cvpr cvpr2013 cvpr2013-54 knowledge-graph by maker-knowledge-mining

54 cvpr-2013-BRDF Slices: Accurate Adaptive Anisotropic Appearance Acquisition


Source: pdf

Author: Jirí Filip, Radomír Vávra, Michal Haindl, Pavel Žid, Mikuláš Krupika, Vlastimil Havran

Abstract: In this paper we introduce unique publicly available dense anisotropic BRDF data measurements. We use this dense data as a reference for performance evaluation of the proposed BRDF sparse angular sampling and interpolation approach. The method is based on sampling of BRDF subspaces at fixed elevations by means of several adaptively-represented, uniformly distributed, perpendicular slices. Although this proposed method requires only a sparse sampling of material, the interpolation provides a very accurate reconstruction, visually and computationally comparable to densely measured reference. Due to the simple slices measurement and method’s robustness it allows for a highly accurate acquisition of BRDFs. This in comparison with standard uniform angular sampling, is considerably faster yet uses far less samples.

Reference: text


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 We use this dense data as a reference for performance evaluation of the proposed BRDF sparse angular sampling and interpolation approach. [sent-6, score-0.506]

2 The method is based on sampling of BRDF subspaces at fixed elevations by means of several adaptively-represented, uniformly distributed, perpendicular slices. [sent-7, score-0.466]

3 Although this proposed method requires only a sparse sampling of material, the interpolation provides a very accurate reconstruction, visually and computationally comparable to densely measured reference. [sent-8, score-0.564]

4 Due to the simple slices measurement and method’s robustness it allows for a highly accurate acquisition of BRDFs. [sent-9, score-0.577]

5 Introduction Accurate acquisition and representation of real-world materials’ appearance is of an ultimate challenge in computer vision and graphics. [sent-12, score-0.204]

6 A directional properties of material reflectance was formalized by Nicodemus et al. [sent-14, score-0.19]

7 measurement setup is introduced and its very dense BRDF measurements are analyzed. [sent-19, score-0.265]

8 Additionally, we introduce a novel adaptive method of highly accurate interpolation of sparsely measured BRDF and have made measured data publicly available for research purposes. [sent-20, score-0.577]

9 Related Work Based on the way the four degrees of mechanical free- dom are realized, BRDF acquisition setups can be divided into three categories. [sent-22, score-0.251]

10 The first is based on gonioreflectometers where all combinations of illumination and viewing directions are achieved by the sequential mutual positioning of light, sensor, and sample [7, 8]. [sent-23, score-0.275]

11 The last two categories have either compromised accuracy, as well as limitations in the effective range of elevation angles, or require certain geometry of the sample making the measurement procedure more efficient. [sent-27, score-0.225]

12 Although four anisotropic BRDFs have been made available for research purposes [14], their minimal azimuthal sampling step is 2o only and the resulting data are extremely noisy. [sent-28, score-0.6]

13 Therefore, we introduce a novel gonioreflectometerbased acquisition setup for measurement of anisotropic BRDF with unique angular density and accuracy. [sent-29, score-0.497]

14 Such precise measurement data are then used as reference data for the proposed interpolation algorithm evaluation. [sent-30, score-0.365]

15 General methods of adaptive sampling [18] have been extensively studied. [sent-31, score-0.273]

16 Their application to adaptive illumination sampling was investigated in [3]. [sent-32, score-0.33]

17 How111444666866 ever, these approaches assume prior knowledge of the entire data, while we use only a sparse adaptive sampling of unknown reflectance data constrained by a typical BRDF behavior, i. [sent-36, score-0.432]

18 To date, we are not aware of any literature on a sparse adaptive acquisition of unknown 4D BRDFs. [sent-39, score-0.338]

19 Our work is motivated by the method of Filip and V a´vra [2], using a sparse set of azimuthal slices placed orthogonally to main reflectance features in BRDF space. [sent-40, score-0.741]

20 These slices allow for an efficient and robust reconstruction. [sent-41, score-0.279]

21 Measurement Setup All the measurements were done using the gonioreflectometer shown in Fig. [sent-43, score-0.16]

22 Mechanical Construction The setup consists of the measured sample held by a rotating stage and two independently controlled arms with camera (one axis) and light (two axes) as shown in Fig. [sent-45, score-0.394]

