cvpr cvpr2013 cvpr2013-21 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Thoma Papadhimitri, Paolo Favaro
Abstract: We investigate the problem of reconstructing normals, albedo and lights of Lambertian surfaces in uncalibrated photometric stereo under the perspective projection model. Our analysis is based on establishing the integrability constraint. In the orthographicprojection case, it is well-known that when such constraint is imposed, a solution can be identified only up to 3 parameters, the so-called generalized bas-relief (GBR) ambiguity. We show that in the perspective projection case the solution is unique. We also propose a closed-form solution which is simple, efficient and robust. We test our algorithm on synthetic data and publicly available real data. Our quantitative tests show that our method outperforms all prior work of uncalibrated photometric stereo under orthographic projection.
Reference: text
sentIndex sentText sentNum sentScore
1 ch Abstract We investigate the problem of reconstructing normals, albedo and lights of Lambertian surfaces in uncalibrated photometric stereo under the perspective projection model. [sent-4, score-1.455]
2 Our analysis is based on establishing the integrability constraint. [sent-5, score-0.268]
3 We show that in the perspective projection case the solution is unique. [sent-7, score-0.404]
4 Our quantitative tests show that our method outperforms all prior work of uncalibrated photometric stereo under orthographic projection. [sent-10, score-1.024]
5 Introduction This paper is concerned with the task of recovering a surface from a collection of images captured from the same position but under different illuminations, a problem known in computer vision as photometric stereo [30]. [sent-12, score-0.632]
6 Arguably, one of the most remarkable results has been obtained for the more challenging problem of uncalibrated photometric stereo (UPS), where lights are unknown. [sent-14, score-0.913]
7 In this paper, we introduce a novel insight in uncalibrated photometric stereo: There is no ambiguity under the perspective projection model. [sent-25, score-1.112]
8 In other words, one can uniquely reconstruct the normals of the object and the lights given only the input images and the camera calibration (focal length and image center). [sent-26, score-0.352]
9 Also, under the perspective projection, one can reconstruct the depth map from the normals up to a scale factor. [sent-27, score-0.468]
10 When the illumination directions and intensities are known, photometric stereo can be solved as a linear system. [sent-31, score-0.623]
11 One of the simplifying assumptions that are typically used (together with the Lambertian image formation model, distant point light sources and ignoring shadows/inter-reflections) is the orthographic projection of the scene onto the image sensor. [sent-32, score-0.526]
12 Another example is the work of Tankus and Kiryati [28], which is based on the perspective image formation model introduced in the shape from shading problem [29, 23, 7]. [sent-34, score-0.339]
13 Here the partial derivatives of the natural logarithm of the depth map (instead of the depth map itself) are recovered via a closed-form solution based on image ratios. [sent-35, score-0.267]
14 How111444777422 ever, such formulation is sensitive to image noise, which may corrupt the estimated gradient map and eventually violate the integrability constraint. [sent-36, score-0.319]
15 For this reason, in [17], the same perspective photometric stereo framework is used without the image ratios, but by imposing the integrability constraint in a numerical optimization scheme, similarly to [1]. [sent-37, score-1.182]
16 This work differs from classical photometric stereo approaches as the final reconstruction is the fusion of different shape from shading reconstructions, each obtained independently from a single image. [sent-39, score-0.676]
17 Other approaches use the perspective projection in hybrid reconstruction algorithms to fuse photometric cues with active stereo [21, 34] or passive stereo [10, 19]. [sent-40, score-1.222]
18 When no prior knowledge about the illumination, geom- × etry, and reflectance is available, the problem is called uncalibrated photometric stereo. [sent-42, score-0.672]
19 In such case, all prior work assumes an orthographic projection. [sent-43, score-0.215]
20 Under this model the normals and lights can be obtained up a 3 3 invertible matrix (9-parameters ambiguity) by computing a singular value decomposition of the data matrix (and by imposing that its rank be 3) [14] . [sent-44, score-0.285]
21 If the integrability constraint is imposed, the ambiguity reduces to 3-parameters (the socalled GBR ambiguity) [5]. [sent-45, score-0.412]
22 In [25], the GBR ambiguity is solved by grouping normals and albedo based respectively on image appearance and color. [sent-48, score-0.332]
