## Surface bidirectional reflection distribution function and the texture of bricks and tiles (2006)

Citations: | 69 - 10 self |

### BibTeX

@MISC{Stavridi06surfacebidirectional,

author = {Marigo Stavridi and Bram Van Ginneken and et al.},

title = {Surface bidirectional reflection distribution function and the texture of bricks and tiles},

year = {2006}

}

### OpenURL

### Abstract

### Citations

549 | Statistical and structural approaches to texture - Haralick - 1979 |

450 | Reflectance and texture of real-world surfaces - Dana, Ginneken, et al. - 1999 |

429 |
T.: Illumination for computer generated pictures
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- 1975
(Show Context)
Citation Context ...e incident position x i (or, for symmetry reasons, the exit position x e), the incident angle � i (or the exit angle � e), and the complement of the local incident angle, �/2, is �x i,e� � cos��/2� . =-=(12)-=- cos �i,e Note that x i cos � i � x e cos � e , where x i and x e have opposite signs. The sign of x i (or �x e , of course) determines the sense of rotation (denoted �) in which the ray travels throu... |

371 |
The Perception of the Visual World
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- 1950
(Show Context)
Citation Context ...57). Many naturally occurring surfaces are boundaries of opaque, often inhomogeneous bulk materials (e.g., wood, granite, paper, cloth, bread, ...) with a geometrically articulated (“rough”) surface (=-=Gibson 1950-=-, Hunter 1975). Although the reflection/refraction of beams of radiation by almost all surfaces (we have to exclude true “fractal” surfaces with structure down to the sub–wavelength scale here) is wel... |

347 |
Theory for off-specular reflection from roughened surfaces
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- 1967
(Show Context)
Citation Context ...solutions are forthcoming. The global nature of the geometrical and radiometrical effects make it virtually impossible to frame anything but approximate statistical models (Beckmann 1965, Smith 1967, =-=Torrance and Sparrow 1967-=-, Wagner 1967, Kerker 1969, Beckmann and Spizzichino 1963). Thus we are stuck with either approximate analytical models or with Monte Carlo simulations. The latter are also important as a check on the... |

260 |
Models of Light Reflection for Computer Synthesized Pictures
- Blinn
- 1977
(Show Context)
Citation Context ... � cos � cos �i . (7) sin � sin �i Likewise, trigonometry in the (right-angled) spherical triangle ikex yields � � arccos�sin � i sin ��, (8) � � arctan�cos � i tan ��, (9) �i � arctan�cos � tan �i�. =-=(10)-=- This enables us to find in the Jacobian the factor that depends on the three-dimensional geometry. We find (note that the right-hand part of the equation is necessarily nonnegative) � d� � d�� cos �i... |

206 |
Geometrical considerations and nomenclature for reflectance. National Bureau of Standards, Monograph 160
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(Show Context)
Citation Context ...he normal irradiance caused by the beam. Let the radiance of the exit beam be N(e), then one defines the “Bidirectional Reflection Distribution Function” or BRDF (Gershun 1939, Moon and Spencer 1981, =-=Nicodemus et al 1977-=-) as the ratio of the radiance of the exit beam to the irradiance Bidirectional Reflection Distribution Function 131 caused by the incident beam, that is to say BRDF(i, e) = N(e) H ⊥ . (1) i · n This ... |

154 |
The Scattering of Electromagnetic Waves from Rough Surfaces
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Citation Context ... (Kortüm 1969), thus (partly) revealing their nature in remote sensing. One may conceive of Lambertian scattering as due to roughness on the micro scale, a scale that is not resolved by the observer (=-=Beckmann and Spizzichino 1963-=-, Kerker 1969). When the scattered radiation has been thoroughly scrambled through multiple scattering the surface may approach the Lambertian limit, in fact many natural surfaces (chalk, blotting pap... |

