A method for correcting geometric attenuation factors based on optical microfacet theory

Abstract

The present invention discloses a method for correcting geometric attenuation factors based on optical microfacet theory. The method utilizes microfacet theory to assume that an object's surface is composed of multiple microfacets, each consisting of a first irradiation surface close to the incident light and a second irradiation surface farther from the incident light. Based on the geometric relationship between the first and second irradiation surfaces and the incident and reflected light, a normal vector angle probability model is employed to obtain a corrected geometric attenuation factor to determine the occlusion probability of the incident light. Substituting the corrected geometric attenuation factor into a bidirectional reflectance distribution function yields the radiant energy of the reflected light to detect the object's topography. This method can obtain an accurate and reasonable geometric attenuation factor, thereby enabling accurate analysis of the target's polarization characteristics and enhancing the effectiveness of polarization detection.

Description

Technical Field

[0001] The present invention belongs to the field of physical optics, and in particular relates to a method for correcting a geometric attenuation factor based on optical microfacet theory. Background Art

[0002] The bidirectional reflectance distribution function is used to characterize the directional scattering and energy distribution of hemispherical space light on the surface of an object. It quantifies the radiation scattered in all directions by the surface of the object in any direction of the hemisphere illuminated by the light source. It is defined as the ratio between the reflected radiation brightness and the irradiance in the incident direction.

[0003]

[0004] where the radiance θ r is the radiation flux per unit area and per unit solid angle in the reflection direction (W / (m 2 ·sr)); irradiance E(θ i ,φ i ) is the radiation flux per unit area in the incident direction (W / m 2 );θ i is the incident zenith angle; θ r is the reflection zenith angle; φ i is the incident azimuth; φ r is the reflection azimuth; λ is the wavelength of incident light; F is the Fresnel reflectivity; A f is the microfacet area; G is the geometric attenuation factor; P(α) is the microfacet normal vector distribution function.

[0005] Using the bidirectional reflectance distribution function to describe the light reflection characteristics of an object's surface is unique. The reflection characteristics it determines depend on the characteristics of the object's surface itself, primarily the surface roughness. Factors such as the dielectric constant and polarization determine this function, effectively unifying the reflection and scattering of a material's surface into a single concept and describing the surface's directional scattering and radiation characteristics. The differences in optical scattering characteristics of different materials are reflected in different bidirectional reflectance distribution function expressions in optical property modeling. The bidirectional reflectance distribution function is indeed the key and core of the process for describing and modeling the target's optical scattering characteristics. By incorporating the polarization state information of the incident and reflected light into the process of light interacting with the target surface, and expanding the traditional scalar bidirectional reflectance distribution function into a vector polarization bidirectional reflectance distribution function, the Stokes vectors reflecting the polarization information of the incident and reflected light can be linked to each other, fully describing the polarization characteristics of the target surface.

[0006] The geometric attenuation factor refers to the shadow and shielding effect of the object surface on light when light is reflected on the surface of an object. It is also an important factor in determining the accuracy of the reflection distribution function. It is related to factors such as the surface model, roughness, and the complex refractive index of the material.

[0007] Research on the geometric attenuation factor began as early as 1977, and new models and corrections have been proposed one after another. However, the existing models still have limitations in practical applications, such as inflection points, inability to maintain bounds, and incomplete model considerations. These problems seriously affect the accuracy of using the bidirectional reflectance distribution function to characterize the directional scattered energy distribution of hemispherical space light on the surface of an object, making it impossible to accurately analyze the polarization characteristics of the object. Summary of the Invention

[0008] The present invention provides a method for correcting the geometric attenuation factor based on optical microfacet theory. This method can obtain an accurate and reasonable geometric attenuation factor. Understanding the polarization characteristics of an object is the first step in polarization detection. The more complete the characteristic analysis, the better the polarization detection effect. Therefore, an accurate and reasonable geometric attenuation factor will enhance the effect of polarization detection.