23 It allows for flexible and adaptive measurements of nearly arbitrary combinations of illumination and viewing directions. [sent-47, score-0.293]

24 Although camera view occlusion by arm with light may occur, it can be analytically detected, and in most cases alternative positioning is possible. [sent-48, score-0.16]

25 Verified illumination and camera arms positioning angular accuracy across all axes is ±0. [sent-49, score-0.298]

26 HDR acquisition is achieved by adaptive exposure times and variable lighting intensity (through current being fed into LEDs); both of this is controlled remotely depending on the dynamic range of the measured sample. [sent-56, score-0.487]

27 ing – Zero initial positions of all axes were found using a spirit level, plummet, and device’s axes intersection, etc. [sent-67, score-0.16]

28 Lighting nonuniformity over the target area was measured using a luxmeter, fitted by a 2D polynomial, and compensated from the photos. [sent-68, score-0.17]

29 The control application stores the list of the required measured positions, which can be adaptively modified during measurement. [sent-75, score-0.18]

30 Uniform Sampling Evaluation View- and illumination-dependent reflectance properties of materials are often measured uniformly over a hemisphere. [sent-79, score-0.356]

31 As examples can serve 81 81 directions sampling (656A1 samples) [s1 c7]a or 1er5v v1e e× 8151 1× d81ire cditrieoncsti sampling (p2li2n8g01 (6 samples) [l1es3)]. [sent-80, score-0.373]

32 [ Unfortunately, even tsuiocnhs relatively dense sampling is insufficient to accurately capture important reflectance behavior. [sent-81, score-0.294]

33 3 compares visualization quality of five materials when the ground truth data and uniform sampling 15 1 151 directions are used. [sent-83, score-0.403]

34 Then all these directions were measured using the gonioreflectometer and visualized. [sent-86, score-0.281]

35 As expected, even with a high number of uniform samples the differences are significant, especially for specular materials. [sent-87, score-0.234]

36 A comparison of BRDF visualization on a sphere: measured 10975 exact directions in each pixel (the first row) vs. [sent-105, score-0.25]

37 uniformly measured and interpolated 15 1 151 directions (the second ×× ×× row). [sent-106, score-0.395]

38 view- and illumination-dependent material appearance sampling to achieve better reconstruction precision using less samples. [sent-109, score-0.318]

39 T yheearres)fore, we focused first on a dense measurement of BRDF subspace for fixed elevations of a single but challenging material. [sent-112, score-0.413]

40 Our goal is to investigate the adaptive sparse sampling algorithm which can represent appearance of this subspace very precisely using a reasonable number of samples. [sent-113, score-0.46]

41 This material provides an intricate golden appearance with a strong anisotropic behavior as shown in example images of various illumination and viewing conditions in the second row of Fig. [sent-116, score-0.349]

42 When the material’s BRDF was measured uniformly in 81 81 and 151 15 1 sampling, we obtained the result ill8u1s×tra8t1ed a nind 1th5e1 ×fir1s5t1 row opfl Fig. [sent-118, score-0.195]

43 Visualization of this BRDF on a ×× ×× × sphere for 151 151 sampling is shown in the second row sopf Fig. [sent-121, score-0.222]

44 In the further experiment we selected BRDF subspace at the highest elevation angles exhibiting the strongest anisotropic behavior, i. [sent-124, score-0.364]

45 Figure 5 compares the reference subspace measurement (left) with two 4096 DPI scan 81 81 directions 151 151 dir. [sent-128, score-0.364]

46 Thefirstrow:Highresolutionscanofthefabricmate- rial (left), its uniformly measured BRDF: in 81 81 (middle) and r1ia5 1l e1f5t1), (right) odrirmecltyio mnse. [sent-130, score-0.195]

47 Densely measured reference data with samples’ distance Δϕ = 0. [sent-138, score-0.197]

48 The middle image corresponds to sampling 81 8 1and 15 1 15 1. [sent-141, score-0.196]

49 The reference data are densely measured using azimuthal sampling step ≈ Δϕ = 2o using 11856 samples and interpoplalitendg in stteop a ≈res Δolϕuti =on 2Δϕ = 0. [sent-143, score-0.807]

50 The subspace measured using 24 azimuthal samples (step Δϕ = 15o) contains n = (360o/15o)2 = 576 samples (middle), and the subspace measured using 48 azimuthal samples (Δϕ = 7. [sent-145, score-1.434]