117 | Surface reflect,ion: Physical and geometrical perspectives
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(Show Context)
Citation Context ...ables us to find the BRDF: BRDFLambertian(i, e,ϱ)= ϱ . (2) π 1.4. Existing models We confine the discussion to models with a basis in physics (Beckmann and Spizzichino 1963, Kerker 1969, Kortüm 1969, =-=Nayar et al 1991-=-, Koenderink and van Doorn 1996), disregarding the purely phenomenological models (such as—among many— Öpik 1924). We limit the discussion to surfaces with a Lambertian BRDF on the micro scale. Our ma... |

99 | Generalization of the lambertian model and implications for machine vision,” IJCV
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- 1995
(Show Context)
Citation Context ...iculations are such that the global interactions are at least confined to finite (and known) regions the chances of obtaining an exact solution are much improved. Oren and Nayar (Nayar and Oren 1995, =-=Oren and Nayar 1995-=-) consider concavities in the form of infinitely extended V–grooves. In this case the interactions are confined to the grooves. In particular the treatment of the vignetting (shadowing) becomes rather... |

69 |
The Scattering of Light and other Electromagnetic Radiation
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(Show Context)
Citation Context ...evealing their nature in remote sensing. One may conceive of Lambertian scattering as due to roughness on the micro scale, a scale that is not resolved by the observer (Beckmann and Spizzichino 1963, =-=Kerker 1969-=-). When the scattered radiation has been thoroughly scrambled through multiple scattering the surface may approach the Lambertian limit, in fact many natural surfaces (chalk, blotting paper) come clos... |

56 |
The reciprocity principle in lunar photometry
- Minnaert
- 1941
(Show Context)
Citation Context ...say BRDF(i, e) = N(e) H ⊥ . (1) i · n This is a useful definition because it essentially represents a way of “bookkeeping of rays”. Thus we have the fundamental symmetry (“Helmholtz reciprocity”, see =-=Minnaert 1941-=-) BRDF(i, e) = BRDF(e, i), which merely expresses the fact that—in geometrical optics— rays can be reversed, that is to say, if one reverses each single ray in some optical ray field, the reversed fie... |

48 |
Using color to separate reflection components”, Color research and applications
- Shafer
- 1985
(Show Context)
Citation Context ...the case of negative (� ��) sense, where � � �� � e � �i� �n � . n (19) � Note that in this case xi ��cos(�n /2)/cos �i . tion of the nth reflection is at an arc The loca� n � ���i � � n � 1 2� � n � =-=(20)-=- from the left edge. Otherwise, we proceed in the same manner. Combining results, we obtain the expression for the BRDF, namely, r�n, � n � �sin �n � �d�/d�� f�i, j� � � cos �e sin � � n,����� i ,� e�... |

43 |
The Measurement of Appearance
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(Show Context)
Citation Context ...urally occurring surfaces are boundaries of opaque, often inhomogeneous bulk materials (e.g., wood, granite, paper, cloth, bread, ...) with a geometrically articulated (“rough”) surface (Gibson 1950, =-=Hunter 1975-=-). Although the reflection/refraction of beams of radiation by almost all surfaces (we have to exclude true “fractal” surfaces with structure down to the sub–wavelength scale here) is well described b... |

35 | Illuminance texture due to surface mesostructure - Koenderink, Doorn - 1996 |

34 |
Geometrical modes as a general method to treat diffuse interreflections in radiometry
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- 1983
(Show Context)
Citation Context ...s somewhat special, for we have the additional condition �e � �i � 0. Thus the overall condition for the positive sense is �� � � n � � �n � � �� ∧ �� � �n � � �n � � �� ∧ ��n � 1� ∨ �� e � �i � 0��. =-=(16)-=- We define the set �(� i , �e) as the collection of rays indexed by the number of reflections n and orientation � (positive or negative). The set is defined through the directions �� i , �e�. The set ... |

32 |
Geometrical Shadowing of a Random Rough Surface
- SMITH
- 1971
(Show Context)
Citation Context ...at no exact solutions are forthcoming. The global nature of the geometrical and radiometrical effects make it virtually impossible to frame anything but approximate statistical models (Beckmann 1965, =-=Smith 1967-=-, Torrance and Sparrow 1967, Wagner 1967, Kerker 1969, Beckmann and Spizzichino 1963). Thus we are stuck with either approximate analytical models or with Monte Carlo simulations. The latter are also ... |

