cvpr cvpr2013 cvpr2013-102 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Donald G. Dansereau, Oscar Pizarro, Stefan B. Williams
Abstract: Plenoptic cameras are gaining attention for their unique light gathering and post-capture processing capabilities. We describe a decoding, calibration and rectification procedurefor lenselet-basedplenoptic cameras appropriatefor a range of computer vision applications. We derive a novel physically based 4D intrinsic matrix relating each recorded pixel to its corresponding ray in 3D space. We further propose a radial distortion model and a practical objective function based on ray reprojection. Our 15-parameter camera model is of much lower dimensionality than camera array models, and more closely represents the physics of lenselet-based cameras. Results include calibration of a commercially available camera using three calibration grid sizes over five datasets. Typical RMS ray reprojection errors are 0.0628, 0.105 and 0.363 mm for 3.61, 7.22 and 35.1 mm calibration grids, respectively. Rectification examples include calibration targets and real-world imagery.
Reference: text
sentIndex sentText sentNum sentScore
1 We describe a decoding, calibration and rectification procedurefor lenselet-basedplenoptic cameras appropriatefor a range of computer vision applications. [sent-7, score-0.367]
2 We derive a novel physically based 4D intrinsic matrix relating each recorded pixel to its corresponding ray in 3D space. [sent-8, score-0.317]
3 We further propose a radial distortion model and a practical objective function based on ray reprojection. [sent-9, score-0.461]
4 Our 15-parameter camera model is of much lower dimensionality than camera array models, and more closely represents the physics of lenselet-based cameras. [sent-10, score-0.35]
5 Results include calibration of a commercially available camera using three calibration grid sizes over five datasets. [sent-11, score-0.623]
6 With increased depth of field and light gathering relative to conventional cameras, and post-capture capabilities ranging from refocus to occlusion removal and closed-form visual odometry [1, 16, 4, 9, 19, 6], plenoptic cameras are poised to play a significant role in computer vision applications. [sent-24, score-0.796]
7 As such, accurate plenoptic calibration and rectification will become increasingly important. [sent-25, score-0.754]
8 Prior work in this area has largely dealt with camera arrays [20, 18], with very little work going toward the calibration of lenselet-based cameras. [sent-26, score-0.365]
9 By exploiting the physical characteristics of a lenselet-based plenoptic camera, we impose significant constraints beyond those present in a multiple-camera scenario. [sent-27, score-0.519]
10 In this work we present a novel 15-parameter plenoptic camera model relating pixels to rays in 3D space, including a 4D intrinsic matrix based on a projective pinhole and thin-lens model, and a radial direction-dependent distortion model. [sent-33, score-0.978]
11 We present a practical method for decoding a camera’s 2D lenselet images into 4D light fields without prior knowledge ofits physical parameters, and describe an efficient projected-ray objective function and calibration scheme. [sent-34, score-1.187]
12 We use these to accurately calibrate and rectify im- ages from a commercially available Lytro plenoptic camera. [sent-35, score-0.503]
13 The latter include the “original” plenoptic camera as described by Ng et al. [sent-39, score-0.584]
14 [17], with which the present work is concerned, and the “focused” plenoptic camera described by Lumsdaine and Georgiev [14]. [sent-40, score-0.584]
15 Each camera has unique characteristics, and so the optimal model and calibration approach for each will differ. [sent-41, score-0.336]
16 Previous work has addressed calibration of grids or freeform collections of multiple cameras [20, 18]. [sent-42, score-0.308]
17 Similar to this is the case of a moving camera in a static scene, for which structure-from-motion can be extended for plenoptic modelling [12]. [sent-43, score-0.584]
18 These approaches introduce more degrees of freedom in their models than are necessary to describe the lenselet-based plenoptic camera. [sent-44, score-0.444]
19 [7] derive a plenoptic camera model using ray transfer matrix analysis. [sent-47, score-0.799]
20 Our model is more detailed, accurately describing a real-world camera by including the effects of lens distortion and projection through the lenticular array. [sent-48, score-0.548]