51 Performance of a barycentric interpolation of these uniform samples into reference data resolution (Δϕ = 0. [sent-148, score-0.5]

52 These results prove unsatisfactory performance ofthe uniform acquisition approaches. [sent-151, score-0.269]

53 The slice aligned with the direction of specular highlights is called axial slice 111444667088 Figure6. [sent-155, score-0.363]

54 The axial slice rec−or ϕds the material’s anisotropic properties (mutual azimuthal position of the light and camera is fixed while the sample rotates), i. [sent-160, score-0.743]

55 The slice perpendicular to the highlights is called diagonal slice sD (blue), i. [sent-163, score-0.35]

56 The diagonal slice captures the shape of the specular peaks (light and camera travel in mutually opposite azimuthal directions over the sample). [sent-166, score-0.6]

57 Both slices can be expressed as sA (ϕv) = BRDF(θi, ϕi = ϕv ,θv ,β (ϕv) = BRDF(θi , ϕi = 2π sA,θi,θv,α − α, sD,θi − ϕv θv, ϕv), (1) + β, θv , ϕv) . [sent-167, score-0.279]

58 While [2] focuses on approximative subspace reconstruction using two slices only, we attempt for very accurate reconstruction of the subspace using the set of 12 axial and 12 diagonal slices. [sent-168, score-0.75]

59 The slices’ placement is realized uniformly across the subspace in azimuthal step 30o. [sent-169, score-0.548]

60 Such a placement divides the subspace image into a grid of rectangles (see Fig. [sent-170, score-0.156]

61 The slices values are adaptively measured; however, the remaining data has to be interpolated. [sent-172, score-0.347]

62 1 explains method of adaptive sampling along slices and Section 6. [sent-174, score-0.552]

63 2 describes method of slices values propagation to missing parts of the BRDF subspace. [sent-175, score-0.304]

64 Adaptive Slice Sampling Each slice can be interpreted as a one dimensional periodic signal with period 360o. [sent-178, score-0.159]

65 , 1o) or adaptively decreasing a number of samples on the one hand and increasing reconstruction accuracy in areas with high variance on the other. [sent-181, score-0.213]

66 As the behavior of the signal is unknown, the adaptive algorithm can work with already measured samples only; adding new samples in areas where it can improve reconstructed signal accuracy. [sent-182, score-0.588]

67 We assume that all the previously taken samples are sorted by their angle ϕv and labeled by indices from 1 to n, when n is a count of samples al- × ready taken. [sent-188, score-0.24]

68 , n}, draw a line through samples wk −ake1 asandm pkl +e k k1 ∈an {d1 compare ,l dinrae wva alu lein u tihn position mofp tlehse sample kd w ki t+h t1h aen sample’s rvea l uinee v. [sent-192, score-0.18]

69 , 10%) in any color channel, mark position s−in the middle of sample k −1 and k and position s+ in the middle mofi sample ska amnpdl ek k k+− −11 as cdan kd ainddate pso sfiotrio a new sample. [sent-195, score-0.206]

70 When all the candidate positions of new samples are known, they can be measured and we can search for new candidate positions again. [sent-198, score-0.299]

71 Algorithm stops when there are no candidate positions (due to a limited signal rate of innovation or measurement resolution) or after a defined number of iterations. [sent-199, score-0.189]

72 density every point on the slice can be interpolated very precisely, using e. [sent-205, score-0.254]

73 interpolation requires knowledge of values of eight points to interpolate desired value rxy at (x, y) inside the rectangle. [sent-215, score-0.314]

74 q0y and q1y are on 111444667199 First, values px0 and px1 are linearly interpolated along axis y yielding value pxy pxy (1 − y) ∗ px0 y ∗ px1 = + . [sent-219, score-0.455]

75 To compute value rxy, the value pxy has to be compensated for a height difference introduced by a linear interpolation and values of the diagonal slices. [sent-220, score-0.414]

76 Therefore, values c0y and c1y are also linearly interpolated along axis y from c00, c01 and c10, c11 respectively c0y (1 − y) ∗ c00 y ∗ c01 c1y (1 − y) ∗ c10 y ∗ c11 = = + + ,. [sent-221, score-0.193]

77 The differences d0y and d1y between the linear interpolations of the corner values and values of the x-aligned slices are computed as d0y = q0y − c0y and d1y = q1y − c1y. [sent-222, score-0.387]

