カメラパラメータを考慮した球体の三次元角速度の算出法に関する研究

抄録

We propose a new method for obtaining the three-dimensional angular velocity of a rotating sphere using one camera. This method has the following advantages: 1) it takes account of optical characteristics of the camera; 2) it needs only one camera; and 3) there is no restriction on the position of the camera (unlike the previous method in which the camera and the target coordinate system have to be aligned). The proposed method consists of the following steps. The angular velocity viewed from the camera is calculated using the geometrical relation between the trajectory of a point on the rotating sphere in the image and the camera condition (position and orientation). The angular velocity that is calculated in this step contains some errors because the image data is distorted due to the characteristics of the camera. Thus, the effect of the characteristics of the cameras canceled using an optimization calculation. At the same time, the angular velocity calculated in the first step is expressed in relation to a global coordinate system using a conversion based on the position and the orientation of the camera. The theoretical reasonability of the proposed and previous methods was verified using simulated data without any kind of noise, such as digitizing error. The result calculated by the proposed method was in good agreement with the ideal value. On the other hand, previous method contained some errors due to theoretical reasons. The proposed method was also tested by Bland-Altman analysis using experimental data obtained by a motion capture system which is regarded as a gold-standard method to check a practical accuracy. The proposed method showed good agreement with the gold-standard method.