[0009] A method for correcting geometric attenuation factors based on optical microfacet theory, comprising:

[0010] Using the microfacet theory, it is assumed that the surface of the object is composed of multiple microfacets, and each microfacet consists of a first irradiation surface close to the incident light and a second irradiation surface far away from the incident light;

[0011] Based on the geometric relationship between the first illumination surface and the incident light, the normal vector angle probability model is used to obtain the probability that the incident light completely passes through the first illumination surface, the probability that the incident light does not pass through the first illumination surface, and the probability that the incident light partially passes through the first illumination surface;

[0012] Based on the geometric relationship of the incident light completely passing through the first illumination surface and then irradiating the second illumination surface, a normal vector angle probability model is used to obtain the probability that the incident light completely passes through the second illumination surface, the probability that the incident light completely blocks the second illumination surface, and the probability that the incident light partially passes through the second illumination surface. The first product probability is obtained by multiplying the probability of the incident light completely passing through, completely blocking, and partially passing through the second illumination surface with the probability of the incident light completely passing through the first illumination surface.

[0013] After the incident light completely passes through the first illumination surface, it forms a first reflected light. Based on the geometric relationship between the first reflected light and the second illumination surface, a normal vector angle probability model is used to obtain the probability that the first reflected light completely passes through the second illumination surface and the probability that the first reflected light is back-reflected by the second illumination surface. The second product probability is obtained by multiplying the probability that the first reflected light completely passes through the second illumination surface and the probability that the first reflected light is back-reflected by the second illumination surface with the probability that the incident light completely passes through the first illumination surface.

[0014] Based on the fact that the incident light partially passes through the first illumination surface to form second reflected light, and based on the geometric relationship between the second reflected light and the second illumination surface, a normal vector angle probability model is used to respectively construct the probability of the second reflected light being reflected forward by the second illumination surface and the probability of the second reflected light being reflected backward by the second illumination surface; a third product probability is obtained by multiplying the probability of the second reflected light being reflected forward and backward by the second illumination surface with the probability of the incident light partially passing through the first illumination surface;

[0015] Based on the probability that the incident light does not pass through the first illumination surface and the first, second, and third product probabilities, a modified geometric attenuation factor is constructed to obtain the occlusion probability of the incident light. The modified geometric attenuation factor is substituted into the bidirectional reflectance distribution function to obtain the radiation energy of the reflected light to detect the morphology of the object.

[0016] Each microfacet consists of a first illumination surface close to the incident light and a second illumination surface away from the incident light, including:

[0017] The bottom sides of each microfacet are equal in length, and the inclination angles of the first irradiation surface and the second irradiation surface of each microfacet obey random Gaussian distribution, and the inclination angle range is (-π / 2, π / 2).

[0018] Based on the surface roughness of the object, the microfacet theory is used to construct the probability model p(χ) of the angle between the normal vector of the microfacet surface and the macro surface of the object:

[0019]

[0020]

[0021] Where χ is the angle between the micro-normal vector of the micro-facet and the macro-normal vector of the object surface, C is the normalization coefficient that makes the function p(·) integral equal to 1 in the entire space, σ is the surface roughness, θ i is the angle of incidence, θ r is the reflection angle.

[0022] Based on the geometric relationship between the first illumination surface and the incident light, the normal vector angle probability model is used to construct the probability P of the incident light completely passing through the first illumination surface. 1a , the probability P that the incident light does not pass through the first illumination surface 1b , the probability P that the incident light partially passes through the first illumination surface 1c :

[0023]

[0024]

[0025]

[0026] Wherein, α is the angle between the micro normal vector of the micro facet of the first irradiation surface and the macro normal vector of the object surface, a is the longitudinal distance through which the incident light passes, and b is the longitudinal distance through which the incident light does not pass.

[0027] Based on the geometric relationship of the incident light completely passing through the first irradiation surface and then irradiating the second irradiation surface, the normal vector angle probability model is used to construct the probability of the incident light completely passing through the second irradiation surface. The probability that the incident light completely blocks the second illuminated surface The probability that part of the incident light passes through the second illumination surface

[0028]

[0029]

[0030]

[0031] Wherein, γ is the angle between the micro normal vector of the micro facet of the second irradiation surface and the macro normal vector of the object surface, and α is the angle between the micro normal vector of the micro facet of the first irradiation surface and the macro normal vector of the object surface.

[0032] Based on the geometric relationship between the first reflected light and the second irradiation surface, the normal vector angle probability model is used to construct the probability that the first reflected light completely passes through the second irradiation surface. The probability of the first reflected light being reflected back through the second irradiation surface

[0033]

[0034]

[0035] Wherein, γ is the angle between the micro normal vector of the micro facet of the second irradiation surface and the macro normal vector of the object surface, and α is the angle between the micro normal vector of the micro facet of the first irradiation surface and the macro normal vector of the object surface.

