cvpr cvpr2013 cvpr2013-443 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Feng Lu, Yasuyuki Matsushita, Imari Sato, Takahiro Okabe, Yoichi Sato
Abstract: We propose an uncalibrated photometric stereo method that works with general and unknown isotropic reflectances. Our method uses a pixel intensity profile, which is a sequence of radiance intensities recorded at a pixel across multi-illuminance images. We show that for general isotropic materials, the geodesic distance between intensity profiles is linearly related to the angular difference of their surface normals, and that the intensity distribution of an intensity profile conveys information about the reflectance properties, when the intensity profile is obtained under uniformly distributed directional lightings. Based on these observations, we show that surface normals can be estimated up to a convex/concave ambiguity. A solution method based on matrix decomposition with missing data is developed for a reliable estimation. Quantitative and qualitative evaluations of our method are performed using both synthetic and real-world scenes.
Reference: text
sentIndex sentText sentNum sentScore
1 jp i Abstract We propose an uncalibrated photometric stereo method that works with general and unknown isotropic reflectances. [sent-7, score-0.644]
2 Our method uses a pixel intensity profile, which is a sequence of radiance intensities recorded at a pixel across multi-illuminance images. [sent-8, score-0.328]
3 Based on these observations, we show that surface normals can be estimated up to a convex/concave ambiguity. [sent-10, score-0.592]
4 Introduction Photometric stereo recovers the surface normals of a scene from a set of images recorded under varying lighting conditions. [sent-14, score-0.802]
5 The original method of Woodham [32] assumes Lambertian reflectance and known directional lightings. [sent-15, score-0.289]
6 There are previous approaches that estimate surface normals under less restricted conditions by making use of intensity profiles [16, 19, 26, 25]. [sent-18, score-1.108]
7 An intensity profile is an ordered sequence of measured intensities at a pixel under varying illumination. [sent-19, score-0.338]
8 However, the previous methods have certain limitations in recovering the surface normals. [sent-23, score-0.283]
9 They either still require calibrated lightings or Lambertian reflectance [25] or only cluster similar surface orientations [19], or require additional assumptions on occluding boundaries, certain reflectance models [26], and calibrated reference objects [16]. [sent-24, score-0.993]
10 In this paper, we further exploit the observation on intensity profiles and develop a photometric stereo method that works with general and unknown isotropic bidirectional reflectance distribution functions (BRDFs) and unknown lighting directions. [sent-25, score-1.46]
11 We show that the proposed method can reliably recover surface normals up to a binary convex/concave ambiguity when the scene has a uniform (up to albedo differences) reflectance. [sent-26, score-0.751]
12 We assume uncalibrated lights and unknown and general isotropic BRDFs. [sent-29, score-0.403]
13 Our solution method is highly deterministic without assuming occluding boundaries or certain reflectance models, and it recovers surface normals up to only a binary convex/concave ambiguity. [sent-30, score-1.027]
14 Second, we show the relation between the surface reflectance property and the intensity distribution of the observed intensity profile. [sent-31, score-1.025]
15 In particular, we calculate the skewness of the intensity distribution and demonstrate that the skewness can be used to infer an important linear coefficient for recovering the surface normals for unknown reflectance, without using reference objects or other priors. [sent-32, score-1.438]
16 Finally, we develop a robust solution technique that only selects and uses reliable measurements for highly correlated surface normals, which makes a step toward practical photometric stereo. [sent-33, score-0.49]
17 Previous work A variety of previous studies have been conducted to relax the constraints of the Lambertian model and known lighting directions in photometric stereo. [sent-36, score-0.319]
18 Non-Lambertian reflectances have been handled either by 1) regarding non- Lambertian components as outliers, or 2) using more general reflectance models. [sent-37, score-0.47]
