cvpr cvpr2013 cvpr2013-447 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Timothy Yau, Minglun Gong, Yee-Hong Yang
Abstract: In underwater imagery, the image formation process includes refractions that occur when light passes from water into the camera housing, typically through a flat glass port. We extend the existing work on physical refraction models by considering the dispersion of light, and derive new constraints on the model parameters for use in calibration. This leads to a novel calibration method that achieves improved accuracy compared to existing work. We describe how to construct a novel calibration device for our method and evaluate the accuracy of the method through synthetic and real experiments.
Reference: text
sentIndex sentText sentNum sentScore
1 Abstract In underwater imagery, the image formation process includes refractions that occur when light passes from water into the camera housing, typically through a flat glass port. [sent-4, score-0.688]
2 We extend the existing work on physical refraction models by considering the dispersion of light, and derive new constraints on the model parameters for use in calibration. [sent-5, score-0.974]
3 We describe how to construct a novel calibration device for our method and evaluate the accuracy of the method through synthetic and real experiments. [sent-7, score-0.325]
4 One of the main difficulties for computer vision is refraction caused by the camera housing. [sent-10, score-0.718]
5 Recently there has been increasing interest in applying a physically correct model of refraction to improve the accuracy of stereo reconstructions [1, 5, 6, 11]. [sent-12, score-0.576]
6 Building upon these results, we further characterize the flat refraction camera model by studying the dispersion of light, which is the phenomenon where light refracts at a different angle depending on its wavelength. [sent-15, score-1.318]
7 While previous authors regarded dispersion as a minor problem to be ignored [9], we show that the disparate light paths can be exploited in a manner similar to triangulation, thereby increasing calibration accuracy. [sent-16, score-0.718]
8 In this paper we first show that dispersion provides additional constraints on the parameters of the refraction model, and explain how they can be used in calibration. [sent-17, score-0.974]
9 The refractive index of each layer varies with the wavelength of light, resulting in a different path for each wavelength. [sent-24, score-0.531]
10 All paths from a single object point lie on a common plane containing the refraction axis. [sent-25, score-0.676]
11 demonstrate how to perform the calibration in practice, including the construction of a calibration device using inexpensive parts. [sent-26, score-0.482]
12 We develop an original procedure to obtain ground truth values for real data, which is missing in previous works on underwater camera calibration. [sent-28, score-0.345]
13 analyzed the case of a single refraction at a flat air-water interface, and showed that such a camera system does not have a single viewpoint. [sent-31, score-0.841]
14 They developed a calibration procedure to find the unknown distance between the camera center and the interface, assuming that the interface is parallel to both the image plane and the checkerboard calibration pattern. [sent-32, score-0.792]
15 Sedlazeck and Koch developed a more flexible calibration method that does not require a calibration object, and also accounts for two refractions when the port of the camera housing is thick. [sent-34, score-0.751]
16 showed that the flat refraction camera model corresponds to an axial camera. [sent-42, score-0.818]
17 With this realization, they formulated a calibration framework that can handle multi-layer refraction models uni- formly through a set of linear constraints on the model parameters. [sent-43, score-0.794]
18 The resulting method still uses nonlinear optimization, but produces initial estimates efficiently by solving a set of linear systems while only assuming that the calibration object geometry is known [1]. [sent-44, score-0.351]
19 Instead, we examine the properties of the refraction camera model with respect to the dispersion of light, and find that by taking these properties into account, we can achieve greater calibration accuracy than if they were ignored. [sent-48, score-1.315]
20 Flat refraction model We first describe the flat refraction camera model and its parameters. [sent-50, score-1.394]