[0036] Based on the geometric relationship between the second reflected light and the second irradiation surface, the normal vector angle probability model is used to construct the probability of the second reflected light being reflected forward by the second irradiation surface. The probability of the second reflected light being reflected back through the second irradiation surface

[0037]

[0038]

[0039] Wherein, γ is the angle between the micro normal vector of the micro element of the second irradiation surface and the macro normal vector of the object surface.

[0040] The modified geometric attenuation factor model G is:

[0041]

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The present invention utilizes microfacet theory to divide a rough surface into multiple microfacets consisting of two surfaces. Through the geometric relationship between the two surfaces of each microfacet and the incident light and reflected light, a normal vector angle probability model is used to obtain the occlusion probability of the incident light under different geometric relationships, so as to obtain a corrected geometric attenuation factor. The corrected geometric attenuation factor is substituted into the bidirectional reflectance distribution function to accurately obtain the radiation energy of the reflected light, thereby achieving the purpose of accurately detecting the object morphology. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A microfacet reflection model provided for specific implementations;

[0045] Figure 2 A geometric relationship diagram between the first illumination surface and the incident light provided for a specific embodiment;

[0046] Figure 3 A geometric relationship diagram between the first reflected light and the second illuminated surface formed after the incident light completely passes through the first illuminated surface provided in a specific embodiment;

[0047] Figure 4 A geometric relationship diagram based on the incident light partially passing through the first illumination surface and then irradiating the second illumination surface provided for a specific embodiment;

[0048] Figure 5 A geometric relationship diagram based on the incident light completely passing through the first irradiation surface and then irradiating the second irradiation surface is provided for a specific embodiment;

[0049] Figure 6 Comparison of normalized data of Blinn, integral, and modified GAF ​​with existing bidirectional reflectance distribution functions in the literature DETAILED DESCRIPTION

[0050] The specific implementation method of the present invention is now described as follows in conjunction with the accompanying drawings:

[0051] The present invention proposes a correction method for the integral form of the geometric attenuation factor and an accurate expression of the corrected model. By analyzing the principle and characteristics of the geometric attenuation factor, the following assumptions are made: (1) the surface of an object is composed of many groups of micro-facets, and the base lengths of the micro-facets are equal and set to unit "1"; (2) adjacent micro-facets on the surface of the object are not only simple "V"-shaped grooves, but also the inclination angles of the micro-facets obey the random Gaussian distribution; (3) the inclination angles of adjacent micro-facets are independent of each other, and the inclination angle range defining the first irradiation surface and the second irradiation surface is (-π / 2, π / 2).

[0052] Combined with the microfacet theory, the angles between the incident and reflecting surfaces and the object's macroscopic surface normal vectors are discussed separately. In each case, the shielding and shadow effects of the object surface on the incident and reflected light are discussed. Finally, a model with a modified integral geometric attenuation factor is constructed. The specific steps are as follows:

[0053] Microfacet reflection model Figure 1 As shown in Figure 2, based on the actual significance of the surface roughness of an object, the microfacet theory is used to construct the probability model p(χ) of the angle between the normal vector of the microfacet surface and the macroscopic surface of the object:

[0054]

[0055]

[0056] Where χ is the angle between the micro-normal vector of the micro-facet and the macro-normal vector of the object surface, C is the normalization coefficient that makes the function p(·) integral equal to 1 in the entire space, σ is the surface roughness, θ i is the angle of incidence, θ r is the reflection angle.

[0057] The geometric relationship between the first irradiation surface and the incident light is shown in the figure Figure 2 As shown, based on the geometric relationship between the first irradiation surface and the incident light, that is, Figure 2 As shown in a in FIG, the incident light completely passes through the first illumination surface, such as Figure 2 As shown in b in FIG, the incident light does not pass through the first irradiation surface, such as Figure 2 As shown in c, the incident light partially passes through the first illumination surface, and the normal vector angle probability model is used to construct the probability model P of the incident light completely passing through the first illumination surface. 1a , the probability P that the incident light does not pass through the first illumination surface 1b , the probability P that the incident light partially passes through the first illumination surface 1c :

[0058]

[0059]

[0060]

[0061] Wherein, α is the angle between the micro normal vector of the micro facet of the first irradiation surface and the macro normal vector of the object surface, a is the longitudinal distance through which the incident light passes, and b is the longitudinal distance through which the incident light does not pass.

