## Helmholtz Stereopsis: Exploiting Reciprocity for Surface Reconstruction (2002)

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Venue: | International Journal of Computer Vision |

Citations: | 100 - 13 self |

### BibTeX

@INPROCEEDINGS{Zickler02helmholtzstereopsis:,

author = {Todd Zickler and Peter N. Belhumeur and David J. Kriegman},

title = {Helmholtz Stereopsis: Exploiting Reciprocity for Surface Reconstruction},

booktitle = {International Journal of Computer Vision},

year = {2002},

pages = {869--884}

}

### Years of Citing Articles

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### Abstract

Abstract. We present a method – termed Helmholtz stereopsis – for reconstructing the geometry of objects from a collection of images. Unlike most existing methods for surface reconstruction (e.g., stereo vision, structure from motion, photometric stereo), Helmholtz stereopsis makes no assumptions about the nature of the bidirectional reflectance distribution functions (BRDFs) of objects. This new method of multinocular stereopsis exploits Helmholtz reciprocity by choosing pairs of light source and camera positions that guarantee that the ratio of the emitted radiance to the incident irradiance is the same for corresponding points in the two images. The method provides direct estimates of both depth and field of surface normals, and consequently weds the advantages of both conventional and photometric stereopsis. Results from our implementations lend empirical support to our technique. 1

### Citations

375 | A reflectance model for computer graphics - Cook, Torrance - 1981 |

365 | Theory for off-specular reflection from roughened surfaces - Torrance, Sparrow - 1967 |

232 |
Geometrical Considerations and Nomenclature for Reflectance
- Nicodemus, Richmond, et al.
- 1977
(Show Context)
Citation Context ...his paper, we present a method for reconstructing the geometryof a surface that has arbitraryand unknown surface reflectance, as described bythe bidirectional reflectance distribution function (BRDF) =-=[17]-=-. This method does not make the assumption that the BRDF is Lambertian or of some other parametric form, and it enables the reconstruction of surfaces for which the BRDF is anisotropic and spatiallyva... |

213 | A method for enforcing integrability in shape from shading algorithms
- Frankot, Chellappa
- 1988
(Show Context)
Citation Context ...ted there. Elsewhere, the depth and orientation are accurately recovered. A 9 × 9 window was used in the depth search. in this way, we enforced integrability (using the method of Frankot and Chellapa =-=[7]-=- with a Fourier basis) and integrated the the vector fields shown in Figs. 7c and 10c. The results are shown in Figs. 11 and 12. As seen in these figures, the high frequencyinformation provided bythe ... |

204 | Numerical shape from shading and occluding boundaries - Ikeuchi, Horn - 1981 |

200 | Variational principles, surface evolution, pdes, level set methods, and the stereo problem
- Faugeras, Keriven
- 1998
(Show Context)
Citation Context ...tured; when they are not textured, regularization is needed to infer the surface. (This can be achieved, for example, using a statistical prior [7, 14, 17, 1] or through regularized surface evolution =-=[5]-=-.) Sparse stereo and motion methods also have difficulty in these regions. These methods only reconstruct the geometry of corresponding feature points, so by their nature, they cannot directly reconst... |

140 |
Stereo vision for planetary rovers: Stochastic modeling to near real-time implementation
- Matthies
- 1992
(Show Context)
Citation Context ... motion methods work best when the surfaces are highlytextured; when theyare not textured, regularization is needed to infer the surface. (This can be achieved, for example, using a statistical prior =-=[8,15,18,2]-=- or through regularized surface evolution [6].) Sparse stereo and motion methods also have difficultyin these regions. These methods onlyreconstruct the geometryof corresponding feature points, so byt... |

133 | Occlusions and binocular stereo
- Geiger, Ladendorf, et al.
- 1995
(Show Context)
Citation Context ... motion methods work best when the surfaces are highlytextured; when theyare not textured, regularization is needed to infer the surface. (This can be achieved, for example, using a statistical prior =-=[8,15,18,2]-=- or through regularized surface evolution [6].) Sparse stereo and motion methods also have difficultyin these regions. These methods onlyreconstruct the geometryof corresponding feature points, so byt... |