19 The latter class of methods studies reflectance properties, such as bilateral symmetry [1], reflective symmetry about the halfway vector [18], isotropy and monotonicity [17, 28], and other reflectance symmetries [30]. [sent-39, score-0.657]
20 There are uncalibrated photometric stereo techniques wherein the lighting directions are unknown. [sent-42, score-0.547]
21 Various surface properties are used for resolving the GBR ambiguity, such as diffuse maxima [12], specularity [11, 10], low-dimensional space [5], minimum entropy [2], interreflections [8], color profiles [27], reflectance symmetry [30], and certain configuration of the light sources [35]. [sent-44, score-1.124]
22 These methods rely on the assumption that the diffuse reflectance component follows the Lambertian model. [sent-45, score-0.351]
23 Handling both non-Lambertian reflectances and uncalibrated light sources is far more challenging and, as a re- sult, has been less studied. [sent-46, score-0.442]
24 Silver [29] and Hertzmann and Seitz [16] use reference objects that have unknown but the same reflectance as a target object for estimating its surface normals. [sent-47, score-0.645]
25 [7] recover surface iso-contours from the differential images by restricting the positions of the light sources to a circle around the camera axis. [sent-50, score-0.438]
26 They need additional information such as an initial normal to determine surface normals. [sent-51, score-0.34]
27 [26] propose a method that uses intensity profiles for estimating surface normals, but the method is limited to the Lambertian or TorranceSparrow reflectance models, while our method can deal with general isotropic reflectances. [sent-53, score-1.18]
28 Both of these methods assume that the surface has visible occluding contours, which provide knowledge of surface normals perpendicular to the viewing direction for resolving the ambiguity. [sent-56, score-0.994]
29 An intensity profile is a sequence of radiance intensities recorded at a pixel across multi-luminance images. [sent-60, score-0.408]
30 Orientation-consistency: Intensity profiles become exactly the same, if and only if they correspond to the same surface normal orientation and material (A and C in Fig. [sent-67, score-0.692]
31 Using this simple observation, surface normals can be determined by looking up a pre-stored table indexed with surface brightness values [29], or match the intensity profiles to those from a reference object [16]. [sent-69, score-1.395]
32 Geometry-extrema: For many materials, intensity profiles reach the extremas synchronously, if and only if they correspond to the same surface normal (A and D in Fig. [sent-71, score-0.856]
33 This fact is used for clustering surface orientations [19] without determining the orientations. [sent-73, score-0.281]
34 Similarity: Similarity between intensity profiles is strongly related with the difference between surface normals for the same material (A and B in Fig. [sent-74, score-1.159]
35 [26] analyze this relationship and exploit it to recover surface normals in the cases of Lambertian and Torrance-Sparrow reflectance and evenly distributed light sources with an assumption of having occluding boundaries. [sent-77, score-1.193]
36 This paper makes a further observation about intensity profiles and introduces the notion of conditional linearity. [sent-78, score-0.542]
37 Different from [26], we do not restrict our analysis to certain reflectance models. [sent-79, score-0.289]
38 Instead, we take into account more general isotropic reflectances in the MERL BRDF database [21]. [sent-80, score-0.273]
39 Conditional linearity: For most real-world isotropic reflectances, we observe a strong linear relation between the distance among intensity profiles seen under evenly distributed lightings and the angular difference of surface normals, up to a certain normal angular difference. [sent-81, score-1.319]
40 We also observe that the linear coefficient is material-dependent and closely related to the intensity distribution of the observed intensity profile. [sent-82, score-0.522]
41 These observations allow us to develop an uncalibrated photometric stereo method that works with general and unknown isotropic reflectances. [sent-83, score-0.644]
42 Geodesic distance of intensity profiles and normal angular difference Let us assume evenly distributed light directions and a scene with a uniform material; we show later that these can be relaxed to some extent. [sent-86, score-0.941]
