Model Evaluation for Computer Graphics Renderings of Artist Paint Surfaces

Light reflection models for computer graphics have been developed over the past several decades. For real paint surfaces, it is possible to model their bidirectional reflectance distribution function with simple models. This research established a framework to evaluate two simple reflection models, Phong and Torrance-Sparrow, which were used to render artist paint surfaces under different illumination angles. An image acquisition system was set up to capture the images under selected illuminated angles. The parameters of the specular and the diffuse components were estimated with these image sequences. At the evaluation stage, both physical-based metrics and psychophysical techniques were used to evaluate the estimation accuracy of each model. For both methods, the comparison of the estimations of two models showed that better estimations were obtained from the TorranceSparrow model for the glossy samples. The estimation accuracies of two models are almost the same for the matte samples. In addition, the numbers of illumination angles of the test samples can be minimized based on both mathematical calculations and psychophysical experiments. Introduction For realistic scenes, the spectral and geometric properties of the light source, object, and observer determine appearance. Thus, the interplay of the lighting, viewing and object properties must be considered in the digital reproduction of objects in display and print. Commonly, the photographer defines a specific set of geometric conditions, reducing the myriad geometric experience to a single representation. Alternatively, if data are available as a function of this interplay, known as the bidirectional reflectance distribution function (BRDF), images can be rendered for a variety of geometries and in combination, simulate the real-time viewing experience. A variety of reflection models have been proposed to calculate BRDF, including both physical-based and empirical models. The Phong and Ward models are two common empirical models, which were derived from measured data. Blinn introduced the Torrance-Sparrow physical-based light reflection model to computer graphics, and replaced the standard Gaussian distribution with ellipsoids of revolution in modeling microfacets. Over the past several decades, more physical-based models were proposed with more optical and physical properties and more complex distribution of microfacets. In addition, Dana defined bidirectional texture function (BTF) to describe the function of the texture surfaces. One difficulty of the measurement system is that the camera position must be calibrated accurately since the camera was moved to different locations. Malzbender in HP Labs presented polynomial texture mapping to reconstruct the luminance of each pixel. However, the specular component was not directly modeled and must be handled separately. Although there are many studies on BRDF and BTF measurement and 3D image rendering, research focusing on artist paint surfaces are limited. Hawkins proposed an approach to render cultural artifacts based on capturing the reflectance fields of the objects, but a large amount of images are required. Tominaga also proposed a method to record and render art paintings. However, only a matte oil painting was tested in his research. The purpose of this research was to develop a practical apparatus for the museum to record 2D artist paint surfaces under different illumination angles, and then render them with different light reflection models and evaluate their accuracy. Because of their mathematical simplicity and small number of parameters, Phong and TorranceSparrow models were selected from the empirical and physicalbased models to estimate the specular and diffuse components. Eight different paint samples with different gloss levels were selected to evaluate the models. The performance of the models were evaluated and compared for both physical-based and psychophysical methods. Furthermore, the numbers of the lighting geometries needed to fit the model can be minimized for different measured samples. Image-based Acquisition System Figure 1. Image sequence acquisition system The image sequence acquisition system is shown as Figure 1. The Mille Luce fiber optic illumination made by StockerYale was used for illumination. Currently, the system has one degree of freedom of illumination position, which can be changed by moving the lighting arm. Thus, only a series of polar illumination angles changed with the constant azimuth illumination angle. In the viewing position, a Nikon D1 CCD camera was fixed. To estimate the parameters in the BRDF models, the relative radiance 54 Copyright 2007 Society for Imaging Science and Technology of each pixel should be known. Thus, the opto-electronic conversion functions (OECF) of three channels of the camera were measured and calculated according to ISO 14524. In order to capture the image with 0° illumination angle, there is a small angle between the optical axis of the camera and sample normal. Lighting Reflection Models Figure 2. Light reflection geometry in terms of illumination and viewing angles and surface tilt angles Figure 2 depicts the light reflection geometry of the complex paint sample surface. Two normal directions are shown in the figure, the sample normal Z and the surface normal N ^ of an element dA . The incident and view directions are specified by i and ( v , v ), respectively. The element surface normal in terms of the sample normal is represented by two tilt angels, n and n . The illumination angle a of the sample surface can be obtained and this angle changes only in the XZ plane. All the angles are defined as either positive or negative angles, since the same angles might exist on two sides of the Z-axis. The angles defined in this reflection geometry are different with that in traditional BRDF specification. The purpose of this definition is to simplify the mathematical calculation. Phong Model The Phong model controls four parameters to determine the gonio-radiometric values. Thus, the relative radiance in the Phong model is expressed as the function of the above angles depicted in Figure 2, shown in Eq. (1). Y = Ae+Ad cos i +As(cos s ) n cos i = cos( a n )cos( n ) cos s = cos v cos r cos( v r ) + sin v sin r sin r = sin(2 n )cos( a n ) (1) where Ae , Ad and As are the magnitude parameters of the ambient, diffuse and specular components; r is the angle between the plane XZ and the perfect mirror reflection direction; r is the angle between the sample normal and the projection of perfect mirror reflection on XZ plane; s is the angle between the view angle and the perfect mirror reflection direction of the incident light; n describes the measured shininess of the surface. Torrance-Sparrow Model Based on geometrical optics, Torrance and Sparrow derived a theoretical model for roughened surfaces. In this model, the surface element was assumed to consist of small randomly dispersed mirror-like facets. This model can be described as Eq. (2). Y = Ad cos i +As DGF cos vn cos i = cos( a n )cos n cos vn = cos n cos v cos( v n ) + sin n sin v (2) where D is the standard Gaussian distribution function of the direction of the microfacets and F is the Fresnel reflection, which is the function of i and refraction index n . In this research, the n value of the resin, 1.5, was used. G is defined as the geometrical attenuation factor and represents the remaining light amount after the shadowing and masking, which is a function of a , n , n , v and v . Another facet distribution function that models the microfacets as ellipsoids of revolution, proposed by Trowbridge and Reitz, provided a better match to the experimental data than that in Torrance-Sparrow model. In order to improve the computation results, this facet distribution function was used in this research, shown in Eq. (3).