23 A recent work [11], solves the ambiguity by introducing the Lambertian Diffuse Reflectance (LDR) maxima and imposing normals and lights to be parallel at those locations. [sent-50, score-0.378]
24 Only in [18], the perspective projection is considered to define notions of shadow equivalence and the Generalized Perspective Bas Relief Ambiguity (KGBR). [sent-52, score-0.404]
25 Here, it is shown that we cannot obtain additional cues from shadows (under both orthographic and perspective projection) to solve the GBR ambiguity. [sent-53, score-0.486]
26 However, the perspective projection was not incorporated into the image formation model and the corresponding analysis was not done. [sent-54, score-0.458]
27 In this work we focus for the first time on uncalibrated photometric stereo under perspective projection. [sent-56, score-1.042]
28 Our main contribution is to show that under this model, the problem can be solved unambiguously by imposing only the integrability constraint and to devise a closed-form solution that is simple, efficient and robust. [sent-57, score-0.401]
29 Image Formation Model A large set of problems in computer vision, such as photometric stereo, is concerned with measuring geometric and photometric properties of a scene from images. [sent-59, score-0.784]
30 A reasonable approximation of this process is the perspective projection model, where 3D points are mapped onto the 2D camera sensor by dividing the first two coordinates by the third one. [sent-63, score-0.485]
31 However, because of the nonlinearity of this mapping, the perspective projection is often dropped in lieu of the more linear, and simpler to analyze, orthographic projection. [sent-64, score-0.619]
32 As it turns out, the added nonlinearity of the perspective projection is also useful to disambiguate the uncalibrated photometric stereo solution (see sec. [sent-65, score-1.213]
33 The Lambertian model When objects in the scene are Lambertian and the illumination is a distant point light, the measured image irradiance due to a point in space X = [x y z]T ∈ R3 can be written as I = ρ? [sent-69, score-0.158]
34 e, (1) where ρ is the albedo of the surface at X, N ∈ S2 is the normal at X, ? [sent-73, score-0.244]
35 While the image irradiance I measured at a pixel is of the camera sensor, the normals and the albedo are related to objects in space. [sent-78, score-0.372]
36 One can define such mapping as a projection π : R3 → R2 where a pixel (u, v) π(X). [sent-80, score-0.171]
37 Then, we can also parametrize the normal map at X as the mapping =. [sent-84, score-0.147]
38 111444777533 In photometric stereo, K images are captured from the same viewing direction, but with different illumination directions Lk [pk qk − 1]T ∈ R3 and illumination intensities ek > 0 for k = 1, . [sent-88, score-0.466]
39 Notice that in our notation we use the convention that both lights and normals point towards the camera (hence, the negative third coordinate). [sent-92, score-0.289]
40 (3) where (u,v) = π⎝⎛⎣⎡ zˆ(xyx,y)⎦⎤⎠⎞ (4) denotes the projection of X to the pixel coordinates (u, v) on the image plane. [sent-98, score-0.204]
41 Orthographic projection Under the orthographic projection, the pixel coordinates satisfy (u, v) = (x, y). [sent-108, score-0.419]
42 (6) Since u ≡ x and v ≡ y, then taking derivatives in x is equivalent to taking derivatives in u and similarly for y and v; hence, zu (u, v) = zx (u, v) zv (u, v) = zy (u, v) . [sent-110, score-0.709]
43 Right: When the focal length tends to ∞ then only the camera center shifts to −∞ and the projection becomes orthographic. [sent-127, score-0.362]
44 As one can see, when changing the focal length we keep scene and image plane fixed and move only the camera center. [sent-134, score-0.156]
45 This model was chosen so that when f → ∞ the perspective projection converges di- rectly to the orthographic one. [sent-135, score-0.619]
46 (5), the image irradiance equation (3) in the perspective case retains the same structure as with the orthographic projection. [sent-137, score-0.567]
47 However, now zx (u, v) zu(u, v) and zy (u, v) zv (u, v). [sent-138, score-0.396]
48 The form of zx (u, v) and zy (u, v) is obtained in the following proposition. [sent-139, score-0.256]
49 1 The derivatives of z with respect to x and y are f+z+fuzzuu+vzv zy(u, v) = f+z+fuzzvu+vzv zx(u,v) = (12) where zu, zv and z are all functions of (u, v). [sent-141, score-0.211]
50 (13) 111444777644 Then, the normal map N can be written again as N(u,v) ∝⎣⎡pq((−uu,1,vv))⎦⎤ yielding the same irradiance equation as in eq. [sent-149, score-0.266]
51 (14) Remark 1 Notice that the above analysis applied to the perspective projection equation of Tankus and Kiryati [28] yields the same formula that they obtain. [sent-151, score-0.438]