21 An example application which fits this model is a perspective camera placed in a watertight housing with a flat glass port. [sent-51, score-0.406]
22 Consider figure 1, which illustrates a pinhole perspective camera observing a scene through n ≥ 1parallel refraction layers. [sent-52, score-0.737]
23 , n risa dleelfi rneefrda by a thickness di and a refractive index μi,λ, which may depend on the wavelength λ oflight. [sent-56, score-0.483]
24 The distance between the camera and the first layer is given by d0, and the refraction axis A is the vector from the camera center that is perpendicular to all of the refraction layers. [sent-57, score-1.679]
25 show how refractive indices can also be estimated [1]). [sent-60, score-0.308]
26 Moreover, if the camera is placed in an underwater housing, the thickness of the port is often known. [sent-61, score-0.425]
27 Dispersion of light In most common substances, the index of refraction varies with the wavelength of the incident light. [sent-67, score-0.905]
28 ) A single ray of polychromatic light will be refracted into multiple rays depending on the wavelength components. [sent-69, score-0.411]
29 In the context of the flat refraction camera model, this implies that a single physical point will be imaged at multiple image points. [sent-70, score-0.845]
30 , distilled water at 19◦C has a refractive index that varies from 1. [sent-74, score-0.402]
31 In the flat refraction model discussed above, for one refraction (n = 1) the amount of dispersion can be characterized as the solution of a quartic equation. [sent-78, score-1.659]
32 Figure 2 (left) shows the plane of refraction for a ray passing through the refraction interface at (0, q) and reaching an object point (d1,p + q); without loss of generality we assume d0 = 1. [sent-79, score-1.387]
33 The refractive indices for this ray are μ0,a and μ1,a on the left and right sides of the interface respectively. [sent-80, score-0.418]
34 Consider another ray with different refractive indices μ0,b, μ1,b passing through the same object point but refracting at a different location (0, q + δ). [sent-81, score-0.433]
35 Figure 2 (right) shows how δ varies with q and d1 for the underwater calibration case. [sent-94, score-0.419]
36 “normal dispersion” where the refractive index increases as the light wavelength decreases. [sent-99, score-0.551]
37 This implies that there will be nonzero dispersion for all rays not perpendicular to the refraction layers. [sent-100, score-1.049]
38 Calibration In this section we develop constraint equations using dispersion for calibration. [sent-102, score-0.452]
39 is that the refraction axis A can be estimated first, which then allows the layer thicknesses to be found by solving a linear system of equations [1]. [sent-104, score-1.0]
40 By considering the dispersion of light, we obtain a new and effective constraint on A. [sent-105, score-0.416]
41 We show how to incorporate dispersion as a form of triangulation in estimating the layer × thicknesses, and also in a final nonlinear optimization step to refine the estimated parameters. [sent-106, score-0.649]
42 Let va, vb be unit vectors for the directions of two rays of different wavelengths a, b, and suppose they correspond to a single point in the scene. [sent-110, score-0.313]
43 Both rays must lie on the same plane of refraction containing the refraction axis A, which passes through the camera center. [sent-111, score-1.543]
44 Therefore, if the refractive indices differ for the two wavelengths such that va vb, we have the following dispersion constraint: = Dispersion : (va vb)? [sent-112, score-0.889]
45 uses a single linear system to solve for both the refraction axis and the calibration object pose [1], even though the two quantities are not inherently related. [sent-118, score-0.96]
46 Image and measurement noise ×× Since the effect of dispersion can be quite small, we added a preprocessing step in our implementation to reduce the impact of random noise. [sent-119, score-0.433]
47 In the absence of noise, these lines must all pass through a point u where the image plane and the refraction axis intersect. [sent-125, score-0.78]
48 The image points + {y, (y w)} are then back-projected into rays and used in t{hye, dispersion acorens thteranin bt. [sent-132, score-0.462]
49 Layer thicknesses Suppose that the geometry of the points P on the calibration object are known. [sent-137, score-0.413]
50 With appropriate estimates of the refraction axis A, object rotation R, and object translation t⊥ in the plane perpendicular to the axis, Agrawal et al. [sent-138, score-0.848]