30 |
The Photic Field
- Moon, Spencer
- 1981
(Show Context)
Citation Context ... to simple addition (of radiant power spectra). As a consequence we can evaluate the effect of extended sources via integration once we know the scattering of directed beams (Fock 1924, Gershun 1939, =-=Moon and Spencer 1981-=-). Thus we need only consider incident beams of vanishing angular spread. Because this is really a singular case (beams of vanishing angular spread have zero “throughput” or étendue (Gershun 1939, Moo... |

25 | Using a color reflection model to separate highlights from object color
- Klinker, Shafer, et al.
- 1987
(Show Context)
Citation Context ... contributes the amount sin � n � � r�n, �n � 4n cos2 �i (18) to the sum in the full BRDF [see Eq. (5)]. Similar reasoning holds for the case of negative (� ��) sense, where � � �� � e � �i� �n � . n =-=(19)-=- � Note that in this case xi ��cos(�n /2)/cos �i . tion of the nth reflection is at an arc The loca� n � ���i � � n � 1 2� � n � (20) from the left edge. Otherwise, we proceed in the same manner. Comb... |

24 |
The light field
- Gershun
- 1939
(Show Context)
Citation Context ...nit vector i � in the plane of incidence, such that i • i � � 0. The angle � is chosen such that the direction of the exit beam can also be specified as j � cos �i � cos � sin �i � � sin � sin �e y . =-=(1)-=- The angles �� e , � e� can be expressed conveniently in terms of the angles �� i , �, �� (or, vice versa, the angles ��, �� in terms of the angles �� i , � e , � e�) by use of trigonometry in the sph... |

24 |
Mutual illumination
- Forsyth, Zisserman
- 1989
(Show Context)
Citation Context ...e �� i , �e�-parameter plane. Figure 6 depicts possible conditions. � For a possible event we find xi � �cos(�n /2)�/ cos �i and � � dxi �dxi /d�n � sin �n �x i � �x i � � d�e� �d�e /d�n �� 4n cos2 . =-=(17)-=- �i Fig. 6. Representation of possible combinations of incident (horizontal axis) and exit (vertical axis) directions for n-times reflected rays (for hemispherical pits) for the positive sense of rota... |

22 |
Reflectance Spectroscopy
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- 1969
(Show Context)
Citation Context ...e micro scale, this description is essentially useless on the macro or mega scale. The surface remission of many so called “matte” surfaces is approximately captured by “Lambert’s Law” (Lambert 1760, =-=Kortüm 1969-=-): The radiance of the remitted beam is independent of the viewing direction and depends only on the irradiance. Such surfaces scatter the incident radiation “completely” in the sense that the directi... |

22 |
Principles of Optics”, Cam bridge
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- 1999
(Show Context)
Citation Context ... � i cos � e � sin � i sin � e cos � e�, (6) � � arccos cos �e � cos � cos �i . (7) sin � sin �i Likewise, trigonometry in the (right-angled) spherical triangle ikex yields � � arccos�sin � i sin ��, =-=(8)-=- � � arctan�cos � i tan ��, (9) �i � arctan�cos � tan �i�. (10) This enables us to find in the Jacobian the factor that depends on the three-dimensional geometry. We find (note that the right-hand par... |

22 |
Optics (Addison-Wesley
- Hecht, Zajac
- 1974
(Show Context)
Citation Context ...cos � e�, (6) � � arccos cos �e � cos � cos �i . (7) sin � sin �i Likewise, trigonometry in the (right-angled) spherical triangle ikex yields � � arccos�sin � i sin ��, (8) � � arctan�cos � i tan ��, =-=(9)-=- �i � arctan�cos � tan �i�. (10) This enables us to find in the Jacobian the factor that depends on the three-dimensional geometry. We find (note that the right-hand part of the equation is necessaril... |