21 However, their piecewise-continuous pixel-ray mapping does not apply to the plenoptic camera, and so our camera model and calibration procedure differ significantly from theirs. [sent-51, score-0.78]
22 Decoding to an Unrectified Light Field Light fields are conventionally represented and processed in 4D, and so we begin by presenting a practical scheme for decoding raw 2D lenselet images to a 4D light field representation. [sent-53, score-1.006]
23 Note that we do not address the question of demosaicing Bayer-pattern plenoptic images we instead refer the reader to [23] and related work. [sent-54, score-0.529]
24 For the purposes of this work, we employ conventional linear demosaicing applied directly to the raw 2D lenselet image. [sent-55, score-0.734]
25 This yields undesired effects in pixels near lenselet edges, and we therefore ignore edge pixels during calibration. [sent-56, score-0.66]
26 In general the exact placement of the lenselet array is unknown, with lenselet spacing being a non-integer multiple of pixel pitch, and unknown translational and rotational offsets further complicating the decode process. [sent-57, score-1.426]
27 A crop of a typical raw lenselet image is shown in Fig. [sent-58, score-0.644]
28 1 note that the lenselet grid is hexagonally packed, further complicating the decoding process. [sent-59, score-0.854]
29 To locate lenselet image centers we employ an image taken through a white diffuser, or of a white scene. [sent-60, score-0.718]
30 Because of vignetting, the brightest spot in each white lenselet image approximates its center. [sent-61, score-0.631]
31 A low-pass filter is applied to reduce sensor noise prior to finding the local maximum within each lenselet image. [sent-64, score-0.59]
32 Grid parameters are estimated by traversing lenselet image centers, finding the mean horizontal and vertical spacing and offset, and performing line fits to estimate rotation. [sent-67, score-0.706]
33 From the estimated grid parameters there are many potential methods for decoding the lenselet image to a 4D light field. [sent-69, score-0.972]
34 The process begins by demosaicing the raw lenselet image, then correcting vignetting by dividing by the white image. [sent-71, score-0.824]
35 At this point the lenselet images, depicted in blue in Fig. [sent-72, score-0.652]
36 We therefore resample the image, rotating and scaling so all lenselet centers fall on pixel centers, as depicted in the second frame of the figure. [sent-74, score-0.725]
37 Aligning the lenselet images to an integer pixel grid allows a very simple slicing scheme: the light field is broken into identically sized, overlapping rectangles centered on the lenselet images, as depicted in the top-right and bottomleft frames of Fig. [sent-76, score-1.538]
38 The spacing in the bottom-left frame represents the hexagonal sampling in the lenselet indices k, l, as well as non-square pixels in the pixel indices i,j. [sent-78, score-0.837]
39 For rectangular lenselet arrays, this interpolation step is omitted. [sent-82, score-0.59]
40 The main lens is modelled as a thin lens and the lenselets as an array of pinholes; gray lines depict lenselet image centers rects for the rectangular pixels in i,j through a 1D interpolation along i. [sent-85, score-1.181]
41 The final step, not shown, is to mask off pixels that fall outside the hexagonal lenselet image. [sent-87, score-0.678]
42 Though each pixel of a plenoptic camera integrates light from a volume, we approximate each as integrating along a single ray [8]. [sent-91, score-0.977]
43 We model the main lens as a thin lens, and the lenselets as an array of pinholes, as depicted in Fig. [sent-92, score-0.412]
44 For lenselet images of N N pixels, iand j neasechle range fer. [sent-95, score-0.613]
45 The conversion from relative to absolute indices, is straightforwardly found from the number of pixels per lenselet N and a translational pixel offset cpix (below). [sent-100, score-0.735]
46 We next convert from absolute coordinates to a light field ray, with the imaging and lenselet planes as the reference planes. [sent-101, score-0.83]
47 Next we express the ray as position and direction via HφΦ (below), and propagate to the main lens using HT: HφΦ= ? [sent-107, score-0.387]
48 Note that in the conventional plenoptic camera, dμ = fμ, the lenselet focal length. [sent-113, score-1.065]
49 Next we apply the main lens using a thin lens and small angle approximation (below), and convert back to a light field ray representation, with the main lens as the s, t plane, and the u, v plane at an arbitrary plane separation D: HM= ? [sent-114, score-1.048]