113 |
A bayesian-approach to binocular stereopsis
- Belhumeur
- 1996
(Show Context)
Citation Context ...ect differentiation of the depth map, regularized estimates of the normal field can be obtained, for example, based on an assumption of local planarity [4], or through the use of an energy functional =-=[1]-=-. In contrast to these methods, photometric stereopsis provides a direct estimate of the field of surface normals which is then integrated (in the absence of depth discontinuities) to obtain a surface... |

109 | Generalization of the Lambertian Model and implications for machine vision - Oren, Nayar - 1995 |

105 |
Determining surface orientations of specular surfaces by using the photometric stereo method
- Ikeuchi
- 1981
(Show Context)
Citation Context ...tian [12, 19,21]. The methods that do not make this assumption either assume that the BRDF (or the reflectance map) is completelyknown a priori, or can be specified using a small number of parameters =-=[9,11,16,20]-=-. These parametric BRDFs are often derived from physical models of reflectance and are therefore restricted to a limited class of surfaces. When the form of the BRDF is unknown, or when the form of th... |

85 |
Determining Shape and Reflectance of Hybrid Surfaces by Photometric Sampling
- Ikeuchi, Kanade
- 1990
(Show Context)
Citation Context ...tian [12, 19,21]. The methods that do not make this assumption either assume that the BRDF (or the reflectance map) is completelyknown a priori, or can be specified using a small number of parameters =-=[9,11,16,20]-=-. These parametric BRDFs are often derived from physical models of reflectance and are therefore restricted to a limited class of surfaces. When the form of the BRDF is unknown, or when the form of th... |

79 | A microfacetbased BRDF generator - ASHIKHMIN, PREMOZE, et al. - 2000 |

78 | A Bayesian treatment of the stereo correspondence problem using half-occluded regions
- Belhumeur, Mumford
- 1992
(Show Context)
Citation Context ...aints of this form. Let W(d) be the NP × 3 matrix where the ith ˆvli row is given by wi(d) = ili |oli−p| 2 ˆvri − iri |ori−p| 2 . Then the set of constraints from (1) can be expressed as W(d) ˆn = 0. =-=(2)-=- Clearly, for the correct depth value d ⋆ the surface normal lies in the null space of W(d ⋆ ), and it can be estimated from a noisy matrix using singular value decomposition. In addition, W(d ⋆ ) wil... |

74 |
Treatise on physiological optics
- Helmholtz
- 1911
(Show Context)
Citation Context ... the surface. It is not an arbitraryfour dimensional function, as it is symmetric about the incoming and outgoing angles fr( î, ê) =fr(ê, î). This symmetry condition was first enunciated byHelmholtz (=-=[10]-=-, p. 231) and is commonlyreferred to as Helmholtz reciprocity. To see how reciprocitycan be used for stereopsis, consider obtaining a pair of images as shown in Fig. 1. The first image is captured whi... |

73 | Bidirectional Reflection Distribution Function Expressed - Koenderink, Doorn, et al. - 1996 |

72 | Computing Differential Properties of 3-D Shapes from Stereoscopic Images without 3-D Models
- Devernay, Faugeras
- 1994
(Show Context)
Citation Context ...red depth map will be very noisy. Instead of direct differentiation of the depth map, regularized estimates of the normal field can be obtained, for example, based on an assumption of local planarity =-=[4]-=-, or through the use of an energy functional [1]. In contrast to these methods, photometric stereopsis provides a direct estimate of the field of surface normals which is then integrated (in the absen... |

67 | The reciprocity principle in lunar photometry - Minnaert |

65 |
Photometric stereo under a light source with arbitrary motion
- Hayakawa
- 1994
(Show Context)
Citation Context ...tian [12, 19,21]. The methods that do not make this assumption either assume that the BRDF (or the reflectance map) is completelyknown a priori, or can be specified using a small number of parameters =-=[9,11,16,20]-=-. These parametric BRDFs are often derived from physical models of reflectance and are therefore restricted to a limited class of surfaces. When the form of the BRDF is unknown, or when the form of th... |

51 |
Analysing images of curved surfaces
- Woodham
- 1981
(Show Context)
Citation Context ...f the field of surface normals which is then integrated to recover the surface depth. Similar to conventional dense multinocular stereopsis, manyphotometric methods assume that the BRDF is Lambertian =-=[12, 19,21]-=-. The methods that do not make this assumption either assume that the BRDF (or the reflectance map) is completelyknown a priori, or can be specified using a small number of parameters [9,11,16,20]. Th... |