52 Uncalibrated Photometric Stereo In the previous sections we have shown that both under the orthographic projection and the perspective projection one can obtain the same imaging equation simply by reparametrizing the normal map. [sent-153, score-0.92]
53 If we are given the light directions and intensities, the reconstruction of the normal map via the straightforward matrix pseudo-inverse (·)† is indeed identical in both cases N(u,v) ∝ ? [sent-155, score-0.235]
54 (15) However, when reconstructing the depth map from the normals the differences between the projection models become evident. [sent-168, score-0.406]
55 In the case of the orthographic projection we can define N(u, v) use −NN13((uu,,vv)) = =. [sent-169, score-0.386]
56 In the case of the perspective projection × we must instead use NN13((uu,,vv)) = f+z+−ufzzuu+vzv and NN23((uu,,vv)) = f+z+−ufzzuv+vzv. [sent-171, score-0.404]
57 To illustrate another fundamental difference, and the main contribution of this paper, we consider the uncalibrated photometric stereo problem, i. [sent-175, score-0.809]
58 hown that the introduction of the surface integrability constraint, which exploits the relationship between the normal map and the derivatives of the depth map, in the orthographic projection case reduces the ambiguities to the so-called Gen? [sent-192, score-0.965]
59 the integrability constraint in the perspective projection case leads to the following outcomes: 1. [sent-209, score-0.723]
60 Integrability Under Perspective Projection The integrability constraint amounts to imposing that the order with which one takes the derivatives does not matter (as long as the depth map is smooth), i. [sent-214, score-0.532]
61 In the case of the orthographic projection this constraint is equivalent to pv (u, v) = qu (u, v), so that the constraints directly applies to the normal map via = In the case of the perspective projection, similarly to [17], we have the following result: ∂∂vNN13((uu,,vv)) ∂∂uNN23((uu,,vv)). [sent-217, score-0.884]
62 1 The integrability constraint zuv holds if and only if the following constraint holds ˆp v = qˆu . [sent-219, score-0.434]
63 Since we are interested in using the integrability constraint to relate the entries of the normal map, we use eqs. [sent-224, score-0.415]
64 2 Given that the scene does not contain degenerate surfaces,2 the integrability constraint in the case of perspective projection is sufficient to uniquely identify the normals N. [sent-229, score-0.89]
65 (18), then we have that N ∝ QTB with Q = [ψ1 ψ2 ψ3]−T, where the ψ1, ψ2, ψ3 solve and P is the N P⎡⎣ψψψ213⎦⎤= 0 9 perspective integrability matrix (23) P × =. [sent-231, score-0.501]
66 Indeed, the first six columns coincide with those obtained from the orthographic projection model as in the notation of [8]. [sent-251, score-0.386]
67 Depth Reconstruction Under Perspective Projection Once the normal map N is reconstructed from the images, one can use eqs. [sent-253, score-0.147]
68 Then, z + (r1u + f) zu + r1vzv = −fr1 r2z + r2uzu + (r2v + f) zv = −fr2 . [sent-259, score-0.311]
69 Synthetic To validate our analysis we run quantitative experiments (the Matlab code will be publicly available) on images synthetically generated under the perspective model with 3 given surfaces: Random, Pot and Coin (see Fig. [sent-275, score-0.233]
70 We consider 10 illumination conditions, a random albedo map, the center of the coordinate system at the center of the image and a focal length f equal to 100. [sent-277, score-0.317]
71 3 we compare the error plots (mean and standard deviation) of the mean angular error of the estimated normal maps obtained from calibrated photometric stereo and our uncalibrated solution. [sent-290, score-0.996]
72 Although we have used the same type of approximation employed by [3], we plan to address noise in photometric stereo in future work. [sent-294, score-0.586]
73 Our perspective model assumes the focal length and the camera center to be known. [sent-299, score-0.424]
74 However, because no camera calibration is available for these datasets we fix the focal length 3http://www. [sent-300, score-0.156]
75 In the yaxis we show the mean angular error of the reconstructed normal map compared to the ground truth. [sent-316, score-0.208]
76 In the top x-axis we show the focal length (in pixels) used for the estimation of the normal map and in the bottom x-axis we show the displacement in x-direction (in pixels) of the camera center used for the estimation from the ground truth one. [sent-320, score-0.338]
77 In the y-axis we show the mean angular error of the reconstructed normal map compared with the ground truth. [sent-321, score-0.208]
78 One can easily show that the reconstruction is obtained up to an unknown scaling, which we then fix based on the ground truth obtained from the photometric stereo results. [sent-323, score-0.624]