78 Finally, the height difference i−n cthe point (x, y) is ob−tai cned with a linear interpolation of the differences in the axis x dxy = (1 − x) ∗ d0y + x ∗ d1y . [sent-223, score-0.287]

79 The final value rxy is a sum of the value pxy and the difference dxy and its minimal value is constrained by a minimal value of px0, px1, q0y and q1y rxy = max(pxy + dxy, min(px0,px1, q0y, q1y)) . [sent-224, score-0.465]

80 ×× It can be proven that changing x, y axes interpolation order yields the same result. [sent-226, score-0.25]

81 Results This section compares performance of the proposed interpolation method with uniform sampling using the same samples count. [sent-228, score-0.536]

82 However, the selected sample has the strongest anisotropic behavior we have seen so far. [sent-230, score-0.237]

83 10 shows densely measured reference BRDF subspace (a), uniform sampling by means of 81 81 (b) and 151 15 1 (d) interpolated to the same azi8m1×uth8a1l rbe)so alnudtio 1n5 as 1th5e1 r (edfe)r ienntceerp using a barycentric aizn-terpolation. [sent-232, score-0.801]

84 10 (c) and (e) shows performance of the proposed interpolation method in suggested representation using 12 axial and 12 diagonal slices (f). [sent-234, score-0.57]

85 1 T0h) ef 1ro0m× th scea rleedfe driefnfceere ndaceta i smhaogwe st (haset eth see proposed parameterization and interpolation is able to achieve significantly better reconstruction of the original data using the same number of samples. [sent-238, score-0.274]

86 As the reconstruction of a single BRDF subspace is insufficient for any appearance visualization we measured eight additional subspaces at elevations 0o, 30o, 75o and ×× their combinations. [sent-239, score-0.6]

87 These measurements were obtained using 6561 samples and their reconstructions using the proposed method are shown in Fig. [sent-240, score-0.187]

88 Furthermore, we interpolated data at missing elevations using a four-dimensional Krig interpolation of spherical angles (θi, ϕi, θv , ϕv) represented in a 0 ≈ 2π azimuthal continuity preserving )d rireepcrteiosnenalte parameterization m[6u]t. [sent-242, score-0.84]

89 9shows a comparison of ground truth measurements on sphere (a), with rendering using barycentrically interpolated 81 81 (b) and 151 15 1 (c) uniform samples. [sent-244, score-0.467]

90 The result 8o1f ×th8e1 proposed d5a1ta× acquisition aonrdm interpolation me erethsuodlt using 6561 adaptive samples is shown in (d). [sent-245, score-0.586]

91 Per-pixel ground truth measurements on a sphere (a) compared with barycentrically interpolated uniform measurements (b), (c) and with the proposed interpolation from sparse measurements (d). [sent-256, score-0.816]

92 although the reconstruction quality gain might look small, we believe that it can be considerably improved by the proposed adaptive measurement at additional elevations, i. [sent-259, score-0.304]

93 The reconstruction of the BRDF subspace (720×720 pixels) adaptively dtiisotnrib oufte tdhe ein B B2R4 DslFice ssu tbaskpeasc typically 712-20 seconds regardless the sample count at Intel Xeon 2. [sent-262, score-0.301]

94 Note that the measured sparse BRDF as well as its densely sampled subspaces are publicly available for research purposes in UTIA BTF Database [5]. [sent-264, score-0.281]

95 Conclusions We presented a sparse BRDF data representation and interpolation methods that outperform in reconstruction quality uniform sampling using the same count of samples. [sent-266, score-0.564]

96 The proposed sliced parametrization allows for fast, continuous acquisition at fixed elevations of camera and light, and fast, robust reconstruction of non-measured values at arbitrary resolution. [sent-267, score-0.481]

97 The methods accuracy is given by a used number of slices and their adaptive sampling density specified 111444777200 (a) reference 518 400 samples (b) uniform sampl. [sent-268, score-0.81]

98 We believe that the proposed data-driven sampling together with the robust reconstruction performance represents an initial framework for intelligent adaptive sampling methods of view- and illuminationdependent material appearance. [sent-298, score-0.564]

99 Fast method of sparse acquisition and reconstruction of view and illumination dependent datasets. [sent-307, score-0.34]

100 A coaxial optical scanner for synchronous acquisition of 3D geometry and surface reflectance. [sent-346, score-0.177]


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