22 |
The Scattering of Electromagnetic Waves from Rough Surfaces
- BECKMAN, SPIZZICHINO
- 1963
(Show Context)
Citation Context ...ns and between the third- and second-order reflections, for which, in general, we find � n � cos �/(2n � 1) and � � 2�/(2n � 1). Thus the event contributes the amount sin � n � � r�n, �n � 4n cos2 �i =-=(18)-=- to the sum in the full BRDF [see Eq. (5)]. Similar reasoning holds for the case of negative (� ��) sense, where � � �� � e � �i� �n � . n (19) � Note that in this case xi ��cos(�n /2)/cos �i . tion o... |

20 |
Diffuse and Specular Reflectance from Rough Surfaces
- Ginneken, Stavridi, et al.
- 1998
(Show Context)
Citation Context ...d ray. Of course, �n is the same for the reversed situation since it is an unsigned angle. For the location of the nth reflection of the reversed situation, we have the arc � �n ���e � �n � 1 � 2�� n =-=(15)-=- from the left edge. The condition for the reversed ray is � � � (� n � �) ∧ (�n � �n � �). The case n � 1 is somewhat special, for we have the additional condition �e � �i � 0. Thus the overall condi... |

18 | Visual appearance of matte surfaces
- Nayar, Oren
- 1995
(Show Context)
Citation Context ...e: If the surface articulations are such that the global interactions are at least confined to finite (and known) regions the chances of obtaining an exact solution are much improved. Oren and Nayar (=-=Nayar and Oren 1995-=-, Oren and Nayar 1995) consider concavities in the form of infinitely extended V–grooves. In this case the interactions are confined to the grooves. In particular the treatment of the vignetting (shad... |

16 | Textural Textural Properties for Pattern Recognition - Hawkins - 1969 |

15 |
Geometrical and Physical Optics
- Longhurst
- 1957
(Show Context)
Citation Context ...rom those commonly encountered in the optics laboratory, that is to say, smoothly polished transparent dielectrics (glass) or metals (silver or aluminum mirror coatings) deposited on smooth surfaces (=-=Longhurst 1957-=-). Many naturally occurring surfaces are boundaries of opaque, often inhomogeneous bulk materials (e.g., wood, granite, paper, cloth, bread, ...) with a geometrically articulated (“rough”) surface (Gi... |

15 |
Directional Distribution, and Off-Specular Peak Phenomena in Light Reflected from Roughened Surfaces
- Torrance, Sparrow, et al.
- 1966
(Show Context)
Citation Context ...hat the location of the nth reflection should be inside the pit, whereas the location of the (n � 1)th would be outside it. The location of the nth reflection is at an arc � �n � �i � �n � 1 � 2 �� n =-=(14)-=- � from the right edge. Thus the condition is (� n � � � �) ∧ ( �n � �n � �). The same constraint applies � to the reversed ray. Of course, �n is the same for the reversed situation since it is an uns... |

12 |
Lightness scale from image intensity distributions. Appl Opt 21:2569–2604
- Richards
- 1982
(Show Context)
Citation Context ...h radiance) can be retraced in measurements of many natural materials. Close study of the changes in the modal structure of the histogram may be expected to be useful in remote sensing applications. (=-=Richards 1982-=- has a rather interesting discussion. Although his model is quite different from the present one the predicted histograms are similar. His data on the histogram of foliage is remarkably like the histo... |

10 |
On the relative brightness of specular and diffuse reflection
- Wolff
- 1994
(Show Context)
Citation Context ... edge. Otherwise, we proceed in the same manner. Combining results, we obtain the expression for the BRDF, namely, r�n, � n � �sin �n � �d�/d�� f�i, j� � � cos �e sin � � n,����� i ,� e� 4n cos2 �i . =-=(21)-=- This is the final expression for the BRDF. It depends only on the directions of the incident and the scattered rays, albeit via the expressions for �, d�/d�, �i,e , �, and � that were derived earlier... |

