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# {Reflection Position Estimation with Primary Scattering of Incident Light and Reflected Light}

{ In recent years, realistic CG is used for movies and games. Createing CG by hand requires extensive man power. Therefore, it is necessary to hold down such cost by creating CG automatically. Measuring 3D shape of real object and using 3D shape as CG model is a solution to do that. As such a background, many 3D shape measurement methods have been proposed. Many methods are proposed for 3D shape measurment that obtain object surface from irradiating surface with light and observing its reflected light with cameras. These methods obtain 3D coordinate of the point where the incident light hits on the object surface. However, these methods cannot obtain a reflection point when the reflected light cannot be observed with cameras. Such case would be met when the reflected light is occluded by object, and when the object surface is black that don't reflect light, and when the object surface is metallic that reflect light only in the specific direction. We focus on the case that reflected light is occluded by objects. In order to solve this problem, we propose a method which uses Tyndall phenomenon, which is one of the optical phenomenon. Due to Tyndall phenomenon, lights are scattered by particulates and the light path can be observed in the space if many particulates exist. That is, under Tyndall phenomenon, the light that incident light and reflected light scattered(primary scattering light) about in participating media. Even if reflected light cannot be observed, reflection point can be estimated if scattered light of reflected light by Tyndall phenomenon can be observed. Koyama's method can measure reflection point of black surface object and metallic surface object. Because Koyama's method trace the path of incident light, his method cannot measure occluded reflection point. We estimate occluded reflection point to analyze distribution of the observed primary scattering light of incident light and reflected light. In order to analyze distribution of the observed primary scattering light of reflected light, we model scattering of light in space under Tyndall phenomenon. We model the intensity o scattered reflected-lights which are observed by cameras. We assume that the intensity is inversely proportional to the distance from the reflection point. We create simulator which replicated light scattering model and show that the intensity is inversely proportional to the distance from the reflection point. We estimate the reflection point to analyze the variation of luminance intensity on observed image. Candidate point of reflection point are on the incident line and the object region. We analyze the alteration of luminance intensity from obtained candidate point of reflection point and obtain evaluation value of candidate point of reflection point by fitting inverse proportion with distance function. One candidate point of reflection point which has largest evaluation value is estimated as the reflection point. In order to verify the validity of the proposed method, we put water into the tank, mix milk with water as participating media, irradiate laser to measurement object, and obtain observed image. Using a steel plate that is strong specular reflection and a cork plate that is no specular reflection as measurement objects. By the result of the experiment, reflection point can be correctly estimated in case specular reflection is fully observed. However, estimation accuracy falls if scattering light is not fully observed and it is caused that the alteration of luminance intensity from the point which is not reflection point is nearly decay in inverse proportion with distance. In order to raise estimation accuracy, we are realized that it was necessary to improve calculation of the evaluation value of candidate points of reflection point. }