Periodic Smoothing Spline Surface with Application to Contour Modeling of Moving Deformable Objects

This paper considers a problem of designing optimal smoothing spline surfaces employing normalized uniform B-splines as the basis functions. Assuming that the data is obtained by sampling some surface with noises, an expression for optimal smoothing surfaces is derived when the number of data becomes infinity. Then, under certain condition, we present the convergent properties of optimal smoothing spline surface. Moreover, they are extended to the case of periodic spline surfaces. The results are applied to the problem of contour modeling of moving deformable objects, and the effectiveness is examined by numerical and experimental studies