79 We compare our estimated normal maps (via the mean angular error with respect to the calibrated case) with the Figure5. [sent-325, score-0.187]
80 Second column: the normal map obtained from calibrated photometric stereo. [sent-328, score-0.569]
81 Third column: the normal map obtained from our perspective uncalibrated method. [sent-329, score-0.603]
82 Fourth column: the normal map obtained from the LDR orthographic uncalibrated method. [sent-330, score-0.585]
83 state-of-art in uncalibrated photometric stereo [3, 25, 11] under orthographic projection (see table 1). [sent-331, score-1.195]
84 Such comparison shows the difference between adopting the orthographic or the perspective projection model (see sec. [sent-332, score-0.619]
85 5 we show the depth maps obtained from the integration of the normals with a Poisson solver [2]. [sent-343, score-0.184]
86 Conclusion In this paper we provided analysis and experiments to demonstrate that uncalibrated photometric stereo under perspective projection can be solved unambiguously and robustly. [sent-345, score-1.251]
87 Rather than exploiting heuristics about the scene, we used the lone integrability constraint and showed that it is sufficient to uniquely identify the light and normals given images satisfying the Lambertian model. [sent-346, score-0.536]
88 We show the mean and the standard deviation of the angular error of the estimated normal maps. [sent-350, score-0.157]
89 By using the perspective projection equations (11) we find the following system of equations zx(u,v) =. [sent-367, score-0.404]
90 By grouping all terms in zx on the left hand side of the first equation and similarly for the second equation, we obtain ×× zx(u,v) zy(u,v) ? [sent-370, score-0.141]
91 (22), the integrability constraint pˆv = qˆu yields the following equation in p, q and their derivatives at each pixel (u, v) fpv − vqpv vpqv − fqu upqu − uqpu = 0. [sent-384, score-0.424]
92 Also, we substitute w1 = [0 − f v]T and ⎣⎡−pq1⎤⎦= −QQT3BB (33) where we notice that Q3 is the last row vector of Q, and the integrability constraint becomes ? [sent-387, score-0.374]
93 Finally, we can rewrite the integrability constraint as =× ×× × × BvT(Q−Tw1) B + BuT(Q−Tw2) B=0 where κ has been removed from both terms. [sent-411, score-0.319]
94 (40) a we (41) Let the perspective integrability matrix P =. [sent-415, score-0.501]
95 A closed-form solution to uncalibrated photometric stereo via diffuse maxima. [sent-498, score-0.842]
96 Surface reconstruction using multiple light sources and perspective projection. [sent-503, score-0.321]
97 Incorporating the torrance and sparrow model of reflectance in uncalibrated photometric stereo. [sent-510, score-0.745]
98 Example-based photometric stereo: Shape reconstruction with general, varying brdfs. [sent-521, score-0.43]
99 Attached shadow coding: Estimating surface normals from shadows under unknown reflectance and lighting conditions. [sent-569, score-0.278]
100 Robust photometric stereo via low-rank matrix completion and recovery. [sent-639, score-0.586]
wordName wordTfidf (topN-words)
[('photometric', 0.392), ('integrability', 0.268), ('qtb', 0.256), ('perspective', 0.233), ('uncalibrated', 0.223), ('orthographic', 0.215), ('stereo', 0.194), ('gbr', 0.175), ('projection', 0.171), ('zu', 0.171), ('zy', 0.149), ('zv', 0.14), ('normals', 0.137), ('fz', 0.11), ('zx', 0.107), ('tankus', 0.107), ('lights', 0.104), ('albedo', 0.102), ('ff', 0.097), ('normal', 0.096), ('ambiguity', 0.093), ('uz', 0.088), ('bern', 0.085), ('vzv', 0.085), ('irradiance', 0.085), ('conference', 0.077), ('vz', 0.076), ('focal', 0.075), ('derivatives', 0.071), ('ups', 0.07), ('lambertian', 0.065), ('bvtb', 0.064), ('kiryati', 0.064), ('zuff', 0.064), ('zuv', 0.064), ('zvf', 0.064), ('zvu', 0.064), ('pot', 0.063), ('angular', 0.061), ('reflectance', 0.057), ('ldr', 0.057), ('notice', 0.055), ('formation', 0.054), ('xz', 0.053), ('coin', 0.053), ('shading', 0.052), ('map', 0.051), ('constraint', 0.051), ('light', 0.05), ('pages', 0.048), ('camera', 0.048), ('int', 0.048), ('favaro', 0.047), ('depth', 0.047), ('surface', 0.046), ('reciprocity', 0.045), ('imposing', 0.044), ('btub', 0.043), ('fvq', 0.043), ('reparametrizations', 0.043), ('ufbutb', 0.043), ('ufzzuu', 0.043), ('ufzzuv', 0.043), ('upq', 0.043), ('vfbvtb', 0.043), ('vqu', 0.043), ('zuf', 0.043), ('zvff', 0.043), ('reconstruction', 0.038), ('thoma', 0.038), ('torrance', 0.038), ('ufp', 0.038), ('unambiguously', 0.038), ('zf', 0.038), ('shadows', 0.038), ('illumination', 0.037), ('matsushita', 0.037), ('pv', 0.037), ('distant', 0.036), ('kriegman', 0.036), ('surfaces', 0.036), ('buddha', 0.035), ('octopus', 0.035), ('sparrow', 0.035), ('center', 0.035), ('equation', 0.034), ('length', 0.033), ('coordinates', 0.033), ('bq', 0.033), ('diffuse', 0.033), ('iam', 0.032), ('gv', 0.032), ('mallick', 0.032), ('proposition', 0.031), ('qu', 0.03), ('yz', 0.03), ('uniquely', 0.03), ('calibrated', 0.03), ('lk', 0.03), ('rock', 0.029)]
