&lt;title&gt;Modified Beckmann-Kirchoff scattering theory for nonparaxial angles&lt;/title&gt;

Vernold, Cynthia L.; Harvey, James E.

doi:10.1117/12.328477

Cited by 49 publications

(41 citation statements)

References 3 publications

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“…The failure of the Kirchhoff theory to handle wide-angle scattering and large angles of incidence has been highlighted by other authors [4] too. Although Vernold and Harvey [11] agree with the observation that the local and mean surface normals do not coincide, they do not agree that a new obliqueness factor must be derived using the local surface normal. Instead, they claim that it is appropriate to use the mean surface normal when modelling rough surfaces, under conditions where the scale of the test or probe beam is much larger than the spatial scales under study.…”

Section: Modification Of Vernold-harveymentioning

confidence: 51%

“…To overcome this problem, Vernold and Harvey [11] have recently developed a modification of the Beckmann model that gives excellent agreement with experimental scattering data from rough surfaces at both large angles of incidence and at large scatter angles. The failure of the Kirchhoff theory to handle wide-angle scattering and large angles of incidence has been highlighted by other authors [4] too.…”

Section: Modification Of Vernold-harveymentioning

confidence: 99%

“…Instead, they claim that it is appropriate to use the mean surface normal when modelling rough surfaces, under conditions where the scale of the test or probe beam is much larger than the spatial scales under study. In the Vernold and Harvey modification [11], the geometrical factor (F 2 ) used in the Beckmann model is replaced by the cosine of the incidence angle which comes from Lambert's cosine reflectance law. They have applied their modification to that variant of the Beckmann model which assumes a Gaussian correlation function for the surface.…”

Section: Modification Of Vernold-harveymentioning

confidence: 99%

“…In its original form, this model is limited to the case of scattering close to the specular direction. However, Vernold and Harvey [11] have recently modified the Beckmann model to overcome this limitation and have extended the model to large angles of both incidence and scatter.…”

Section: Introductionmentioning

confidence: 99%

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Rough Surface Analysis using Kirchhoff Theory

Ragheb¹,

Hancock²

2003

Procedings of the British Machine Vision Conference 2003

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In this paper we illustrate the use of the Beckmann-Kirchhoff model for analysing rough surface reflectance. The Beckmann-Kirchhoff model is a physical model that describes the reflectance of light from rough surfaces. The parameter of the model is the surface slope, or ratio of the surface roughness to the correlation length. We show how this parameter may be estimated using pairs of surface images, subject to different illumination directions. With the parameter to hand, the Beckmann-Kirchhoff model may be used to perform Lambertian reflectance correction, and hence shape-from-shading may be applied to the rough surfaces. The model may also be used for surface re-illumination. We present experiments to illustrate the utility of the method for each of these tasks.

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Section: Modification Of Vernold-harveymentioning

confidence: 51%

Section: Modification Of Vernold-harveymentioning

confidence: 99%

Section: Modification Of Vernold-harveymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Rough Surface Analysis using Kirchhoff Theory

Ragheb¹,

Hancock²

2003

Procedings of the British Machine Vision Conference 2003

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“…While it is based on physically meaningful surface parameters, the Beckmann theory relies on the evaluation of the Kirchoff wave scattering integral and breaks down when the surface roughness or the scattering angle are large. To overcome this problem, Vernold and Harvey [51] have developed a model which accounts for self shadowing on rough surfaces. Ragheb and Hancock [40] have exploited this modification of the Beckman-Kirchoff theory to develop a means of measuring surface roughness parameters using reflectance.…”

Section: Introductionmentioning

confidence: 99%

An optimisation approach to the recovery of reflection parameters from a single hyperspectral image

Rahman

Robles-Kelly

2013

Computer Vision and Image Understanding

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In this paper, we present a method to recover the parameters governing the reflection of light from a surface making use of a single hyperspectral image. To do this, we view the image radiance as a combination of specular and diffuse reflection components and present a cost functional which can be used for purposes of iterative least squares optimisation. This optimisation process is quite general in nature and can be applied to a number of reflectance models widely used in the computer vision and graphics communities. We elaborate on the use of these models in our optimisation process and provide a variant of the Beckmann-Kirchhoff model which incorporates the Fresnel reflection term. We show results on synthetic images and illustrate how the recovered photometric parameters can be employed for skin recognition in real world imagery, where our estimated albedo yields a classification rate of 95.09 ± 4.26% as compared to an alternative, whose classification rate is of 90.94 ± 6.12%. We also show quantitative results on the estimation of the index of refraction, where our method delivers an average per-pixel angular error of 0.15 degrees. This is a considerable improvement with respect to an alternative, which yields an error of 9.9 degrees.

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Microfacet rendering with diffraction compensation

Yang,

Lyu,

Xian

et al. 2024

Computer Animation & Virtual

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The traditional microfacet rendering models usually only consider the straight propagation of light and do not take into account the diffraction effect when calculating the radiance of outgoing light. However, ignoring the energy generated by diffraction can lead to darker rendering results when the object's surface has many small details. To address this issue, we introduce a diffraction energy term in the microfacet model to compensate for the energy loss caused by diffraction. Starting from the Fresnel‐Kirchhoff diffraction theorem, we combine it with the Cook‐Torrance model. By incorporating the computed diffraction radiance into the outgoing radiance of the microfacet, we obtain a diffraction‐compensated BRDF (Bidirectional Reflectance Distribution Function) model. Experimental results demonstrate that our proposed method has a significant effect in compensating for outgoing light and produces more realistic rendering results.

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<title>Modified Beckmann-Kirchoff scattering theory for nonparaxial angles</title>

Cited by 49 publications

References 3 publications

Rough Surface Analysis using Kirchhoff Theory

Rough Surface Analysis using Kirchhoff Theory

An optimisation approach to the recovery of reflection parameters from a single hyperspectral image

Microfacet rendering with diffraction compensation

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