50 (5) In a model with pixel or lenselet skew we would expect more non-zero terms. [sent-130, score-0.617]
51 Projection Through the Lenselets We have hidden some complexity in deriving the 4D intrinsic matrix by assuming prior knowledge of the lenselet associated with each pixel. [sent-134, score-0.665]
52 3, the projected image centers will deviate from the lenselet centers, and as a result a pixel will not necessarily associate with its nearest lenselet. [sent-136, score-0.663]
53 By resizing, rotating, interpolating, and centering on the projected lenselet images, we have created a virtual light field camera with its own parameters. [sent-138, score-0.983]
54 Lenselet-based plenoptic cameras are constructed with careful attention to the coplanarity of the lenselet array and image plane [17]. [sent-140, score-1.199]
55 Lens Distortion Model The physical alignment and characteristics ofthe lenselet array as well as all the elements of the main lens potentially contribute to lens distortion. [sent-148, score-1.079]
56 In the results section we show that the consumer plenoptic camera we employ suffers primarily from directionally dependent radial distortion, θd = (1+ k1r2 + k2r4 + · · · ) ? [sent-149, score-0.621]
57 ial distortion coefficients, and θu and θd are the undistorted and distorted 2D ray directions, respectively. [sent-154, score-0.401]
58 Calibration and Rectification The plenoptic camera gathers enough information to perform calibration from unstructured and unknown environments. [sent-160, score-0.78]
59 Plenoptic calibration is complicated by the fact that a single feature will appear in the imaging plane multiple times, as depicted in Fig. [sent-164, score-0.323]
60 The problem arises that the observed and expected features do not generally appear in the same lenselet images indeed the number of expected and observed features is not generally equal. [sent-167, score-0.59]
61 In conventional projective calibration (a) a 3D feature P has one projected image, and a convenient error metric is the 2D distance between the expected and observed image locations | nˆ n|. [sent-175, score-0.295]
62 In the plenoptic camera (b) each feature has multiple expected |an. [sent-176, score-0.584]
63 dIn o tbhseer pvleedno images nˆ j , ni ∈ aRch4, weahtuicrhe generally pdleo nexotappear beneath the same lenselets; we propose the per-observation ray reprojection metric |Ei | taken as the 3D distance between the reprojected ray φˆi eatrndic t |hEe f|ea tatukreen la osc tahteion 3D DP d. [sent-177, score-0.542]
64 The observed feature locations are extracted by treating the decoded light field from Section 3 as an array of Ni Nj 2D images in k and l, applying a conventional feature d×eteNction scheme [11] to each. [sent-182, score-0.399]
65 If the plenoptic camera takes on M poses in the calibration dataset and there are nc features on the calibration target, the total feature set over which we optimize is of size ncMNiNj . [sent-183, score-1.017]
66 Our goal is to find the intrin- “ray sic matrix H, camera poses T, and distortion parameters d which minimize the error across all features, ? [sent-184, score-0.419]
67 =1||φˆcs,t(H,Tm,d),Pc||pt-ray, (8) where | | · | |pt-ray is the ray reprojection error described above. [sent-192, score-0.33]
68 The number of parameters over which we optimize is now reduced to 10 for intrinsics, 5 for lens distortion, and 6 for each of the M camera poses, for a total of 6M + 15. [sent-199, score-0.335]
69 The Jacobian sparsity pattern is easy to derive: each of the M pose estimates will only influence that pose’s ncNiNj error terms, while all of the 15 intrinsic and distortion parameters will affect every error term. [sent-204, score-0.342]
70 Initialization The calibration process proceeds in stages: first initial pose and intrinsic estimates are formed, then an optimization is carried out with no distortion parameters, and finally a full optimization is carried out with distortion parameters. [sent-209, score-0.643]
71 To form initial pose estimates, we again treat the decoded light fields across M poses each as an array of Ni Nj 2D images. [sent-210, score-0.347]
72 By passing all the images through a conv×eNntional × camera calibration process, for example that proposed by Heikkil a¨ [10], we obtain a per-image pose estimate. [sent-211, score-0.336]
73 Note that distortion parameters are excluded from this process, and the camera intrinsics that it yields are ignored. [sent-213, score-0.419]
74 In Section 4 we derived a closed-form expression for the intrinsic matrix H based on the plenoptic camera’s physical parameters and the parameters of the decoding process (1), (6). [sent-214, score-0.792]