simIndex simValue paperId paperTitle
same-paper 1 1.0 21 cvpr-2013-A New Perspective on Uncalibrated Photometric Stereo
Author: Thoma Papadhimitri, Paolo Favaro
Abstract: We investigate the problem of reconstructing normals, albedo and lights of Lambertian surfaces in uncalibrated photometric stereo under the perspective projection model. Our analysis is based on establishing the integrability constraint. In the orthographicprojection case, it is well-known that when such constraint is imposed, a solution can be identified only up to 3 parameters, the so-called generalized bas-relief (GBR) ambiguity. We show that in the perspective projection case the solution is unique. We also propose a closed-form solution which is simple, efficient and robust. We test our algorithm on synthetic data and publicly available real data. Our quantitative tests show that our method outperforms all prior work of uncalibrated photometric stereo under orthographic projection.
2 0.34961522 443 cvpr-2013-Uncalibrated Photometric Stereo for Unknown Isotropic Reflectances
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.
3 0.21849284 75 cvpr-2013-Calibrating Photometric Stereo by Holistic Reflectance Symmetry Analysis
Author: Zhe Wu, Ping Tan
Abstract: Under unknown directional lighting, the uncalibrated Lambertian photometric stereo algorithm recovers the shape of a smooth surface up to the generalized bas-relief (GBR) ambiguity. We resolve this ambiguity from the halfvector symmetry, which is observed in many isotropic materials. Under this symmetry, a 2D BRDF slice with low-rank structure can be obtained from an image, if the surface normals and light directions are correctly recovered. In general, this structure is destroyed by the GBR ambiguity. As a result, we can resolve the ambiguity by restoring this structure. We develop a simple algorithm of auto-calibration from separable homogeneous specular reflection of real images. Compared with previous methods, this method takes a holistic approach to exploiting reflectance symmetry and produces superior results.
4 0.19706 303 cvpr-2013-Multi-view Photometric Stereo with Spatially Varying Isotropic Materials
Author: Zhenglong Zhou, Zhe Wu, Ping Tan
Abstract: We present a method to capture both 3D shape and spatially varying reflectance with a multi-view photometric stereo technique that works for general isotropic materials. Our data capture setup is simple, which consists of only a digital camera and a handheld light source. From a single viewpoint, we use a set of photometric stereo images to identify surface points with the same distance to the camera. We collect this information from multiple viewpoints and combine it with structure-from-motion to obtain a precise reconstruction of the complete 3D shape. The spatially varying isotropic bidirectional reflectance distributionfunction (BRDF) is captured by simultaneously inferring a set of basis BRDFs and their mixing weights at each surface point. According to our experiments, the captured shapes are accurate to 0.3 millimeters. The captured reflectance has relative root-mean-square error (RMSE) of 9%.
5 0.19618632 465 cvpr-2013-What Object Motion Reveals about Shape with Unknown BRDF and Lighting
Author: Manmohan Chandraker, Dikpal Reddy, Yizhou Wang, Ravi Ramamoorthi
Abstract: We present a theory that addresses the problem of determining shape from the (small or differential) motion of an object with unknown isotropic reflectance, under arbitrary unknown distant illumination, , for both orthographic and perpsective projection. Our theory imposes fundamental limits on the hardness of surface reconstruction, independent of the method involved. Under orthographic projection, we prove that three differential motions suffice to yield an invariant that relates shape to image derivatives, regardless of BRDF and illumination. Under perspective projection, we show that four differential motions suffice to yield depth and a linear constraint on the surface gradient, with unknown BRDF and lighting. Further, we delineate the topological classes up to which reconstruction may be achieved using the invariants. Finally, we derive a general stratification that relates hardness of shape recovery to scene complexity. Qualitatively, our invariants are homogeneous partial differential equations for simple lighting and inhomogeneous for complex illumination. Quantitatively, our framework shows that the minimal number of motions required to resolve shape is greater for more complex scenes. Prior works that assume brightness constancy, Lambertian BRDF or a known directional light source follow as special cases of our stratification. We illustrate with synthetic and real data how potential reconstruction methods may exploit our framework.
