Optical parameters of materials are used for implementing cinematic rendering in the field of graphics. Critical elements for extracting these optical characteristics are the accuracy of the extracted parameters and the required time for extraction. In this paper, a novel method for improving these elements as well as a comparison to the existing methodology is presented. By using a spectrophotometer and custom designed optical imaging equipment (OIE), our method made it possible to enhance accuracy and accelerate computing speed by reducing the number of unknowns in the fitting equations. Further, we validated the superiority of the extracted optical characteristic parameters with a rendering simulation.
Optical parameters, including absorption and reduced scattering coefficients, have played a key role in many diagnostic and therapeutic optical techniques [
Some critical unknown variables of the bidirectional subsurface scattering reflectance distribution function (BSSRDF) are the index of refraction, the reduced albedo, the absorption coefficient, and the reduced scattering coefficient. It is critical to be able to acquire the reflectance distribution of the reflected light using an optical device since permeated light is not measureable in some materials. By fitting the measured sample data obtained from an image-based measurement system, Lee et al. suggested a method to determine the reduced scattering coefficient and the absorption coefficient [
Other new image-based measurement techniques have been proposed where the index of refraction and the reduced albedo are estimated [
Hence, we need a time efficient method that also outputs high quality results using optical parameters and index of refraction.
In this paper, we propose a method for extracting the optical parameters with less time required than existing methods by removing an unknown variable and enhancing the corresponding accuracy while acquiring the index of refraction.
To this end, we used a spectrophotometer and optical imaging equipment (OIE) designed and manufactured by the authors. First, the parameters of BSSRDF were optimized for fitting in order to extract optical parameters from a high dynamic range image (HDRI) acquired by the OIE, thereby improving the fitting performance by measuring the reduced albedo directly with the spectrophotometer. We conducted the experiments on a total of 32 different materials with various optical characteristics. Further, in order to verify the reliability of the measured parameters, we compared the rendering results obtained using the measured optical coefficients. We have also validated our proposed method for extracting optical parameters using the rendering results in two different equations. In short, we show that our rendering results and mean squared error (MSE) are superior to existing methods.
The remainder of this paper is organized as follows. In Section
The optical characteristics discussed include absorption coefficient
The general measurement process of the optical characteristics is as follows: a laser beam is incident normal (perpendicular) to the material, and, then, the permeability distribution of the permeated light is determined using the result of numerical analysis or an analysis model [
A novel high speed approach for the acquisition of bidirectional reflectance distribution functions (BRDFs) is proposed. In this work the authors address a new theory for directly measuring BRDFs that represent a basis by projecting incident light, that is, a sequence of basis functions from a spherical zone of directions. By derivation of an orthonormal basis over spherical zones, they acquire an ideally suited process for this task. By reprojecting the zonal measurements into a spherical harmonics basis or by fitting analytical reflection models to the data, BRDF values are deduced [
To extract skin reflectance parameters, custom-built devices are used. Three-dimensional face geometry, skin reflectance, and subsurface scattering are measured of 149 subjects. The participants from whom these parameters are measured vary in age, gender, and race. In this work the authors show a novel skin reflectance model of which parameters are estimated from the measurements. The model is composed of measured skin data put into a spatially varying analytic BRDF, a diffuse albedo map, and diffuse subsurface scattering [
A steady-state imaging technique using non-normally incident light to determine anisotropy parameter is presented. To make it work, the authors perform a fitting Monte Carlo simulation to obtain high dynamic range images of the intensity profiles of samples [
However, because permeated light cannot be used with some materials, there are methods that measure the reflectance distribution of the reflected light using an optical imaging device. These methods determine the reflectance coefficient by fitting the measured reflectance distribution to the BSSRDF, a rendering model that takes into account optical characteristics [
In this section, we explain the equipment for measurement used in this work. There are two pieces of equipment, including the spectrophotometer (CM-600D, Konica Minolta) and the optical imaging equipment (OIE), used to make the HDRI.
The refractive index
(a) Spectrophotometer (CM-600D Konica Minolta) and (b) measured reflectance graph.
The scattering reflectance distribution could be obtained from the pictures taken with the OIE. Figure
Optical imaging equipment (OIE) and its specifications.
Measurements were conducted in a darkroom without ambient light. The focus was set by controlling the distance of the lens and the light source to minimize the diameter of the focus point depending on material thickness and shape. During the filming, in order to obtain the HDR image, multiple images were taken under the same conditions by varying the exposure levels. LED light was used as the light source, and a total of 13 HDR images were taken by setting the aperture to 8.0 and the ISO value to 400 for the considered exposure level. Only the shutter speed was changed from 1/600 to 3 sec. The obtained images were merged with the HDRI having 16 bits per channel for each RGB channel [
(a) Twelve HDR shooting images and (b) red circle marking the pixels that are at the same distance from the focus point as the center of the merged HDRI.