75 Rectification We wish to rectify the light field imagery, reversing the effects of lens distortion and yielding square pixels in i,j and k, l. [sent-220, score-0.717]
76 Our approach is to interpolate from the decoded light field LA at a set of continuous-domain indices n˜ A such that the interpolated light field approximates a distortionfree rectified light field LR. [sent-221, score-0.838]
77 To find n˜ A we begin with the indices of the rectified light field nR, and project through the ideal optical system by applying HR, yielding the ideal ray φR. [sent-242, score-0.6]
78 Referring to the distortion model (7), the desired ray φR is arrived at by applying the forward model to some unknown undistorted ray φA. [sent-243, score-0.616]
79 applying the inverse of the estimated intrinsic matrix There is no closed-form solution to the problem of reversing the distortion model (7), and so we propose an iterative approach similar to that of Melen [15]. [sent-245, score-0.308]
80 Results We carried out calibration on five datasets collected with the commercially available Lytro plenoptic camera. [sent-249, score-0.675]
81 The decoding process requires a white image for locating lenselet image centers and correcting for vignetting. [sent-354, score-0.857]
82 Table 2 shows the estimated parameters for Dataset B at the three stages of the calibration process: initial estimate, intrinsics without distortion, and intrinsics with distortion. [sent-372, score-0.359]
83 Table 3 summarizes the root mean square (RMS) ray reprojection error, as described in Section 5, at the three calibration stages and across the five datasets. [sent-373, score-0.497]
84 The first represents the plenoptic camera as an array of projective sub-cameras with independent relative poses and identical intrinsics and distortion parameters, while the second also includes per-sub-camera intrinsic and distortion parameters. [sent-375, score-1.251]
85 These represent the dependence of a ray’s position on the lenselet through which it passes, and a consequence of these nonzero values is that rays take on a wide variety of rational-valued positions in the s, t plane. [sent-379, score-0.624]
86 6 depicts typical ray reprojection error in our proposed model as a function of direction and position. [sent-385, score-0.33]
87 This shows the proposed distortion model to account for most lens distortion for this camera. [sent-388, score-0.544]
88 ray position; top: no distortion model; bottom: the proposed five-parameter distortion model note the order of magnitude difference in the error scale. [sent-399, score-0.616]
89 The proposed model has accounted for most lens distortion for this camera. [sent-400, score-0.358]
90 – Examples of decoded and rectified light fields are shown in Figs. [sent-401, score-0.3]
91 The straight – – red rulings aid visual confirmation that rectification has significantly reduced the effects of lens distortion. [sent-406, score-0.37]
92 Conclusions and Future Work We have presented a 15-parameter camera model and method for calibrating a lenselet-based plenoptic camera. [sent-411, score-0.584]
93 This included derivation of a novel physically based 4D intrinsic matrix and distortion model which relate the indices of a pixel to its corresponding spatial ray. [sent-412, score-0.338]
94 We also presented a method for decoding hexagonal lenselet-based plenoptic images without prior knowledge of the camera’s parameters, and related the resulting images to the camera model. [sent-414, score-0.801]
95 Finally, we showed a method for rectifying the decoded images, reversing the effects of lens distortion and yielding square pixels in i,j and k, l. [sent-415, score-0.565]
96 In the rectified images, the ray corresponding to each pixel is easily found through a single matrix multiplication (5). [sent-416, score-0.306]
97 (a)(b) grid, and b) the demosaiced and vignetting-corrected raw checkerboard image; c–h) examples of (left) unrectified and (right) rectified light fields; red rulings aid confirmation that rectification has significantly reduced the effect of lens distortion. [sent-417, score-0.677]
98 Validation included five datasets captured with a com- mercially available plenoptic tion grid sizes. [sent-418, score-0.5]
99 Focusing on everything – light field cameras promise an imaging revolution. [sent-497, score-0.297]
100 A four-step camera calibration procedure with implicit image correction. [sent-502, score-0.336]
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