6 0.17819889 394 cvpr-2013-Shading-Based Shape Refinement of RGB-D Images
7 0.17750064 423 cvpr-2013-Template-Based Isometric Deformable 3D Reconstruction with Sampling-Based Focal Length Self-Calibration
8 0.15174517 130 cvpr-2013-Discriminative Color Descriptors
9 0.14358376 330 cvpr-2013-Photometric Ambient Occlusion
10 0.13283595 227 cvpr-2013-Intrinsic Scene Properties from a Single RGB-D Image
12 0.11724962 305 cvpr-2013-Non-parametric Filtering for Geometric Detail Extraction and Material Representation
13 0.11359098 147 cvpr-2013-Ensemble Learning for Confidence Measures in Stereo Vision
14 0.10171454 397 cvpr-2013-Simultaneous Super-Resolution of Depth and Images Using a Single Camera
15 0.10140426 71 cvpr-2013-Boundary Cues for 3D Object Shape Recovery
16 0.099429414 149 cvpr-2013-Evaluation of Color STIPs for Human Action Recognition
17 0.089460798 428 cvpr-2013-The Episolar Constraint: Monocular Shape from Shadow Correspondence
18 0.089287832 155 cvpr-2013-Exploiting the Power of Stereo Confidences
19 0.084684663 354 cvpr-2013-Relative Volume Constraints for Single View 3D Reconstruction
20 0.081801005 56 cvpr-2013-Bayesian Depth-from-Defocus with Shading Constraints
topicId topicWeight
[(0, 0.149), (1, 0.224), (2, 0.0), (3, 0.084), (4, -0.017), (5, -0.138), (6, -0.13), (7, 0.059), (8, 0.042), (9, -0.001), (10, -0.096), (11, -0.117), (12, -0.041), (13, -0.045), (14, 0.042), (15, 0.088), (16, 0.095), (17, -0.108), (18, 0.016), (19, -0.096), (20, 0.017), (21, -0.019), (22, 0.029), (23, 0.069), (24, 0.042), (25, -0.043), (26, -0.039), (27, 0.011), (28, 0.013), (29, 0.033), (30, 0.038), (31, -0.045), (32, -0.05), (33, 0.062), (34, 0.01), (35, 0.043), (36, -0.026), (37, 0.029), (38, 0.049), (39, 0.004), (40, 0.093), (41, -0.024), (42, -0.078), (43, -0.014), (44, 0.024), (45, -0.027), (46, 0.044), (47, -0.03), (48, 0.012), (49, -0.001)]
simIndex simValue paperId paperTitle
same-paper 1 0.93861228 21 cvpr-2013-A New Perspective on Uncalibrated Photometric Stereo
Author: Thoma Papadhimitri, Paolo Favaro
Abstract: We investigate the problem of reconstructing normals, albedo and lights of Lambertian surfaces in uncalibrated photometric stereo under the perspective projection model. Our analysis is based on establishing the integrability constraint. In the orthographicprojection case, it is well-known that when such constraint is imposed, a solution can be identified only up to 3 parameters, the so-called generalized bas-relief (GBR) ambiguity. We show that in the perspective projection case the solution is unique. We also propose a closed-form solution which is simple, efficient and robust. We test our algorithm on synthetic data and publicly available real data. Our quantitative tests show that our method outperforms all prior work of uncalibrated photometric stereo under orthographic projection.
2 0.9073019 443 cvpr-2013-Uncalibrated Photometric Stereo for Unknown Isotropic Reflectances
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.
3 0.83869964 303 cvpr-2013-Multi-view Photometric Stereo with Spatially Varying Isotropic Materials
Author: Zhenglong Zhou, Zhe Wu, Ping Tan
Abstract: We present a method to capture both 3D shape and spatially varying reflectance with a multi-view photometric stereo technique that works for general isotropic materials. Our data capture setup is simple, which consists of only a digital camera and a handheld light source. From a single viewpoint, we use a set of photometric stereo images to identify surface points with the same distance to the camera. We collect this information from multiple viewpoints and combine it with structure-from-motion to obtain a precise reconstruction of the complete 3D shape. The spatially varying isotropic bidirectional reflectance distributionfunction (BRDF) is captured by simultaneously inferring a set of basis BRDFs and their mixing weights at each surface point. According to our experiments, the captured shapes are accurate to 0.3 millimeters. The captured reflectance has relative root-mean-square error (RMSE) of 9%.