The process of extracting the optical characteristic parameters implemented in this study will be outlined briefly. First, the refractive index
The following is a more detailed description of the optical parameter’s derivation process. First, we derive the refractive index
Third,
In order to minimize the fitting time and to improve accuracy,
We then substituted the right hand term of (
Fitting results using Levenberg-Marquardt algorithm.
A total of 32 samples were tested with the OIE and the spectrophotometer using the method proposed in this study. The extracted parameters were
Optical properties.
Material | Color | Optical parameter | |||
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Fitting time | ||
Pink plastic | R | 1.979 | 0.000792 | 1.2886 | 0.2216 |
G | 1.893 | 0.049600 | 0.2243 | ||
B | 1.992 | 0.022700 | 0.2279 | ||
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Blue coating | R | 1.189 | 1.189000 | 1.9432 | 0.2793 |
G | 1.742 | 0.090597 | 0.2742 | ||
B | 1.865 | 0.016372 | 0.2768 | ||
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Brown leather | R | 1.659 | 0.116993 | 1.2391 | 0.2859 |
G | 1.383 | 0.272607 | 0.2889 | ||
B | 1.113 | 0.428075 | 0.2872 | ||
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Nephrite | R | 1.439 | 0.066138 | 1.0777 | 0.2847 |
G | 1.565 | 0.053121 | 0.2775 | ||
B | 1.414 | 0.046018 | 0.2835 | ||
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Wood tile | R | 2.35 | 0.017508 | 1.3108 | 0.2769 |
G | 2.33 | 0.065100 | 0.2800 | ||
B | 1.461 | 0.138360 | 0.2789 | ||
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Sulfur | R | 1.896 | 0.002359 | 1.1159 | 0.2738 |
G | 1.954 | 0.004151 | 0.2892 | ||
B | 1.622 | 0.073041 | 0.2796 | ||
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Red aluminum | R | 1.89 | 0.018700 | 2.4102 | 0.2920 |
G | 1.171 | 0.768300 | 0.2811 | ||
B | 0.7498 | 0.558000 | 0.2879 |
The color-rendering model was used for entering the optical parameters, following which the material’s ultimate color was determined [
The total diffuse reflectance
By first converting the integration over the 3D model surface into an integration over a 2D texture space, the method acquires the results of subsurface scattering. Irradiance values stored in the texture are used to make a feasible implementation [
The approach is composed of a precomputation process and a three-stage GPU based translucent rendering process that includes rendering the irradiance to a texture map, carrying out critical sampling, and evaluating the outgoing radiance.
The final outcome for computing outgoing radiance becomes
To validate our proposed method, we carried out two experiments that implemented only the optical imaging equipment [
OpenGL was used to verify the extracted parameters implemented with shader codes. A statue of Athena was used for rendering; it is a model provided as freeware (
We show the rendering result of the subsurface color method in Figure
((a1), (b1), and (c1)) Subsurface color method and ((a3), (b3), and (c3)) texture space method rendering results using the existing method. ((a2), (b2), and (c2)) Subsurface color method and ((a4), (b4), and (c4)) texture space method rendering results using the proposed method. (a) is for pink plastic. (b) is for blue coating. (c) is for brown leather.
In Figures
We performed comparisons of three sets of reflectance data. The first reflectance data set was acquired from the sampled data called HDRI and is denoted by the lines with blank circles shown in Figure
Comparisons among sampled data, the existing method, and the proposed method. The reflectance corresponding to Figure
Pink plastic
Blue coating
Brown leather
In addition, the mean squared errors (MSE) between the data sampled directly from the HDRI and two rendered data (from the existing and the proposed methods) were calculated to analyze the experiments of the rendering results. Table
Mean squared errors values.
Material | Existing method | Proposed method | ||||
---|---|---|---|---|---|---|
R | G | B | R | G | B | |
Pink plastic | 1.2096 | 30.3132 | 0.3914 | 1.1015 | 2.0981 | 0.2845 |
Blue coating | 228.163 | 205.483 | 9.639 | 70.930 | 0.842 | 0.268 |
Brown leather | 242.743 | 379.711 | 420.816 | 5.422 | 9.154 | 14.554 |
This paper proposes a method for extracting the optical parameters, including reduced subsurface scattering, absorption, and refractive index. This newly proposed method reduces the required calculation time of the existing method by removing an unknown variable while enhancing the corresponding accuracy. Also, we can acquire the index of refraction that can be derived from the light reflection measured by a spectrophotometer. To validate the method, we have carried out experiments that show rendering results by using optical parameters in two rendering equations. We found that rendering results and the MSE are superior to those of the existing method as well.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was partially funded by the Korean Government (CiMR: Physically Based Cinematic Material Rendering Techniques Optimized for Gameplay, no. 10043453).