10 |
The opposition effect of the moon - the contribution of coherent backscatter
- Hapke, Nelson, et al.
- 1993
(Show Context)
Citation Context ... the case n � 1 we have x 1 � sin(� e /2), for � 0 � x i � � 1 with � 0 � 0, � 1 � 1/2. Since dA � 2�x idx i and d� � 2� sin � e d� e , we have �J�dA, d��� � 1/4. Thus the contribution to the BRDF is =-=(22)-=- f1�� e� � �1�� e� , 4� cos �e (23) with �1(� e) � 1 for �e � �/3 and zero otherwise.s2462 J. Opt. Soc. Am. A/Vol. 19, No. 12/December 2002 S. C. Pont and J. J. Koenderink For the case of multiple ref... |

9 |
Shadowing of Random Rough Surface
- Beckmann
(Show Context)
Citation Context ...the drawback that no exact solutions are forthcoming. The global nature of the geometrical and radiometrical effects make it virtually impossible to frame anything but approximate statistical models (=-=Beckmann 1965-=-, Smith 1967, Torrance and Sparrow 1967, Wagner 1967, Kerker 1969, Beckmann and Spizzichino 1963). Thus we are stuck with either approximate analytical models or with Monte Carlo simulations. The latt... |

8 |
On Interreflections
- Moon
- 1940
(Show Context)
Citation Context ...herical cavity is an especially convenient case because the interreflection problem can be solved algebraically: In general one has to solve an (often nasty) Fredholm integral equation (Buckley 1927, =-=Moon 1940-=-, Koenderink and van Doorn 1983). The reason is that the étendue of the beam defined by two surface elements on the cavity does not depend on the location of the surface elements at all! In fact, the ... |

6 |
Photometria Sive de Mensure de Gradibus Luminis, Colorum et Umbræ
- LAMBERT
- 1760
(Show Context)
Citation Context ...tion coefficient is r(n i , � i) � �F �(� i) n i � F �(� i) n i�/2 and has still to be introduced into the BRDF. Thus the full BRDF is f�i, j� � �d�/d�� � cos �e sin � � r�n i , �i�x i� i�1 ... dxi , =-=(5)-=- d�� where we have introduced the dimensionless parameter x i � � i /R. Because we assume that the diameter of the concavity is much larger than the wavelength, a dimensionless parameter does indeed f... |

6 |
Columbia-Utrecht reflectance and texture database. http://www.cs.columbia.edu/CAVE/curet
- Curet
(Show Context)
Citation Context ...ghtforward trigonometry in the spherical triangle ije z (by use of the cosine theorem for the sides of a general spherical triangle) then yields � � arccos�cos � i cos � e � sin � i sin � e cos � e�, =-=(6)-=- � � arccos cos �e � cos � cos �i . (7) sin � sin �i Likewise, trigonometry in the (right-angled) spherical triangle ikex yields � � arccos�sin � i sin ��, (8) � � arctan�cos � i tan ��, (9) �i � arct... |

5 |
On the radiation from the inside of a circular cylinder
- Buckley
- 1927
(Show Context)
Citation Context ...ections The spherical cavity is an especially convenient case because the interreflection problem can be solved algebraically: In general one has to solve an (often nasty) Fredholm integral equation (=-=Buckley 1927-=-, Moon 1940, Koenderink and van Doorn 1983). The reason is that the étendue of the beam defined by two surface elements on the cavity does not depend on the location of the surface elements at all! In... |

4 |
Reradiation and thermal emission from illuminated craters on the lunar surface
- Buhl, Welch, et al.
- 1968
(Show Context)
Citation Context ...he V–groove model. Notice that the pitted surface model (like the V– groove model) strictly confines the global interactions to a finite region, in this case the interior surfaces of the concavities (=-=Buhl et al 1968-=-). This makes these models viable in the first place. In the case of the thoroughly pitted surface this means that we need only treat the case of a single concavity: More general cases (distributions ... |

4 |
The light
- Gershun
- 1939
(Show Context)
Citation Context ...position leads to simple addition (of radiant power spectra). As a consequence we can evaluate the effect of extended sources via integration once we know the scattering of directed beams (Fock 1924, =-=Gershun 1939-=-, Moon and Spencer 1981). Thus we need only consider incident beams of vanishing angular spread. Because this is really a singular case (beams of vanishing angular spread have zero “throughput” or éte... |