4 0.77875394 75 cvpr-2013-Calibrating Photometric Stereo by Holistic Reflectance Symmetry Analysis
Author: Zhe Wu, Ping Tan
Abstract: Under unknown directional lighting, the uncalibrated Lambertian photometric stereo algorithm recovers the shape of a smooth surface up to the generalized bas-relief (GBR) ambiguity. We resolve this ambiguity from the halfvector symmetry, which is observed in many isotropic materials. Under this symmetry, a 2D BRDF slice with low-rank structure can be obtained from an image, if the surface normals and light directions are correctly recovered. In general, this structure is destroyed by the GBR ambiguity. As a result, we can resolve the ambiguity by restoring this structure. We develop a simple algorithm of auto-calibration from separable homogeneous specular reflection of real images. Compared with previous methods, this method takes a holistic approach to exploiting reflectance symmetry and produces superior results.
5 0.7653991 465 cvpr-2013-What Object Motion Reveals about Shape with Unknown BRDF and Lighting
Author: Manmohan Chandraker, Dikpal Reddy, Yizhou Wang, Ravi Ramamoorthi
Abstract: We present a theory that addresses the problem of determining shape from the (small or differential) motion of an object with unknown isotropic reflectance, under arbitrary unknown distant illumination, , for both orthographic and perpsective projection. Our theory imposes fundamental limits on the hardness of surface reconstruction, independent of the method involved. Under orthographic projection, we prove that three differential motions suffice to yield an invariant that relates shape to image derivatives, regardless of BRDF and illumination. Under perspective projection, we show that four differential motions suffice to yield depth and a linear constraint on the surface gradient, with unknown BRDF and lighting. Further, we delineate the topological classes up to which reconstruction may be achieved using the invariants. Finally, we derive a general stratification that relates hardness of shape recovery to scene complexity. Qualitatively, our invariants are homogeneous partial differential equations for simple lighting and inhomogeneous for complex illumination. Quantitatively, our framework shows that the minimal number of motions required to resolve shape is greater for more complex scenes. Prior works that assume brightness constancy, Lambertian BRDF or a known directional light source follow as special cases of our stratification. We illustrate with synthetic and real data how potential reconstruction methods may exploit our framework.
6 0.66785252 409 cvpr-2013-Spectral Modeling and Relighting of Reflective-Fluorescent Scenes
8 0.61604488 435 cvpr-2013-Towards Contactless, Low-Cost and Accurate 3D Fingerprint Identification
9 0.61258602 71 cvpr-2013-Boundary Cues for 3D Object Shape Recovery
10 0.61049092 354 cvpr-2013-Relative Volume Constraints for Single View 3D Reconstruction
11 0.6082899 394 cvpr-2013-Shading-Based Shape Refinement of RGB-D Images
12 0.60783207 330 cvpr-2013-Photometric Ambient Occlusion
13 0.60599899 466 cvpr-2013-Whitened Expectation Propagation: Non-Lambertian Shape from Shading and Shadow
14 0.58925366 423 cvpr-2013-Template-Based Isometric Deformable 3D Reconstruction with Sampling-Based Focal Length Self-Calibration
15 0.56634182 56 cvpr-2013-Bayesian Depth-from-Defocus with Shading Constraints
16 0.56169176 227 cvpr-2013-Intrinsic Scene Properties from a Single RGB-D Image
17 0.53702629 54 cvpr-2013-BRDF Slices: Accurate Adaptive Anisotropic Appearance Acquisition
18 0.52356899 428 cvpr-2013-The Episolar Constraint: Monocular Shape from Shadow Correspondence
19 0.51071286 305 cvpr-2013-Non-parametric Filtering for Geometric Detail Extraction and Material Representation
20 0.46936497 286 cvpr-2013-Mirror Surface Reconstruction from a Single Image
topicId topicWeight
[(10, 0.083), (15, 0.236), (16, 0.033), (22, 0.012), (26, 0.085), (28, 0.016), (33, 0.202), (63, 0.011), (66, 0.063), (67, 0.029), (69, 0.026), (87, 0.114)]
simIndex simValue paperId paperTitle
same-paper 1 0.80302733 21 cvpr-2013-A New Perspective on Uncalibrated Photometric Stereo
Author: Thoma Papadhimitri, Paolo Favaro
Abstract: We investigate the problem of reconstructing normals, albedo and lights of Lambertian surfaces in uncalibrated photometric stereo under the perspective projection model. Our analysis is based on establishing the integrability constraint. In the orthographicprojection case, it is well-known that when such constraint is imposed, a solution can be identified only up to 3 parameters, the so-called generalized bas-relief (GBR) ambiguity. We show that in the perspective projection case the solution is unique. We also propose a closed-form solution which is simple, efficient and robust. We test our algorithm on synthetic data and publicly available real data. Our quantitative tests show that our method outperforms all prior work of uncalibrated photometric stereo under orthographic projection.
