1 Estimation of a 3D Spectral Reflection Model for Color Image Rendering Norihiro TANAKA and Shoji TOMINAGA Osaka Electro-Communication University Purpose Reflection models are used in many fields including computer graphics, computer vision, image understanding, and digital archives. A three-dimensional (3D) reflection model is crucial for rendering realistic color images [1-3]. We should note that (1) the reflection properties of an object surface depend on the surface material, and (2) the reflection model is described as a function including various parameters related to color (spectrum) and geometry. However, it is difficult to find suitable values for such parameters for a real object, and so far those were selected by the method of trial and error. In a previous paper [1], we proposed a method for estimating various parameters of a reflection model from a single image of an object taken by a CCD camera. The Phong model was used for modeling light reflection on an object surface composed of non-conducting materials called inhomogeneous dielectric materials. This model is too simple to produce realistic images. In fact, the Phong model has difficulty in describing the specular reflection component because the Fresnel term is neglected. The present paper proposes a method for estimating reflection parameters using the Torrance-Sparrow model. Spectral functions such as surface-spectral reflectance, illuminant spectrum, and geometric parameters are estimated from a multi-band image by a multi-channel CCD camera system. The Torrance-Sparrow model is more precise than the Phong model. The specular reflection is described in terms of the distribution of isotopic orientation, the geometrical attenuation factor, and the Fresnel term. The proposed method has a much higher advantage of being able to estimate a 3D spectral reflection model from only a single image of a multi-bandl camera, compared with the other gonio-metric methods [2]-[3]. First we examine validity of the Torrance-Sparrow model based on the spectral reflectance data measured with different angles of viewing and incidence. Next, we propose algorithms for estimating various parameters of the reflection model from images by a multi-band CCD camera The feasibility of the proposed method is demonstrated in an experiment using a plastic object. The estimation accuracy is also confirmed based on computer graphics images. Camera system A six-color camera is used as the multi-band camera for image measurement and reflection parameter estimation. Use of this camera system makes it possible to estimate the reflection model parameters and the spectral information such as surface-spectral reflectance, which is difficult to be estimated in use of an ordinary RGB color system. The system of a six-color camera is composed of a monochromatic CCD camera, a standard photographic lens, six color filters, and a personal computer. Parameter estimation algorithms The spectral radiance distribution Y( λ, x) from a reflective object surface is a function of the spatial location x and the wavelength λ. Torrance-Sparrow described this function as Q i r () ( ) ( ,) (, ) cos( )() () ( ), cos( ) D G F n Yx S E E ϕ θ λ α θ λ λ β λ θ = + N,V,L (1) where the first and second terms represent, respectively, the body and interface reflection components. S(λ) : spectral reflectance, E(λ): illuminant spectral distribution, θi : angle of incidence, θr: viewing angle, ϕ: angle between global surface normal and micro-facet normal, θ Q: : angle of incidence to micro-facet. The interface reflection component consists of several terms: D: function providing the index of surface roughness defined as 2 2 exp{ ln(2) / } ϕ γ - , where the γ is constant. G : geometrical attenuation factor, and F: Fresnel spectral reflectance, where n is the index of refraction.