxels. [sent-304, score-0.205]
83 0W ien apply the same approach to iteratively recover the RIF and the light paths. [sent-306, score-0.238]
84 Specifically, we have implemented the multi-camera BOS gas flow reconstruction algorithm [2] and conducted comparisons under various configurations: w. [sent-315, score-0.759]
85 When testing different numbers of cameras, we fix the gas-pattern distance to 5 the gas volume sriazse,; wweh feinx studying pthatete impact aonfc gas-pattern ed gisasta vncole-, we use 4 camera-pattern pairs. [sent-318, score-0.716]
86 This is because point-pixel correspondences are insufficient for determining the light paths unless the pattern is placed far away. [sent-340, score-0.49]
87 × Since the gas flow is fast-evolving, we use a fast shutter of 1/320 s. [sent-360, score-0.745]
88 To generate real 3D gas flows, we use an alcohol lamp whose flame temperature can reach around 600◦C. [sent-363, score-0.676]
89 9 shows our reconstructed gas flows at three different time instances. [sent-367, score-0.807]
90 The gas flow inside the volume is highly inhomogeneous. [sent-370, score-0.781]
91 Our reconstructed RIF indicates that the central portion of the volume has a lower refractive index, i. [sent-373, score-0.292]
92 (a) The captured LF-probe images; (b) Measured ray direction variations through the flow; (c)-(e) Three vertical slices of the reconstructed RIFs where (d) is the central slice. [sent-385, score-0.25]
93 Discussions and Conclusions We have presented a new computational imaging solution for reconstructing dynamic 3D gas flows. [sent-397, score-0.703]
94 We have then used these 222555 111311 correspondences to iteratively estimate the light paths and the refractive index field of the gas volume. [sent-399, score-1.323]
95 Experiments on synthetic and real data have shown that our approach provides a portable and reliable solution for reconstructing dynamic and inhomogeneous gas flows of small to medium scales. [sent-400, score-0.936]
96 To reduce image noise, we illuminate the LF-probes with ultrabright light sources. [sent-403, score-0.232]
97 We plan to use the light field camera such as Lytro (www. [sent-417, score-0.299]
98 Compared with our current setting that each microlens on the LF-probe generates a single rayray correspondence, the new setup will map each pixel of the microlens pattern to a ray-ray correspondence. [sent-422, score-0.331]
99 At the same time, we can use the acquired gas flows to improve fluid simulations for producing more realistic animations. [sent-425, score-0.901]
100 A theory of refractive and specular 3D shape by light-path triangulation. [sent-526, score-0.272]
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Abstract: Transparent gas flows are difficult to reconstruct: the refractive index field (RIF) within the gas volume is uneven and rapidly evolving, and correspondence matching under distortions is challenging. We present a novel computational imaging solution by exploiting the light field probe (LFProbe). A LF-probe resembles a view-dependent pattern where each pixel on the pattern maps to a unique ray. By . ude l. edu observing the LF-probe through the gas flow, we acquire a dense set of ray-ray correspondences and then reconstruct their light paths. To recover the RIF, we use Fermat’s Principle to correlate each light path with the RIF via a Partial Differential Equation (PDE). We then develop an iterative optimization scheme to solve for all light-path PDEs in conjunction. Specifically, we initialize the light paths by fitting Hermite splines to ray-ray correspondences, discretize their PDEs onto voxels, and solve a large, over-determined PDE system for the RIF. The RIF can then be used to refine the light paths. Finally, we alternate the RIF and light-path estimations to improve the reconstruction. Experiments on synthetic and real data show that our approach can reliably reconstruct small to medium scale gas flows. In particular, when the flow is acquired by a small number of cameras, the use of ray-ray correspondences can greatly improve the reconstruction.
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