2 0.75513595 41 cvpr-2013-An Iterated L1 Algorithm for Non-smooth Non-convex Optimization in Computer Vision
Author: Peter Ochs, Alexey Dosovitskiy, Thomas Brox, Thomas Pock
Abstract: Natural image statistics indicate that we should use nonconvex norms for most regularization tasks in image processing and computer vision. Still, they are rarely used in practice due to the challenge to optimize them. Recently, iteratively reweighed ?1 minimization has been proposed as a way to tackle a class of non-convex functions by solving a sequence of convex ?2-?1 problems. Here we extend the problem class to linearly constrained optimization of a Lipschitz continuous function, which is the sum of a convex function and a function being concave and increasing on the non-negative orthant (possibly non-convex and nonconcave on the whole space). This allows to apply the algorithm to many computer vision tasks. We show the effect of non-convex regularizers on image denoising, deconvolution, optical flow, and depth map fusion. Non-convexity is particularly interesting in combination with total generalized variation and learned image priors. Efficient optimization is made possible by some important properties that are shown to hold.
3 0.71434796 75 cvpr-2013-Calibrating Photometric Stereo by Holistic Reflectance Symmetry Analysis
Author: Zhe Wu, Ping Tan
Abstract: Under unknown directional lighting, the uncalibrated Lambertian photometric stereo algorithm recovers the shape of a smooth surface up to the generalized bas-relief (GBR) ambiguity. We resolve this ambiguity from the halfvector symmetry, which is observed in many isotropic materials. Under this symmetry, a 2D BRDF slice with low-rank structure can be obtained from an image, if the surface normals and light directions are correctly recovered. In general, this structure is destroyed by the GBR ambiguity. As a result, we can resolve the ambiguity by restoring this structure. We develop a simple algorithm of auto-calibration from separable homogeneous specular reflection of real images. Compared with previous methods, this method takes a holistic approach to exploiting reflectance symmetry and produces superior results.
4 0.71313524 443 cvpr-2013-Uncalibrated Photometric Stereo for Unknown Isotropic Reflectances
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.
5 0.71132702 303 cvpr-2013-Multi-view Photometric Stereo with Spatially Varying Isotropic Materials
Author: Zhenglong Zhou, Zhe Wu, Ping Tan
Abstract: We present a method to capture both 3D shape and spatially varying reflectance with a multi-view photometric stereo technique that works for general isotropic materials. Our data capture setup is simple, which consists of only a digital camera and a handheld light source. From a single viewpoint, we use a set of photometric stereo images to identify surface points with the same distance to the camera. We collect this information from multiple viewpoints and combine it with structure-from-motion to obtain a precise reconstruction of the complete 3D shape. The spatially varying isotropic bidirectional reflectance distributionfunction (BRDF) is captured by simultaneously inferring a set of basis BRDFs and their mixing weights at each surface point. According to our experiments, the captured shapes are accurate to 0.3 millimeters. The captured reflectance has relative root-mean-square error (RMSE) of 9%.
6 0.71065974 127 cvpr-2013-Discovering the Structure of a Planar Mirror System from Multiple Observations of a Single Point
7 0.70734578 241 cvpr-2013-Label-Embedding for Attribute-Based Classification
8 0.70657539 227 cvpr-2013-Intrinsic Scene Properties from a Single RGB-D Image
9 0.70534891 465 cvpr-2013-What Object Motion Reveals about Shape with Unknown BRDF and Lighting
10 0.70350552 222 cvpr-2013-Incorporating User Interaction and Topological Constraints within Contour Completion via Discrete Calculus
11 0.70264107 298 cvpr-2013-Multi-scale Curve Detection on Surfaces
12 0.70224929 71 cvpr-2013-Boundary Cues for 3D Object Shape Recovery
13 0.70186681 209 cvpr-2013-Hypergraphs for Joint Multi-view Reconstruction and Multi-object Tracking
14 0.70082808 337 cvpr-2013-Principal Observation Ray Calibration for Tiled-Lens-Array Integral Imaging Display
15 0.70001966 365 cvpr-2013-Robust Real-Time Tracking of Multiple Objects by Volumetric Mass Densities
16 0.69965357 38 cvpr-2013-All About VLAD
17 0.69869417 107 cvpr-2013-Deformable Spatial Pyramid Matching for Fast Dense Correspondences
18 0.69804025 394 cvpr-2013-Shading-Based Shape Refinement of RGB-D Images
19 0.697272 39 cvpr-2013-Alternating Decision Forests
20 0.69676995 19 cvpr-2013-A Minimum Error Vanishing Point Detection Approach for Uncalibrated Monocular Images of Man-Made Environments