導関数群の融合に基づく未知関数の近似

抄録

Progress in recent sensor technology has inspired us to start research on recovering an object surface from depth data together with additional sensory information, i.e. data on its differential geometry or a priori knowledge about its smoothness. Any method for the recovery with both classes of the additional information, however, has not been proposed yet. Such a problem can be generalized to that of function approximation using its different order derivatives, which covers many important applications. To solve the problems generally, we propose a method of fusing all the information as follows : (1) To evaluate the smoothness and penalties for the derivative data of each order, we define a functional. (2) All the information are related to one another by restricting the fused results in the set of stationary functions of the functional. By the fusion, a new approximation is realized as the stationary function that minimizes all penalties simultaneously.