[0062] Based on the geometric relationship that the incident light completely passes through the first irradiation surface and then illuminates the second irradiation surface, that is, the incident light completely passes through the second irradiation surface, such as Figure 3 As shown in a in FIG, the incident light completely blocks the second illumination surface, as shown in FIG. Figure 3 As shown in b, the incident light partially passes through the second illumination surface, as shown in Figure 3 As shown in c, the normal vector angle probability model is used to construct the probability model of the incident light completely passing through the second illumination surface. Probability model of incident light completely blocking the second illumination surface The probability that part of the incident light passes through the second illumination surface

[0063]

[0064]

[0065]

[0066] Wherein, γ is the angle between the micro normal vector of the micro facet of the second irradiation surface and the macro normal vector of the object surface, and α is the angle between the micro normal vector of the micro facet of the first irradiation surface and the macro normal vector of the object surface.

[0067] The incident light completely passes through the first irradiation surface to form the first reflected light. Based on the geometric relationship between the first reflected light and the second irradiation surface, the normal vector angle probability model is used to construct the probability model of the first reflected light completely passing through the second irradiation surface. The probability of the first reflected light being reflected back through the second irradiation surface

[0068]

[0069]

[0070] Wherein, γ is the angle between the micro normal vector of the micro facet of the second irradiation surface and the macro normal vector of the object surface, and α is the angle between the micro normal vector of the micro facet of the first irradiation surface and the macro normal vector of the object surface.

[0071] Based on the fact that the incident light partially passes through the first irradiation surface to form the second reflected light, the probability of the second reflected light being reflected forward by the second irradiation surface is constructed based on the geometric relationship between the second reflected light and the second irradiation surface using the normal vector angle probability model. like Figure 4As shown in a, the probability of the second reflected light being reflected back through the second illumination surface is like Figure 4 As shown in b:

[0072]

[0073]

[0074] Wherein, γ is the angle between the micro normal vector of the micro element of the second irradiation surface and the macro normal vector of the object surface.

[0075] When the second irradiation surface tilt angle γ is large, that is, the angle is (π / 2, θ i / 2), the light reflected by the second irradiation surface is considered as back reflection, and the incident light will be reflected by the second irradiation surface and then reach the first irradiation surface, thus causing multiple reflections, such as Figure 5 As shown in the figure, since the probability of this situation is extremely small and multiple reflections are considered to be diffuse reflections, the pass rate of this situation is considered to be 0.

[0076] Based on the probability that the incident light does not pass through the first illumination surface and the first, second, and third product probabilities, the modified geometric attenuation factor G is constructed as follows:

[0077]

[0078] like Figure 6 To verify the effectiveness of the model, bidirectional reflectance distribution functions (BRDFs) with the modified geometric attenuation factor, the Blinn type, the integral type, and the absence of the geometric attenuation factor were compared with published experimental data. The results show that the BRDF with the modified geometric attenuation factor better matches the experimental data curve in terms of both numerical value and overall trend.

Claims

1. A method for correcting geometric attenuation factors based on optical microfacet theory, characterized in that: include: Using the microfacet theory, it is assumed that the surface of the object is composed of multiple microfacets, and each microfacet consists of a first irradiation surface close to the incident light and a second irradiation surface far away from the incident light; Based on the geometric relationship between the first illumination surface and the incident light, the normal vector angle probability model is used to obtain the probability that the incident light completely passes through the first illumination surface, the probability that the incident light does not pass through the first illumination surface, and the probability that the incident light partially passes through the first illumination surface; A first product probability is obtained based on that the incident light completely passes through the first illumination surface and then completely passes through, is completely blocked, or partially passes through the second illumination surface; After the incident light completely passes through the first illumination surface, it forms a first reflected light. Based on the geometric relationship between the first reflected light and the second illumination surface, a normal vector angle probability model is used to obtain the probability that the first reflected light completely passes through the second illumination surface and the probability that the first reflected light is back-reflected by the second illumination surface. The second product probability is obtained by multiplying the sum of the probabilities that the first reflected light completely passes through the second illumination surface and the probabilities that the first reflected light is back-reflected by the second illumination surface with the probability that the incident light completely passes through the first illumination surface. Based on the fact that the incident light partially passes through the first illumination surface to form second reflected light, and based on the geometric relationship between the second reflected light and the second illumination surface, a normal vector angle probability model is used to respectively construct the probability of the second reflected light being reflected forward by the second illumination surface and the probability of the second reflected light being reflected backward by the second illumination surface; the third product probability is obtained by multiplying the sum of the probabilities of the second reflected light being reflected forward and backward by the second illumination surface with the probability of the incident light partially passing through the first illumination surface; Based on the probability that the incident light does not pass through the first illumination surface and the first, second, and third product probabilities, a modified geometric attenuation factor is constructed to obtain the occlusion probability of the incident light. The modified geometric attenuation factor is substituted into the bidirectional reflectance distribution function to calculate the radiant energy of the light reflected by the object to detect the object's morphology.