43 Using geodesic distance (right) preserves a linear relationship over a greater range of angular differences in comparison with using Euclidean distance (left). [sent-98, score-0.327]
44 mal pair, and {Ip, Iq} be the corresponding pixel intensity profiles i,n a a dno {rImaliz}ed b efo trhme as r breelsopwo:n Ip= ? [sent-99, score-0.516]
45 The previous methods have shown that the similarity of intensity profiles and surface normals are strongly correlated [19, 26]. [sent-118, score-1.108]
46 The similarity can be straightforwardly defined using the Euclidean distance of two intensity profiles as ? [sent-119, score-0.542]
47 nq) of surface normals np and nq at scene points p and q (np, nq ∈ R3×1); however, the linear relationship holds only in a ∈lim Rited range as depicted in Fig. [sent-124, score-0.79]
48 Therefore, the linearity is well preserved in the geodesic distance over a greater range of angular differences, as shown in Fig. [sent-139, score-0.287]
49 use of geodesic distance generally shows the linear relationship with the angular difference of normals in a large range. [sent-164, score-0.634]
50 Please note that inferring such linear coefficient αm is important for determining the surface normals without assuming the occluding boundaries used in [26] or other priors. [sent-177, score-0.815]
51 , it is related to the surface reflectance property of a material. [sent-182, score-0.571]
52 To characterize such a reflectance property, we show that the intensity distribution observed in an intensity profile conveys information about the reflectance property for the material. [sent-183, score-1.14]
53 The top row shows intensity profiles captured at two surface normals for a specular material. [sent-198, score-1.191]
54 The bottom row shows intensity profiles captured at two surface normals for a diffuse material. [sent-199, score-1.17]
55 Error bars for different surface nor- mals and the line fitting result are shown. [sent-205, score-0.288]
56 These figures indicate that an intensity profile’s shape depends on both material (reflectance property) and surface normal. [sent-207, score-0.525]
57 However, its intensity distribution, which does not rely on the intensity order as shown by the 1D plots in Fig. [sent-208, score-0.43]
58 4, appears stable against surface normal changes for the same material. [sent-209, score-0.34]
59 Based on these observations, we compute the skewness of the intensity distribution for characterizing it with an aim of deriving the linear coefficient αm via the skewness. [sent-210, score-0.516]
60 The skewness γ of an intensity distribution, which is irrelevant to the intensity/lighting order, is calculated as γ(I) = L21? [sent-211, score-0.424]
61 23 ,(5) where Iis an intensity profile, and Il is its l-th element that corresponds to the l-th lighting direction. [sent-216, score-0.262]
62 Indeed, the skewness of the intensity distributions has high correlation with the inverse of the linear coefficient α−m1 . [sent-217, score-0.516]
63 To examine this, we plot the skewness γ and inverse slope α−m1 using all 100 materials using synthetic scenes as shown in Fig. [sent-218, score-0.495]
64 5 also shows error bars that demonstrate the stability of skewness values computed across diverse surface normals. [sent-223, score-0.497]
65 Therefore, it is efficient to estimate αm for unknown materials from the skewness of the intensity distribution. [sent-224, score-0.689]
66 5 also shows that the skewness increases as the materials vary from matte to shiny ones. [sent-228, score-0.405]
67 This is because specular components generate large pixel intensities only under a limited light directions, which increases the skewness of the intensity distribution. [sent-229, score-0.667]
68 5; they correspond to materials that have both significant diffuse and very narrow specular lobes. [sent-231, score-0.341]
69 Surface normal recovery We describe our proposed method for recovering surface normals based on the discussion in Sec. [sent-235, score-0.697]
70 From the observed intensity profiles {Ip}, we compute the geodesic distsaenrcvee dd iGn (Ip, Iq) using Eq. [sent-237, score-0.644]
71 Formulation We wish to recover surface normals of scene points that correspond to P pixels in the observed image from a set of images taken under varying unknown lightings. [sent-253, score-0.686]
