Evaluating an image based multi-angle measurement setup using different reflection models

Image based measurement setups are widely used for multidirectional reflectance measurements of materials. Different reflection models are used to estimate the material reflectance. In this paper we use two commonly known simple reflection models to evaluate an image based measurement setup proposed in our previous studies. Sample material is measured at multiple incident and viewing directions using the setup. The captured data is divided into training and test set to evaluate the setup. Two reflection models are trained using the training dataset. To evaluate the measurement setup, one of the sample materials is measured at few incident and viewing directions using a light source and a Tele-Spectro-Radiometer (TSR). This measured data is then compared with the reflectance estimated by the two reflection models. Results shows that image based multi-directional reflectance measurements can be performed using measurement setup proposed in our previous work. The data captured using the setup can be used to fit different reflections models for the sample materials used in this setup. Introduction Image based instruments that are relatively cheap and fast, are being increasingly used in multi-angle reflectance measurements of the material [1, 2, 3]. The multi-angle data captured can be further processed (for example to estimate the material BRDF). Where the need is to acquire fast and cheap measurements, image based instruments can be a good alternative compared to the expensive, time consuming, but precise instruments (like Goniospectrometers). These measurements can then be used to train reflection models to calculate the BRDF and simulate or reproduce the material appearance. A number of reflection models are proposed till now which mainly aim towards fulfilling the needs of the computer graphics field to simulate material appearance in a given scence/situation. One of the main aims of the computer graphics field is to accurately measure the appearance of materials and simulate/reproduce synthetically the real object using simple methods/techniques [4]. A Bidirectional Reflection Distribution Function (BRDF) is a distribution function that describes the surface reflectance properties of opaque and homogenous materials [5] as given in Equation (1). fBRDF (θi,φi;θr,φr,λ ) = dLr(θi,φi,θr,φr,Ei) dEi(θi,φr) (1) Here, i and r denote incidence and reflection respectively. θ and φ together indicate the direction, Ei is incident irradiance, Lr is radiance and d is the differential. Guarnera [4] presented an overview of the BRDF models used to represent surface/material reflection characteristics. As discussed in [4], BRDF models can be classified into Physically-based models and Phenomenological models. Physically-based models are based on physics and optics and are described using micro-facets of varying size and orientations. One of the very well known and widely used physical models is the Cook-Torrance [6] model. Phenomenological models are approximations of the reflectance data using measured data and fitting of the same using analytical models. Some of the commonly known phenomenological models are the Phong [7], Ward [8], Lafortune [9], etc. In our previous studies [3] we presented a measurement setup which can perform multi-angle reflectance measurements of homogenous, flexible materials in a fast and relatively cheap way. In this setup, we mount the flexible sample onto a cylinder of known radius and measure using a RGB camera [10, 3]. The captured RGB data is converted into the colorimetric space CIEXYZ using the conversion matrix M̂. Matrix M̂ is derived using the camera spectral sensitivity (measured using a monochromator) and the CIE 2◦ colour matching functions by minimising the error using least square technique [11]. This data can be used further as training data to train different reflection models (like Cook-torrance or Ward model) to estimate the sample BRDF and simulate the material appearance. The objectives of the work presented in this paper are: • to estimate the surface reflectance properties of the sample materials used in the experimental setup using the image based multi-angle measurement setup proposed in previous studies [3], • to train different reflection models using the colorimetric data captured with the image based multi-angle measurement setup and evaluate the setup against measurements obtained using a TSR, • test the trained reflection models to predict the sample material reflectance at different illumination and viewing directions. Background In order to evaluate the measurement setup we used 2 reflections models; Cook-Torrance (hereby referred as CT in this paper) and Ward to fit the measurement data obtained in the measurement setup by using the RGB camera [3]. The trained model parameters were then used to estimate the BRDF measurement at different incident and viewing directions. CT model is a physical model that describes the intensity and spectral composition of the light reflected from the object/material. CT model as described in