46 | Beyond lambert: Reconstructing surfaces with arbitrary brdfs
- Magda, Zickler, et al.
- 2001
(Show Context)
Citation Context ...the direction of the light source) is the same for both images. This is not true for general stereo pairs that are acquired under fixed illumination (unless the BRDF of the surface is Lambertian.) In =-=[14]-=-, it was shown that three or more pairs of images acquired in this manner are needed to establish a matching constraint, which leads to a multinocular stereo imaging geometry. It was also shown that i... |

46 |
Determining shape and reflectance using multiple images," master's thesis
- Silver
- 1980
(Show Context)
Citation Context ...f the field of surface normals which is then integrated to recover the surface depth. Similar to conventional dense multinocular stereopsis, manyphotometric methods assume that the BRDF is Lambertian =-=[12, 19,21]-=-. The methods that do not make this assumption either assume that the BRDF (or the reflectance map) is completelyknown a priori, or can be specified using a small number of parameters [9,11,16,20]. Th... |

45 | DeFigueiredo, 'A theory of photometric stereo for a class of diffuse nonLambertian surface
- Tagare, P
- 1991
(Show Context)
Citation Context |

39 | A binocular stereo algorithm for reconstructing sloping, creased, and broken surfaces in the presence of half-occlusion
- Belhumeur
- 1993
(Show Context)
Citation Context ...irect differentiation of the depth map, regularized estimates of the normal field can be obtained, for example, based on an assumption of local planarity[5], or through the use of an energyfunctional =-=[1]-=-. In contrast to these methods, photometric stereopsis provides a direct estimate of the field of surface normals which is then integrated (in the absence of depth discontinuities) to obtain a surface... |

33 | Stereo without disparity gradient smoothing: A Bayesian sensor fusion solution
- Cox, Hingorani, et al.
- 1992
(Show Context)
Citation Context ...each matrix Wq(d), we compute the singular value decomposition, W = UΣV T where Σ = diag(σ1, σ2, σ3), σ1 ≥ σ2 ≥ σ3. Then, our support measure to be used in the depth search is the ratio rq(d) = σ2 . =-=(3)-=- Note that at correct depth values, the ratio rq(d) will be large. The condition shown in (2) is a necessary condition that will be satisfied by true values of surface depth, but it is not sufficient.... |

33 | Illumination for computer-generated pictures - Phong - 1975 |

31 |
Shape-from-shading on a cloudy day
- Langer, Zucker
- 1994
(Show Context)
Citation Context ...f the field of surface normals which is then integrated to recover the surface depth. Similar to conventional dense multinocular stereopsis, manyphotometric methods assume that the BRDF is Lambertian =-=[12, 19,21]-=-. The methods that do not make this assumption either assume that the BRDF (or the reflectance map) is completelyknown a priori, or can be specified using a small number of parameters [9,11,16,20]. Th... |

15 |
Reflectance and Shape from Images using a Collinear Light Source
- Lu, Little
- 1999
(Show Context)
Citation Context ...a limited class of surfaces. When the form of the BRDF is unknown, or when the form of the BRDF is spatiallyvarying, there is insufficient information to reconstruct both the geometryand the BRDF. In =-=[13]-=-, a hybrid method with controlled lighting and object rotation was used to estimate both surface structure and a non-parametric reflectance map. This is similar to our method in that it: 1) is an acti... |

11 | Helmholtz reciprocity: its validity and application to reflectometry - Clarke, Parry - 1985 |

11 | A fast and accurate light reflection model - He, Heynen, et al. - 1992 |

6 | Thermodynamic constraints on reflectance reciprocity and kirchoff’s law - Snyder, Wan, et al. - 1998 |

6 |
Computational vision and regularisation theory
- Poggio, Torre, et al.
- 1985
(Show Context)
Citation Context ... motion methods work best when the surfaces are highlytextured; when theyare not textured, regularization is needed to infer the surface. (This can be achieved, for example, using a statistical prior =-=[8,15,18,2]-=- or through regularized surface evolution [6].) Sparse stereo and motion methods also have difficultyin these regions. These methods onlyreconstruct the geometryof corresponding feature points, so byt... |

3 | Computational vision and regularisation theory. Nature 317 - Poggio, Torre, et al. - 1985 |