2. The method for correcting the geometric attenuation factor based on the optical microfacet theory according to claim 1, characterized in that: Each microfacet consists of a first illumination surface close to the incident light and a second illumination surface away from the incident light, including: The bottom sides of each microfacet are equal in length, and the inclination angles of the first irradiation surface and the second irradiation surface of each microfacet obey random Gaussian distribution, and the inclination angle range is (-π / 2, π / 2).

3. The method for correcting the geometric attenuation factor based on the optical microfacet theory according to claim 1, characterized in that: Based on the surface roughness of the object, the microfacet theory is used to construct the probability model p(χ) of the angle between the normal vector of the microfacet surface and the macro surface of the object: Where χ is the angle between the micro-normal vector of the micro-facet and the macro-normal vector of the object surface, C is the normalization coefficient that makes the function p(·) integral equal to 1 in the entire space, σ is the surface roughness, θ i is the angle of incidence, θ r is the reflection angle; Based on the geometric relationship between the first illumination surface and the incident light, the normal vector angle probability model is used to construct the probability P of the incident light completely passing through the first illumination surface. 1a , the probability P that the incident light does not pass through the first illumination surface 1b , the probability P that the incident light partially passes through the first illumination surface 1c : Wherein, α is the angle between the micro-normal vector of the micro-facet of the first irradiation surface and the macro-normal vector of the object surface, a is the longitudinal distance that the incident light passes through, and b is the longitudinal distance that the incident light does not pass through; The first product probability is obtained based on the incident light completely passing through the first illumination surface and then completely passing through, completely shielded by, or partially passing through the second illumination surface, including: Based on the geometric relationship of the incident light completely passing through the first illumination surface and then illuminating the second illumination surface, a normal vector angle probability model is used to obtain the probability that the incident light completely passes through the second illumination surface, the probability that the incident light completely blocks the second illumination surface, and the probability that the incident light partially passes through the second illumination surface. The first product probability is obtained by multiplying the sum of the probabilities of the incident light completely passing through, completely blocking, and partially passing through the second illumination surface with the probability that the incident light completely passes through the first illumination surface. Based on the geometric relationship of the incident light completely passing through the first irradiation surface and then irradiating the second irradiation surface, the normal vector angle probability model is used to construct the probability of the incident light completely passing through the second irradiation surface. The probability that the incident light completely blocks the second illuminated surface The probability that part of the incident light passes through the second illumination surface Wherein, γ is the angle between the micro-normal vector of the micro-facet of the second irradiation surface and the macro-normal vector of the object surface, and α is the angle between the micro-normal vector of the micro-facet of the first irradiation surface and the macro-normal vector of the object surface; Based on the geometric relationship between the first reflected light and the second irradiation surface, the normal vector angle probability model is used to construct the probability that the first reflected light completely passes through the second irradiation surface. The probability of the first reflected light being reflected back through the second irradiation surface Wherein, γ is the angle between the micro-normal vector of the micro-facet of the second irradiation surface and the macro-normal vector of the object surface, and α is the angle between the micro-normal vector of the micro-facet of the first irradiation surface and the macro-normal vector of the object surface; Based on the geometric relationship between the second reflected light and the second irradiation surface, the normal vector angle probability model is used to construct the probability of the second reflected light being reflected forward by the second irradiation surface. The probability of the second reflected light being reflected back through the second irradiation surface Wherein, γ is the angle between the micro normal vector of the micro element of the second irradiation surface and the macro normal vector of the object surface.

4. The method for correcting the geometric attenuation factor based on optical microfacet theory according to claim 3, characterized in that: The corrected geometric attenuation factor G is:

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