51 showed that the thicknesses of the refraction layers can be formulated as a linear system (Eqn. [sent-139, score-0.741]
52 We follow their method, but incorporate a form of triangulation through the use of multiple wavelengths of light. [sent-141, score-0.298]
53 1, a single object point projects to multiple image points when dispersion is present. [sent-143, score-0.436]
54 More formally, if F is a function that projects a 3D point X to a point q on the refractive surface closest to the camera, then for two different wavelengths a and b we define the wavelength triangulation constraint: Triangulation : ? [sent-144, score-0.78]
55 This constraint is imposed sim- × ply by including all rays for each object point in the linear system for layer thicknesses (as well as in the linear system for recovering object pose, described below). [sent-149, score-0.405]
56 ’s solution for finding the refraction layer thicknesses, the required object pose parameters R and t⊥ are computed together with A through the “coplanarity constraint” (Eqn. [sent-152, score-0.694]
57 The coplanarity constraint states that each camera ray v and its corresponding object point P, after being transformed into camera coordinates, must lie on a plane of refraction containing the refraction axis: (RP + t)? [sent-156, score-1.659]
58 (10) Furthermore, for a planar calibration object such as a checkerboard where P(3) = 0, columns 7-9 of B are zero (Eqn. [sent-179, score-0.307]
59 Two further solutions are obtained by negating the signs of r8 and r7, corresponding to a reflection across the plane parallel to the refraction layers and passing through the object origin. [sent-193, score-0.653]
60 The correct solution is found after estimating the refraction layer thicknesses by choosing the one with the minimum reprojection error. [sent-194, score-0.826]
61 Nonlinear refinement The estimated refraction axis A, layer thicknesses di, as well as object pose parameters R and t are refined by a nonlinear optimization. [sent-197, score-1.062]
62 Therefore, the optimization implicitly tries to satisfy wavelength triangulation constraint as defined in Section 4. [sent-199, score-0.298]
63 Then we perform a 1D bisection search for the angle of a camera ray on that plane such that the back-projected ray intersects the given point. [sent-205, score-0.316]
64 Calibration object A standard checkerboard pattern does not suffice for our method because the dispersion effect is not readily apparent under normal lighting conditions. [sent-211, score-0.468]
65 We designed and built a new device that illuminates a perforated grid with two distinct wavelengths of light, forming a precisely known pat222555000200 the illuminated points viewed through an air-water interface (best × viewed in color; one pair of points marked for visibility). [sent-212, score-0.413]
66 The dispersion seen here is typical at around 6-7 pixels. [sent-213, score-0.379]
67 The top curve shows the average intensity of a blue pixel as a function of the intensity of the neighboring red pixels when the camera observes a 660nm light source; similarly for the bottom curve for red pixels. [sent-215, score-0.282]
68 We chose the two light wavelengths to be as far apart as possible to maximize the amount of dispersion, while remaining visible to typical cameras equipped with CCD or CMOS sensors and a Bayer-pattern color filter array (CFA). [sent-223, score-0.311]
69 Longer wavelengths in the infrared range suffer from high attenuation in water, while shorter wavelengths are not readily available for LEDs and may pose a hazard to the user. [sent-224, score-0.4]
70 Point localization Our calibration object provides point light sources emitting two wavelengths of light simultaneously. [sent-227, score-0.701]
71 Lens chromatic aberrations An important consideration with refraction-based lenses is that dispersion also occurs within the lens elements, the effects of which are known as chromatic aberrations (CA). [sent-237, score-0.55]
72 It is necessary to correct for CA in order to isolate the dispersive effect of the refraction planes in front of the camera. [sent-238, score-0.638]
73 We first capture images of our calibration object in air, and obtain two sets of camera intrinsic × parameters using the red and the blue channels separately. [sent-240, score-0.398]
74 Synthetic data For our synthetic data experiments we simulated a camera with a resolution of 4368 2912 pixels and a focal length ohf a4 r6e3s3o pixels, wfh 4i3ch68 8is × × ba 2s9e1d2 on xtheles i anntrdins ai cf parameters of the camera used in our real experiments. [sent-246, score-0.387]