4 | Photometria sive de mensura de gradibus luminis, colorum et umbrae. Eberhard Klett - Lambert - 1760 |

3 |
Theory of the integrating sphere
- Jacquez, Kuppenheim
- 1955
(Show Context)
Citation Context ... and van Doorn 1983). The reason is that the étendue of the beam defined by two surface elements on the cavity does not depend on the location of the surface elements at all! In fact, the étendue is (=-=Jacquez and Kuppenheim 1955-=-, Koenderink and van Doorn 1983) r ε(p1, p2) = da1da2 4R2 , (3) here (p1, p2) are two positions on the surface, (da1,da2) infinitesimal surface elements at these positions, and R the radius of the sph... |

2 |
Zur Berechnung der Beleuchtungsstärke. Zeitschrift für Physik
- Fock
- 1924
(Show Context)
Citation Context ...s the superposition leads to simple addition (of radiant power spectra). As a consequence we can evaluate the effect of extended sources via integration once we know the scattering of directed beams (=-=Fock 1924-=-, Gershun 1939, Moon and Spencer 1981). Thus we need only consider incident beams of vanishing angular spread. Because this is really a singular case (beams of vanishing angular spread have zero “thro... |

1 |
Models of light reflection from computer synthesized pictures
- Blinn
- 1977
(Show Context)
Citation Context ...eir photometrical properties are quite distinct from those associated with the Lambertian surface. Although ad hoc phenomenological models are quite common (especially in computer graphics rendering (=-=Blinn 1977-=-, Foley et al 1990)), it is obviously preferable to develop realistic models that reflect the relevant physics. One advantage of such models is that the model can also predict texture and radiance his... |

1 | Photometric properties of lunar crater floors - Diggelen - 1959 |

1 |
Photometric measures of the moon and the earth– shine. Publ. de L’Observ. Astron. de L’Univ
- Öpik
- 1924
(Show Context)
Citation Context ...ith a basis in physics (Beckmann and Spizzichino 1963, Kerker 1969, Kortüm 1969, Nayar et al 1991, Koenderink and van Doorn 1996), disregarding the purely phenomenological models (such as—among many— =-=Öpik 1924-=-). We limit the discussion to surfaces with a Lambertian BRDF on the micro scale. Our main interest is a better understanding of the relative contributions of cast shadow, vignetting and interreflecti... |

1 |
A negative branch of polarization for comets and atmosphereless celestial bodies and the light scattering by aggregate particles
- Petrova, Jockers, et al.
- 2001
(Show Context)
Citation Context ... e /2), for � 0 � x i � � 1 with � 0 � 0, � 1 � 1/2. Since dA � 2�x idx i and d� � 2� sin � e d� e , we have �J�dA, d��� � 1/4. Thus the contribution to the BRDF is (22) f1�� e� � �1�� e� , 4� cos �e =-=(23)-=- with �1(� e) � 1 for �e � �/3 and zero otherwise.s2462 J. Opt. Soc. Am. A/Vol. 19, No. 12/December 2002 S. C. Pont and J. J. Koenderink For the case of multiple reflections n � 1, we obtain contribut... |

1 |
Polarization of light reflected from rough planetary surface
- Wolff
- 1975
(Show Context)
Citation Context ...multiple reflections n � 1, we obtain contributions for � n � x i � � n�1 . Since x i � cos�(� � � e)/(2n)�, one finds with dA � 2�x idx i and d� � 2� sin � ed� e that �J�dA, d��� � sin��� � �e�/n� , =-=(24)-=- 4n sin �e thus the contribution to the BRDF is fn�� e� � �n�� e�sin��� � �e�/n� , (25) 2�n sin 2� e where �n(� e) � 1 for ��/(2n � 1) � �e � �/(2n � 1) and otherwise zero. Finally, the BRDF for the c... |

1 | Statistical approaches to surface texture classification,” Wear 167 - Ramamoorthy, Radhakrishnan - 1993 |

1 | Texture from illuminated 3D surface articulation - Koenderink, Doorn - 1994 |