72 With a sparse error matrix E that accounts for the errors due to the missing entries, the relationship between the observation matrix O and surface normal N can be written as NTN = O + E. [sent-264, score-0.502]
73 (8) 111444999311 We wish to solve for surface normal N by using the incomplete matrix O and unknown but sparse error matrix E. [sent-265, score-0.455]
74 W≤e ξ finally obtain the solution of the surface normals as Nˆ Nˆ = S(213)UT = S(213)VT. [sent-302, score-0.592]
75 Therefore, by using integrability constraint, our method recovers surface normals up to only a binary convex/concave ambiguity. [sent-322, score-0.682]
76 , a hemi- × sphere, a spherical cap whose surface normals deviate from the viewing direction by 0◦ ∼ 75◦, and another spherical cap with the smaller range of 0◦ ∼ 60◦, as shown in Fig. [sent-330, score-0.717]
77 Our method performs better for normals that are less perpendicular to the viewing direction, because the intensity distribution is more stable for these normals. [sent-340, score-0.575]
78 Next we estimate the linear coefficient αm via the skewness of intensity distributions and perform the whole pipeline. [sent-359, score-0.516]
79 7 shows the results of the hemispherical surface scene with 100 BRDFs. [sent-362, score-0.292]
80 Strictly speaking, it is not easy to find prior methods that can completely handle unknown reflectances and uncalibrated illuminations without additional assumptions to ours. [sent-365, score-0.357]
81 For instance, [26] does not work when occluding boundaries with normals perpen- dicular to the viewing direction are unavailable. [sent-366, score-0.469]
82 Therefore, we choose the following ones that at least separate the reflectance and illumination factors without knowing the light directions: 1. [sent-367, score-0.406]
83 SVD [15]: we implement it as a baseline method that assumes Lambertian reflectance and no shadows. [sent-368, score-0.289]
84 Normal recovery errors under 1) uniform lights, 2) GBR transformed lights, 3) light sources distorted by Gaussian noise with standard deviations of 3◦ and 7◦, and 4) lights from only the upper hemisphere. [sent-392, score-0.307]
85 This is because specular materials have rapidly changing intensities, as shown in Fig. [sent-403, score-0.279]
86 In particular, using only upper lights causes large errors especially near the occluding boundaries for specular materials. [sent-405, score-0.312]
87 A few scenes on the right do not have occluding boundaries, while we can still estimate their surface normals purely from the images of the surface patches. [sent-420, score-0.932]
88 Conclusion We present a photometric stereo technique that recovers surface normals with unknown real-world reflectances in an uncalibrated manner. [sent-425, score-1.314]
89 We have shown that the information extracted from the pixel intensity profiles across images offers a strong cue for solving the problem. [sent-426, score-0.516]
90 re- will enhance the apSince our method can naturally distinguish different reflectances and recover surface normals accordingly, our next goal is to fully exploit such ability to deal with surfaces composed of more complex spatially-variant reflectances. [sent-430, score-0.825]
91 Toward reconstructing surfaces with arbitrary isotropic reflectance : A stratified photometric stereo approach. [sent-434, score-0.784]
92 The 4-source photometric stereo technique for three-dimensional surfaces in the presence ofhighlights and shadows. [sent-457, score-0.379]
93 A theory of differential photometric stereo for unknown isotropic brdfs. [sent-479, score-0.513]
94 Efficient photometric stereo on glossy surfaces with wide specular lobes. [sent-494, score-0.462]
95 A closed-form solution to uncalibrated [13] [14] [15] [16] [17] [18] [19] [20] [21] [24] [25] photometric stereo via diffuse maxima. [sent-518, score-0.521]
96 Incorporating the torrance and sparrow model of reflectance in uncalibrated photometric stereo. [sent-524, score-0.651]
97 Attached shadow coding: Estimating surface normals from shadows under unknown reflectance and lighting conditions. [sent-587, score-1.041]
98 Elevation angle from reflectance monotonicity: Photometric stereo for general isotropic reflectances. [sent-623, score-0.502]
99 photometric method for determining surface orientation from multiple images. [sent-650, score-0.512]
100 Robust photometric stereo via low-rank matrix completion and recov- [354]pATZ7ae. [sent-659, score-0.351]
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