75 We performed experiments for the refraction model configurations listed in Table 1. [sent-247, score-0.576]
76 All refractive indices are assumed known and are listed in table 2. [sent-248, score-0.307]
77 The angle between the refraction axis and the camera’s optical axis was set to 4. [sent-256, score-0.822]
78 The calibration pattern was a 27 29 planar grid of points emitting o bnot hp t4te05rnnm w aasnd a 26760n ×m 2 light. [sent-446, score-0.298]
79 For each noise level we generated 100 trials with the calibration pattern placed 440 units in front of the camera and rotated randomly by up to 20 degrees. [sent-451, score-0.421]
80 We include results before the nonlinear refinement step to show the effectiveness of the dispersion and wavelength triangulation constraints. [sent-453, score-0.722]
81 We believe that the refraction model is correct because the error goes to zero in the absence of noise, the refraction axis estimates appear reasonable, and the reprojection error is being minimized properly. [sent-785, score-1.372]
82 222555000422 × a checkerboard inside the tank, a checkerboard affixed to the tank surface, and the camera mounted on a SlyderDolly translation rail. [sent-788, score-0.499]
83 In light of our results, we believe that the additional constraints provided by dispersion and wavelength triangulation have a significant impact on calibration accuracy beyond simply doubling the number of feature points. [sent-789, score-1.032]
84 We collected two sets of data, one using our novel calibration device with a 27 ×29 grid of points, and a second using a 3 d4e v×i 3e5 w cihthec ak 2er7b×oa2r9d pattern pfooirn comparison cwonithd Agrawal e4t ×al. [sent-795, score-0.29]
85 ) The calibration objects were placed inside an acrylic water tank approximately 45cm behind the front surface and moved around slightly within the camera’s field of view. [sent-801, score-0.55]
86 Although our method gives accurate results, we noticed that the nonlinear refinement step did not improve the estimate of the refraction axis, which was very close to the ground truth to begin with (see Figure 7). [sent-807, score-0.658]
87 Since these observations disagree with our results using synthetic data, we attribute the source of error to measurement noise, lens distortions, and/or the pinhole camera approximation. [sent-810, score-0.276]
88 Interestingly, we found that the estimated d0 was particularly sensitive to variations in the refractive index difference λ2,405nm −λ2,660nm for water, but much less sensitive to variations in− bλoth index values that do not change this difference. [sent-812, score-0.331]
89 This is in line with the theory since the triangulation constraint is based on the difference in refraction angle. [sent-813, score-0.721]
90 Instead, we mounted our camera on a SlyderDolly translation rail, which allowed us to move the camera precisely in a straight line. [sent-820, score-0.337]
91 Translate the camera backwards until the tank surface is just in focus. [sent-826, score-0.327]
92 The refraction model parameters were then determined in two steps. [sent-833, score-0.595]
93 Firstly, since the camera orientation is not changed by linear motion, we averaged the rotation measurements to obtain the ground truth for the refraction axis. [sent-834, score-0.718]
94 The parameter d0 was then computed as the initial camera translation in the axis direction. [sent-837, score-0.291]
95 ‡Error of each measurement flat refraction layers. [sent-1020, score-0.709]
96 Our method exploits the effect of dispersion, which has previously been ignored, to develop constraints on the calibration parameters by using multiple wavelengths of light. [sent-1021, score-0.427]
97 Additionally, with appropriate scene illumination techniques, the wavelength triangulation constraint may be directly applicable in single-view 3D reconstruction or as a means to improve multi-view reconstruction quality. [sent-1025, score-0.298]
98 Another direction to investigate is calibration with unknown refractive indices, where the dispersion effect may aid in recovering these unknowns. [sent-1026, score-0.862]
99 Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region. [sent-1049, score-0.38]
100 Perspective and non-perspective camera models in underwater imaging - overview and error analysis. [sent-1085, score-0.341]
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